Mercurial > hg > sv-dependency-builds
changeset 161:4797bbf470e7
No, that isn't going to end well. Back it out.
| author | Chris Cannam <cannam@all-day-breakfast.com> |
|---|---|
| date | Sat, 16 Feb 2019 18:32:35 +0000 |
| parents | cff480c41f97 |
| children | d43aab368df9 9fa11135915a |
| files | any/include/boost/math/distributions.hpp any/include/boost/math/distributions/arcsine.hpp any/include/boost/math/distributions/bernoulli.hpp any/include/boost/math/distributions/beta.hpp any/include/boost/math/distributions/binomial.hpp any/include/boost/math/distributions/cauchy.hpp any/include/boost/math/distributions/chi_squared.hpp any/include/boost/math/distributions/complement.hpp any/include/boost/math/distributions/detail/common_error_handling.hpp any/include/boost/math/distributions/detail/derived_accessors.hpp any/include/boost/math/distributions/detail/generic_mode.hpp any/include/boost/math/distributions/detail/generic_quantile.hpp any/include/boost/math/distributions/detail/hypergeometric_cdf.hpp any/include/boost/math/distributions/detail/hypergeometric_pdf.hpp any/include/boost/math/distributions/detail/hypergeometric_quantile.hpp any/include/boost/math/distributions/detail/inv_discrete_quantile.hpp any/include/boost/math/distributions/exponential.hpp any/include/boost/math/distributions/extreme_value.hpp any/include/boost/math/distributions/find_location.hpp any/include/boost/math/distributions/find_scale.hpp any/include/boost/math/distributions/fisher_f.hpp any/include/boost/math/distributions/fwd.hpp any/include/boost/math/distributions/gamma.hpp any/include/boost/math/distributions/geometric.hpp any/include/boost/math/distributions/hyperexponential.hpp any/include/boost/math/distributions/hypergeometric.hpp any/include/boost/math/distributions/inverse_chi_squared.hpp any/include/boost/math/distributions/inverse_gamma.hpp any/include/boost/math/distributions/inverse_gaussian.hpp any/include/boost/math/distributions/laplace.hpp any/include/boost/math/distributions/logistic.hpp any/include/boost/math/distributions/lognormal.hpp any/include/boost/math/distributions/negative_binomial.hpp any/include/boost/math/distributions/non_central_beta.hpp any/include/boost/math/distributions/non_central_chi_squared.hpp any/include/boost/math/distributions/non_central_f.hpp any/include/boost/math/distributions/non_central_t.hpp any/include/boost/math/distributions/normal.hpp any/include/boost/math/distributions/pareto.hpp any/include/boost/math/distributions/poisson.hpp any/include/boost/math/distributions/rayleigh.hpp any/include/boost/math/distributions/skew_normal.hpp any/include/boost/math/distributions/students_t.hpp any/include/boost/math/distributions/triangular.hpp any/include/boost/math/distributions/uniform.hpp any/include/boost/math/distributions/weibull.hpp |
| diffstat | 46 files changed, 0 insertions(+), 19045 deletions(-) [+] |
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--- a/any/include/boost/math/distributions.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,53 +0,0 @@ -// Copyright John Maddock 2006, 2007. -// Copyright Paul A. Bristow 2006, 2007, 2009, 2010. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -// This file includes *all* the distributions. -// this *may* be convenient if many are used -// - to avoid including each distribution individually. - -#ifndef BOOST_MATH_DISTRIBUTIONS_HPP -#define BOOST_MATH_DISTRIBUTIONS_HPP - -#include <boost/math/distributions/arcsine.hpp> -#include <boost/math/distributions/bernoulli.hpp> -#include <boost/math/distributions/beta.hpp> -#include <boost/math/distributions/binomial.hpp> -#include <boost/math/distributions/cauchy.hpp> -#include <boost/math/distributions/chi_squared.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/exponential.hpp> -#include <boost/math/distributions/extreme_value.hpp> -#include <boost/math/distributions/fisher_f.hpp> -#include <boost/math/distributions/gamma.hpp> -#include <boost/math/distributions/geometric.hpp> -#include <boost/math/distributions/hyperexponential.hpp> -#include <boost/math/distributions/hypergeometric.hpp> -#include <boost/math/distributions/inverse_chi_squared.hpp> -#include <boost/math/distributions/inverse_gamma.hpp> -#include <boost/math/distributions/inverse_gaussian.hpp> -#include <boost/math/distributions/laplace.hpp> -#include <boost/math/distributions/logistic.hpp> -#include <boost/math/distributions/lognormal.hpp> -#include <boost/math/distributions/negative_binomial.hpp> -#include <boost/math/distributions/non_central_chi_squared.hpp> -#include <boost/math/distributions/non_central_beta.hpp> -#include <boost/math/distributions/non_central_f.hpp> -#include <boost/math/distributions/non_central_t.hpp> -#include <boost/math/distributions/normal.hpp> -#include <boost/math/distributions/pareto.hpp> -#include <boost/math/distributions/poisson.hpp> -#include <boost/math/distributions/rayleigh.hpp> -#include <boost/math/distributions/skew_normal.hpp> -#include <boost/math/distributions/students_t.hpp> -#include <boost/math/distributions/triangular.hpp> -#include <boost/math/distributions/uniform.hpp> -#include <boost/math/distributions/weibull.hpp> -#include <boost/math/distributions/find_scale.hpp> -#include <boost/math/distributions/find_location.hpp> - -#endif // BOOST_MATH_DISTRIBUTIONS_HPP -
--- a/any/include/boost/math/distributions/arcsine.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,535 +0,0 @@ -// boost/math/distributions/arcsine.hpp - -// Copyright John Maddock 2014. -// Copyright Paul A. Bristow 2014. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -// http://en.wikipedia.org/wiki/arcsine_distribution - -// The arcsine Distribution is a continuous probability distribution. -// http://en.wikipedia.org/wiki/Arcsine_distribution -// http://www.wolframalpha.com/input/?i=ArcSinDistribution - -// Standard arcsine distribution is a special case of beta distribution with both a & b = one half, -// and 0 <= x <= 1. - -// It is generalized to include any bounded support a <= x <= b from 0 <= x <= 1 -// by Wolfram and Wikipedia, -// but using location and scale parameters by -// Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat/index.html -// http://www.math.uah.edu/stat/special/Arcsine.html -// The end-point version is simpler and more obvious, so we implement that. -// TODO Perhaps provide location and scale functions? - - -#ifndef BOOST_MATH_DIST_ARCSINE_HPP -#define BOOST_MATH_DIST_ARCSINE_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/distributions/complement.hpp> // complements. -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks. -#include <boost/math/constants/constants.hpp> - -#include <boost/math/special_functions/fpclassify.hpp> // isnan. - -#if defined (BOOST_MSVC) -# pragma warning(push) -# pragma warning(disable: 4702) // Unreachable code, -// in domain_error_imp in error_handling. -#endif - -#include <utility> -#include <exception> // For std::domain_error. - -namespace boost -{ - namespace math - { - namespace arcsine_detail - { - // Common error checking routines for arcsine distribution functions: - // Duplicating for x_min and x_max provides specific error messages. - template <class RealType, class Policy> - inline bool check_x_min(const char* function, const RealType& x, RealType* result, const Policy& pol) - { - if (!(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "x_min argument is %1%, but must be finite !", x, pol); - return false; - } - return true; - } // bool check_x_min - - template <class RealType, class Policy> - inline bool check_x_max(const char* function, const RealType& x, RealType* result, const Policy& pol) - { - if (!(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "x_max argument is %1%, but must be finite !", x, pol); - return false; - } - return true; - } // bool check_x_max - - - template <class RealType, class Policy> - inline bool check_x_minmax(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol) - { // Check x_min < x_max - if (x_min >= x_max) - { - std::string msg = "x_max argument is %1%, but must be > x_min = " + lexical_cast<std::string>(x_min) + "!"; - *result = policies::raise_domain_error<RealType>( - function, - msg.c_str(), x_max, pol); - // "x_max argument is %1%, but must be > x_min !", x_max, pol); - // "x_max argument is %1%, but must be > x_min %2!", x_max, x_min, pol); would be better. - // But would require replication of all helpers functions in /policies/error_handling.hpp for two values, - // as well as two value versions of raise_error, raise_domain_error and do_format ... - // so use slightly hacky lexical_cast to string instead. - return false; - } - return true; - } // bool check_x_minmax - - template <class RealType, class Policy> - inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if ((p < 0) || (p > 1) || !(boost::math::isfinite)(p)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } // bool check_prob - - template <class RealType, class Policy> - inline bool check_x(const char* function, const RealType& x_min, const RealType& x_max, const RealType& x, RealType* result, const Policy& pol) - { // Check x finite and x_min < x < x_max. - if (!(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "x argument is %1%, but must be finite !", x, pol); - return false; - } - if ((x < x_min) || (x > x_max)) - { - // std::cout << x_min << ' ' << x << x_max << std::endl; - *result = policies::raise_domain_error<RealType>( - function, - "x argument is %1%, but must be x_min < x < x_max !", x, pol); - // For example: - // Error in function boost::math::pdf(arcsine_distribution<double> const&, double) : x argument is -1.01, but must be x_min < x < x_max ! - // TODO Perhaps show values of x_min and x_max? - return false; - } - return true; - } // bool check_x - - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol) - { // Check both x_min and x_max finite, and x_min < x_max. - return check_x_min(function, x_min, result, pol) - && check_x_max(function, x_max, result, pol) - && check_x_minmax(function, x_min, x_max, result, pol); - } // bool check_dist - - template <class RealType, class Policy> - inline bool check_dist_and_x(const char* function, const RealType& x_min, const RealType& x_max, RealType x, RealType* result, const Policy& pol) - { - return check_dist(function, x_min, x_max, result, pol) - && arcsine_detail::check_x(function, x_min, x_max, x, result, pol); - } // bool check_dist_and_x - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, const RealType& x_min, const RealType& x_max, RealType p, RealType* result, const Policy& pol) - { - return check_dist(function, x_min, x_max, result, pol) - && check_prob(function, p, result, pol); - } // bool check_dist_and_prob - - } // namespace arcsine_detail - - template <class RealType = double, class Policy = policies::policy<> > - class arcsine_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - arcsine_distribution(RealType x_min = 0, RealType x_max = 1) : m_x_min(x_min), m_x_max(x_max) - { // Default beta (alpha = beta = 0.5) is standard arcsine with x_min = 0, x_max = 1. - // Generalized to allow x_min and x_max to be specified. - RealType result; - arcsine_detail::check_dist( - "boost::math::arcsine_distribution<%1%>::arcsine_distribution", - m_x_min, - m_x_max, - &result, Policy()); - } // arcsine_distribution constructor. - // Accessor functions: - RealType x_min() const - { - return m_x_min; - } - RealType x_max() const - { - return m_x_max; - } - - private: - RealType m_x_min; // Two x min and x max parameters of the arcsine distribution. - RealType m_x_max; - }; // template <class RealType, class Policy> class arcsine_distribution - - // Convenient typedef to construct double version. - typedef arcsine_distribution<double> arcsine; - - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const arcsine_distribution<RealType, Policy>& dist) - { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max())); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const arcsine_distribution<RealType, Policy>& dist) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max())); - } - - template <class RealType, class Policy> - inline RealType mean(const arcsine_distribution<RealType, Policy>& dist) - { // Mean of arcsine distribution . - RealType result; - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - - if (false == arcsine_detail::check_dist( - "boost::math::mean(arcsine_distribution<%1%> const&, %1% )", - x_min, - x_max, - &result, Policy()) - ) - { - return result; - } - return (x_min + x_max) / 2; - } // mean - - template <class RealType, class Policy> - inline RealType variance(const arcsine_distribution<RealType, Policy>& dist) - { // Variance of standard arcsine distribution = (1-0)/8 = 0.125. - RealType result; - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - if (false == arcsine_detail::check_dist( - "boost::math::variance(arcsine_distribution<%1%> const&, %1% )", - x_min, - x_max, - &result, Policy()) - ) - { - return result; - } - return (x_max - x_min) * (x_max - x_min) / 8; - } // variance - - template <class RealType, class Policy> - inline RealType mode(const arcsine_distribution<RealType, Policy>& /* dist */) - { //There are always [*two] values for the mode, at ['x_min] and at ['x_max], default 0 and 1, - // so instead we raise the exception domain_error. - return policies::raise_domain_error<RealType>( - "boost::math::mode(arcsine_distribution<%1%>&)", - "The arcsine distribution has two modes at x_min and x_max: " - "so the return value is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); - } // mode - - template <class RealType, class Policy> - inline RealType median(const arcsine_distribution<RealType, Policy>& dist) - { // Median of arcsine distribution (a + b) / 2 == mean. - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - RealType result; - if (false == arcsine_detail::check_dist( - "boost::math::median(arcsine_distribution<%1%> const&, %1% )", - x_min, - x_max, - &result, Policy()) - ) - { - return result; - } - return (x_min + x_max) / 2; - } - - template <class RealType, class Policy> - inline RealType skewness(const arcsine_distribution<RealType, Policy>& dist) - { - RealType result; - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - - if (false == arcsine_detail::check_dist( - "boost::math::skewness(arcsine_distribution<%1%> const&, %1% )", - x_min, - x_max, - &result, Policy()) - ) - { - return result; - } - return 0; - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const arcsine_distribution<RealType, Policy>& dist) - { - RealType result; - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - - if (false == arcsine_detail::check_dist( - "boost::math::kurtosis_excess(arcsine_distribution<%1%> const&, %1% )", - x_min, - x_max, - &result, Policy()) - ) - { - return result; - } - result = -3; - return result / 2; - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const arcsine_distribution<RealType, Policy>& dist) - { - RealType result; - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - - if (false == arcsine_detail::check_dist( - "boost::math::kurtosis(arcsine_distribution<%1%> const&, %1% )", - x_min, - x_max, - &result, Policy()) - ) - { - return result; - } - - return 3 + kurtosis_excess(dist); - } // kurtosis - - template <class RealType, class Policy> - inline RealType pdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& xx) - { // Probability Density/Mass Function arcsine. - BOOST_FPU_EXCEPTION_GUARD - BOOST_MATH_STD_USING // For ADL of std functions. - - static const char* function = "boost::math::pdf(arcsine_distribution<%1%> const&, %1%)"; - - RealType lo = dist.x_min(); - RealType hi = dist.x_max(); - RealType x = xx; - - // Argument checks: - RealType result = 0; - if (false == arcsine_detail::check_dist_and_x( - function, - lo, hi, x, - &result, Policy())) - { - return result; - } - using boost::math::constants::pi; - result = static_cast<RealType>(1) / (pi<RealType>() * sqrt((x - lo) * (hi - x))); - return result; - } // pdf - - template <class RealType, class Policy> - inline RealType cdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& x) - { // Cumulative Distribution Function arcsine. - BOOST_MATH_STD_USING // For ADL of std functions. - - static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)"; - - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - - // Argument checks: - RealType result = 0; - if (false == arcsine_detail::check_dist_and_x( - function, - x_min, x_max, x, - &result, Policy())) - { - return result; - } - // Special cases: - if (x == x_min) - { - return 0; - } - else if (x == x_max) - { - return 1; - } - using boost::math::constants::pi; - result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>(); - return result; - } // arcsine cdf - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function arcsine. - BOOST_MATH_STD_USING // For ADL of std functions. - static const char* function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)"; - - RealType x = c.param; - arcsine_distribution<RealType, Policy> const& dist = c.dist; - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - - // Argument checks: - RealType result = 0; - if (false == arcsine_detail::check_dist_and_x( - function, - x_min, x_max, x, - &result, Policy())) - { - return result; - } - if (x == x_min) - { - return 0; - } - else if (x == x_max) - { - return 1; - } - using boost::math::constants::pi; - // Naive version x = 1 - x; - // result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>(); - // is less accurate, so use acos instead of asin for complement. - result = static_cast<RealType>(2) * acos(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>(); - return result; - } // arcine ccdf - - template <class RealType, class Policy> - inline RealType quantile(const arcsine_distribution<RealType, Policy>& dist, const RealType& p) - { - // Quantile or Percent Point arcsine function or - // Inverse Cumulative probability distribution function CDF. - // Return x (0 <= x <= 1), - // for a given probability p (0 <= p <= 1). - // These functions take a probability as an argument - // and return a value such that the probability that a random variable x - // will be less than or equal to that value - // is whatever probability you supplied as an argument. - BOOST_MATH_STD_USING // For ADL of std functions. - - using boost::math::constants::half_pi; - - static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)"; - - RealType result = 0; // of argument checks: - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - if (false == arcsine_detail::check_dist_and_prob( - function, - x_min, x_max, p, - &result, Policy())) - { - return result; - } - // Special cases: - if (p == 0) - { - return 0; - } - if (p == 1) - { - return 1; - } - - RealType sin2hpip = sin(half_pi<RealType>() * p); - RealType sin2hpip2 = sin2hpip * sin2hpip; - result = -x_min * sin2hpip2 + x_min + x_max * sin2hpip2; - - return result; - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c) - { - // Complement Quantile or Percent Point arcsine function. - // Return the number of expected x for a given - // complement of the probability q. - BOOST_MATH_STD_USING // For ADL of std functions. - - using boost::math::constants::half_pi; - static const char* function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)"; - - // Error checks: - RealType q = c.param; - const arcsine_distribution<RealType, Policy>& dist = c.dist; - RealType result = 0; - RealType x_min = dist.x_min(); - RealType x_max = dist.x_max(); - if (false == arcsine_detail::check_dist_and_prob( - function, - x_min, - x_max, - q, - &result, Policy())) - { - return result; - } - // Special cases: - if (q == 1) - { - return 0; - } - if (q == 0) - { - return 1; - } - // Naive RealType p = 1 - q; result = sin(half_pi<RealType>() * p); loses accuracy, so use a cos alternative instead. - //result = cos(half_pi<RealType>() * q); // for arcsine(0,1) - //result = result * result; - // For generalized arcsine: - RealType cos2hpip = cos(half_pi<RealType>() * q); - RealType cos2hpip2 = cos2hpip * cos2hpip; - result = -x_min * cos2hpip2 + x_min + x_max * cos2hpip2; - - return result; - } // Quantile Complement - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#if defined (BOOST_MSVC) -# pragma warning(pop) -#endif - -#endif // BOOST_MATH_DIST_ARCSINE_HPP
--- a/any/include/boost/math/distributions/bernoulli.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,336 +0,0 @@ -// boost\math\distributions\bernoulli.hpp - -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -// http://en.wikipedia.org/wiki/bernoulli_distribution -// http://mathworld.wolfram.com/BernoulliDistribution.html - -// bernoulli distribution is the discrete probability distribution of -// the number (k) of successes, in a single Bernoulli trials. -// It is a version of the binomial distribution when n = 1. - -// But note that the bernoulli distribution -// (like others including the poisson, binomial & negative binomial) -// is strictly defined as a discrete function: only integral values of k are envisaged. -// However because of the method of calculation using a continuous gamma function, -// it is convenient to treat it as if a continous function, -// and permit non-integral values of k. -// To enforce the strict mathematical model, users should use floor or ceil functions -// on k outside this function to ensure that k is integral. - -#ifndef BOOST_MATH_SPECIAL_BERNOULLI_HPP -#define BOOST_MATH_SPECIAL_BERNOULLI_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/tools/config.hpp> -#include <boost/math/distributions/complement.hpp> // complements -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> // isnan. - -#include <utility> - -namespace boost -{ - namespace math - { - namespace bernoulli_detail - { - // Common error checking routines for bernoulli distribution functions: - template <class RealType, class Policy> - inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& /* pol */) - { - if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, Policy()); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& /* pol */, const mpl::true_&) - { - return check_success_fraction(function, p, result, Policy()); - } - template <class RealType, class Policy> - inline bool check_dist(const char* , const RealType& , RealType* , const Policy& /* pol */, const mpl::false_&) - { - return true; - } - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& /* pol */) - { - return check_dist(function, p, result, Policy(), typename policies::constructor_error_check<Policy>::type()); - } - - template <class RealType, class Policy> - inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol) - { - if(check_dist(function, p, result, Policy(), typename policies::method_error_check<Policy>::type()) == false) - { - return false; - } - if(!(boost::math::isfinite)(k) || !((k == 0) || (k == 1))) - { - *result = policies::raise_domain_error<RealType>( - function, - "Number of successes argument is %1%, but must be 0 or 1 !", k, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& /* pol */) - { - if((check_dist(function, p, result, Policy(), typename policies::method_error_check<Policy>::type()) && detail::check_probability(function, prob, result, Policy())) == false) - { - return false; - } - return true; - } - } // namespace bernoulli_detail - - - template <class RealType = double, class Policy = policies::policy<> > - class bernoulli_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - bernoulli_distribution(RealType p = 0.5) : m_p(p) - { // Default probability = half suits 'fair' coin tossing - // where probability of heads == probability of tails. - RealType result; // of checks. - bernoulli_detail::check_dist( - "boost::math::bernoulli_distribution<%1%>::bernoulli_distribution", - m_p, - &result, Policy()); - } // bernoulli_distribution constructor. - - RealType success_fraction() const - { // Probability. - return m_p; - } - - private: - RealType m_p; // success_fraction - }; // template <class RealType> class bernoulli_distribution - - typedef bernoulli_distribution<double> bernoulli; - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const bernoulli_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k = {0, 1}. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1)); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const bernoulli_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k = {0, 1}. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1)); - } - - template <class RealType, class Policy> - inline RealType mean(const bernoulli_distribution<RealType, Policy>& dist) - { // Mean of bernoulli distribution = p (n = 1). - return dist.success_fraction(); - } // mean - - // Rely on dereived_accessors quantile(half) - //template <class RealType> - //inline RealType median(const bernoulli_distribution<RealType, Policy>& dist) - //{ // Median of bernoulli distribution is not defined. - // return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); - //} // median - - template <class RealType, class Policy> - inline RealType variance(const bernoulli_distribution<RealType, Policy>& dist) - { // Variance of bernoulli distribution =p * q. - return dist.success_fraction() * (1 - dist.success_fraction()); - } // variance - - template <class RealType, class Policy> - RealType pdf(const bernoulli_distribution<RealType, Policy>& dist, const RealType& k) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - // Error check: - RealType result = 0; // of checks. - if(false == bernoulli_detail::check_dist_and_k( - "boost::math::pdf(bernoulli_distribution<%1%>, %1%)", - dist.success_fraction(), // 0 to 1 - k, // 0 or 1 - &result, Policy())) - { - return result; - } - // Assume k is integral. - if (k == 0) - { - return 1 - dist.success_fraction(); // 1 - p - } - else // k == 1 - { - return dist.success_fraction(); // p - } - } // pdf - - template <class RealType, class Policy> - inline RealType cdf(const bernoulli_distribution<RealType, Policy>& dist, const RealType& k) - { // Cumulative Distribution Function Bernoulli. - RealType p = dist.success_fraction(); - // Error check: - RealType result = 0; - if(false == bernoulli_detail::check_dist_and_k( - "boost::math::cdf(bernoulli_distribution<%1%>, %1%)", - p, - k, - &result, Policy())) - { - return result; - } - if (k == 0) - { - return 1 - p; - } - else - { // k == 1 - return 1; - } - } // bernoulli cdf - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<bernoulli_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function bernoulli. - RealType const& k = c.param; - bernoulli_distribution<RealType, Policy> const& dist = c.dist; - RealType p = dist.success_fraction(); - // Error checks: - RealType result = 0; - if(false == bernoulli_detail::check_dist_and_k( - "boost::math::cdf(bernoulli_distribution<%1%>, %1%)", - p, - k, - &result, Policy())) - { - return result; - } - if (k == 0) - { - return p; - } - else - { // k == 1 - return 0; - } - } // bernoulli cdf complement - - template <class RealType, class Policy> - inline RealType quantile(const bernoulli_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile or Percent Point Bernoulli function. - // Return the number of expected successes k either 0 or 1. - // for a given probability p. - - RealType result = 0; // of error checks: - if(false == bernoulli_detail::check_dist_and_prob( - "boost::math::quantile(bernoulli_distribution<%1%>, %1%)", - dist.success_fraction(), - p, - &result, Policy())) - { - return result; - } - if (p <= (1 - dist.success_fraction())) - { // p <= pdf(dist, 0) == cdf(dist, 0) - return 0; - } - else - { - return 1; - } - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<bernoulli_distribution<RealType, Policy>, RealType>& c) - { // Quantile or Percent Point bernoulli function. - // Return the number of expected successes k for a given - // complement of the probability q. - // - // Error checks: - RealType q = c.param; - const bernoulli_distribution<RealType, Policy>& dist = c.dist; - RealType result = 0; - if(false == bernoulli_detail::check_dist_and_prob( - "boost::math::quantile(bernoulli_distribution<%1%>, %1%)", - dist.success_fraction(), - q, - &result, Policy())) - { - return result; - } - - if (q <= 1 - dist.success_fraction()) - { // // q <= cdf(complement(dist, 0)) == pdf(dist, 0) - return 1; - } - else - { - return 0; - } - } // quantile complemented. - - template <class RealType, class Policy> - inline RealType mode(const bernoulli_distribution<RealType, Policy>& dist) - { - return static_cast<RealType>((dist.success_fraction() <= 0.5) ? 0 : 1); // p = 0.5 can be 0 or 1 - } - - template <class RealType, class Policy> - inline RealType skewness(const bernoulli_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING; // Aid ADL for sqrt. - RealType p = dist.success_fraction(); - return (1 - 2 * p) / sqrt(p * (1 - p)); - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const bernoulli_distribution<RealType, Policy>& dist) - { - RealType p = dist.success_fraction(); - // Note Wolfram says this is kurtosis in text, but gamma2 is the kurtosis excess, - // and Wikipedia also says this is the kurtosis excess formula. - // return (6 * p * p - 6 * p + 1) / (p * (1 - p)); - // But Wolfram kurtosis article gives this simpler formula for kurtosis excess: - return 1 / (1 - p) + 1/p -6; - } - - template <class RealType, class Policy> - inline RealType kurtosis(const bernoulli_distribution<RealType, Policy>& dist) - { - RealType p = dist.success_fraction(); - return 1 / (1 - p) + 1/p -6 + 3; - // Simpler than: - // return (6 * p * p - 6 * p + 1) / (p * (1 - p)) + 3; - } - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_SPECIAL_BERNOULLI_HPP - - -
--- a/any/include/boost/math/distributions/beta.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,541 +0,0 @@ -// boost\math\distributions\beta.hpp - -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2006. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -// http://en.wikipedia.org/wiki/Beta_distribution -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm -// http://mathworld.wolfram.com/BetaDistribution.html - -// The Beta Distribution is a continuous probability distribution. -// The beta distribution is used to model events which are constrained to take place -// within an interval defined by maxima and minima, -// so is used extensively in PERT and other project management systems -// to describe the time to completion. -// The cdf of the beta distribution is used as a convenient way -// of obtaining the sum over a set of binomial outcomes. -// The beta distribution is also used in Bayesian statistics. - -#ifndef BOOST_MATH_DIST_BETA_HPP -#define BOOST_MATH_DIST_BETA_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for beta. -#include <boost/math/distributions/complement.hpp> // complements. -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. - -#if defined (BOOST_MSVC) -# pragma warning(push) -# pragma warning(disable: 4702) // unreachable code -// in domain_error_imp in error_handling -#endif - -#include <utility> - -namespace boost -{ - namespace math - { - namespace beta_detail - { - // Common error checking routines for beta distribution functions: - template <class RealType, class Policy> - inline bool check_alpha(const char* function, const RealType& alpha, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(alpha) || (alpha <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Alpha argument is %1%, but must be > 0 !", alpha, pol); - return false; - } - return true; - } // bool check_alpha - - template <class RealType, class Policy> - inline bool check_beta(const char* function, const RealType& beta, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(beta) || (beta <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Beta argument is %1%, but must be > 0 !", beta, pol); - return false; - } - return true; - } // bool check_beta - - template <class RealType, class Policy> - inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if((p < 0) || (p > 1) || !(boost::math::isfinite)(p)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } // bool check_prob - - template <class RealType, class Policy> - inline bool check_x(const char* function, const RealType& x, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(x) || (x < 0) || (x > 1)) - { - *result = policies::raise_domain_error<RealType>( - function, - "x argument is %1%, but must be >= 0 and <= 1 !", x, pol); - return false; - } - return true; - } // bool check_x - - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& alpha, const RealType& beta, RealType* result, const Policy& pol) - { // Check both alpha and beta. - return check_alpha(function, alpha, result, pol) - && check_beta(function, beta, result, pol); - } // bool check_dist - - template <class RealType, class Policy> - inline bool check_dist_and_x(const char* function, const RealType& alpha, const RealType& beta, RealType x, RealType* result, const Policy& pol) - { - return check_dist(function, alpha, beta, result, pol) - && beta_detail::check_x(function, x, result, pol); - } // bool check_dist_and_x - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, const RealType& alpha, const RealType& beta, RealType p, RealType* result, const Policy& pol) - { - return check_dist(function, alpha, beta, result, pol) - && check_prob(function, p, result, pol); - } // bool check_dist_and_prob - - template <class RealType, class Policy> - inline bool check_mean(const char* function, const RealType& mean, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(mean) || (mean <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "mean argument is %1%, but must be > 0 !", mean, pol); - return false; - } - return true; - } // bool check_mean - template <class RealType, class Policy> - inline bool check_variance(const char* function, const RealType& variance, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(variance) || (variance <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "variance argument is %1%, but must be > 0 !", variance, pol); - return false; - } - return true; - } // bool check_variance - } // namespace beta_detail - - // typedef beta_distribution<double> beta; - // is deliberately NOT included to avoid a name clash with the beta function. - // Use beta_distribution<> mybeta(...) to construct type double. - - template <class RealType = double, class Policy = policies::policy<> > - class beta_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - beta_distribution(RealType l_alpha = 1, RealType l_beta = 1) : m_alpha(l_alpha), m_beta(l_beta) - { - RealType result; - beta_detail::check_dist( - "boost::math::beta_distribution<%1%>::beta_distribution", - m_alpha, - m_beta, - &result, Policy()); - } // beta_distribution constructor. - // Accessor functions: - RealType alpha() const - { - return m_alpha; - } - RealType beta() const - { // . - return m_beta; - } - - // Estimation of the alpha & beta parameters. - // http://en.wikipedia.org/wiki/Beta_distribution - // gives formulae in section on parameter estimation. - // Also NIST EDA page 3 & 4 give the same. - // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366h.htm - // http://www.epi.ucdavis.edu/diagnostictests/betabuster.html - - static RealType find_alpha( - RealType mean, // Expected value of mean. - RealType variance) // Expected value of variance. - { - static const char* function = "boost::math::beta_distribution<%1%>::find_alpha"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_mean(function, mean, &result, Policy()) - && beta_detail::check_variance(function, variance, &result, Policy()) - ) - ) - { - return result; - } - return mean * (( (mean * (1 - mean)) / variance)- 1); - } // RealType find_alpha - - static RealType find_beta( - RealType mean, // Expected value of mean. - RealType variance) // Expected value of variance. - { - static const char* function = "boost::math::beta_distribution<%1%>::find_beta"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_mean(function, mean, &result, Policy()) - && - beta_detail::check_variance(function, variance, &result, Policy()) - ) - ) - { - return result; - } - return (1 - mean) * (((mean * (1 - mean)) /variance)-1); - } // RealType find_beta - - // Estimate alpha & beta from either alpha or beta, and x and probability. - // Uses for these parameter estimators are unclear. - - static RealType find_alpha( - RealType beta, // from beta. - RealType x, // x. - RealType probability) // cdf - { - static const char* function = "boost::math::beta_distribution<%1%>::find_alpha"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_prob(function, probability, &result, Policy()) - && - beta_detail::check_beta(function, beta, &result, Policy()) - && - beta_detail::check_x(function, x, &result, Policy()) - ) - ) - { - return result; - } - return ibeta_inva(beta, x, probability, Policy()); - } // RealType find_alpha(beta, a, probability) - - static RealType find_beta( - // ibeta_invb(T b, T x, T p); (alpha, x, cdf,) - RealType alpha, // alpha. - RealType x, // probability x. - RealType probability) // probability cdf. - { - static const char* function = "boost::math::beta_distribution<%1%>::find_beta"; - RealType result = 0; // of error checks. - if(false == - ( - beta_detail::check_prob(function, probability, &result, Policy()) - && - beta_detail::check_alpha(function, alpha, &result, Policy()) - && - beta_detail::check_x(function, x, &result, Policy()) - ) - ) - { - return result; - } - return ibeta_invb(alpha, x, probability, Policy()); - } // RealType find_beta(alpha, x, probability) - - private: - RealType m_alpha; // Two parameters of the beta distribution. - RealType m_beta; - }; // template <class RealType, class Policy> class beta_distribution - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const beta_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1)); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const beta_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1)); - } - - template <class RealType, class Policy> - inline RealType mean(const beta_distribution<RealType, Policy>& dist) - { // Mean of beta distribution = np. - return dist.alpha() / (dist.alpha() + dist.beta()); - } // mean - - template <class RealType, class Policy> - inline RealType variance(const beta_distribution<RealType, Policy>& dist) - { // Variance of beta distribution = np(1-p). - RealType a = dist.alpha(); - RealType b = dist.beta(); - return (a * b) / ((a + b ) * (a + b) * (a + b + 1)); - } // variance - - template <class RealType, class Policy> - inline RealType mode(const beta_distribution<RealType, Policy>& dist) - { - static const char* function = "boost::math::mode(beta_distribution<%1%> const&)"; - - RealType result; - if ((dist.alpha() <= 1)) - { - result = policies::raise_domain_error<RealType>( - function, - "mode undefined for alpha = %1%, must be > 1!", dist.alpha(), Policy()); - return result; - } - - if ((dist.beta() <= 1)) - { - result = policies::raise_domain_error<RealType>( - function, - "mode undefined for beta = %1%, must be > 1!", dist.beta(), Policy()); - return result; - } - RealType a = dist.alpha(); - RealType b = dist.beta(); - return (a-1) / (a + b - 2); - } // mode - - //template <class RealType, class Policy> - //inline RealType median(const beta_distribution<RealType, Policy>& dist) - //{ // Median of beta distribution is not defined. - // return tools::domain_error<RealType>(function, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); - //} // median - - //But WILL be provided by the derived accessor as quantile(0.5). - - template <class RealType, class Policy> - inline RealType skewness(const beta_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // ADL of std functions. - RealType a = dist.alpha(); - RealType b = dist.beta(); - return (2 * (b-a) * sqrt(a + b + 1)) / ((a + b + 2) * sqrt(a * b)); - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const beta_distribution<RealType, Policy>& dist) - { - RealType a = dist.alpha(); - RealType b = dist.beta(); - RealType a_2 = a * a; - RealType n = 6 * (a_2 * a - a_2 * (2 * b - 1) + b * b * (b + 1) - 2 * a * b * (b + 2)); - RealType d = a * b * (a + b + 2) * (a + b + 3); - return n / d; - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const beta_distribution<RealType, Policy>& dist) - { - return 3 + kurtosis_excess(dist); - } // kurtosis - - template <class RealType, class Policy> - inline RealType pdf(const beta_distribution<RealType, Policy>& dist, const RealType& x) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - - static const char* function = "boost::math::pdf(beta_distribution<%1%> const&, %1%)"; - - BOOST_MATH_STD_USING // for ADL of std functions - - RealType a = dist.alpha(); - RealType b = dist.beta(); - - // Argument checks: - RealType result = 0; - if(false == beta_detail::check_dist_and_x( - function, - a, b, x, - &result, Policy())) - { - return result; - } - using boost::math::beta; - return ibeta_derivative(a, b, x, Policy()); - } // pdf - - template <class RealType, class Policy> - inline RealType cdf(const beta_distribution<RealType, Policy>& dist, const RealType& x) - { // Cumulative Distribution Function beta. - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(beta_distribution<%1%> const&, %1%)"; - - RealType a = dist.alpha(); - RealType b = dist.beta(); - - // Argument checks: - RealType result = 0; - if(false == beta_detail::check_dist_and_x( - function, - a, b, x, - &result, Policy())) - { - return result; - } - // Special cases: - if (x == 0) - { - return 0; - } - else if (x == 1) - { - return 1; - } - return ibeta(a, b, x, Policy()); - } // beta cdf - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<beta_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function beta. - - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(beta_distribution<%1%> const&, %1%)"; - - RealType const& x = c.param; - beta_distribution<RealType, Policy> const& dist = c.dist; - RealType a = dist.alpha(); - RealType b = dist.beta(); - - // Argument checks: - RealType result = 0; - if(false == beta_detail::check_dist_and_x( - function, - a, b, x, - &result, Policy())) - { - return result; - } - if (x == 0) - { - return 1; - } - else if (x == 1) - { - return 0; - } - // Calculate cdf beta using the incomplete beta function. - // Use of ibeta here prevents cancellation errors in calculating - // 1 - x if x is very small, perhaps smaller than machine epsilon. - return ibetac(a, b, x, Policy()); - } // beta cdf - - template <class RealType, class Policy> - inline RealType quantile(const beta_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile or Percent Point beta function or - // Inverse Cumulative probability distribution function CDF. - // Return x (0 <= x <= 1), - // for a given probability p (0 <= p <= 1). - // These functions take a probability as an argument - // and return a value such that the probability that a random variable x - // will be less than or equal to that value - // is whatever probability you supplied as an argument. - - static const char* function = "boost::math::quantile(beta_distribution<%1%> const&, %1%)"; - - RealType result = 0; // of argument checks: - RealType a = dist.alpha(); - RealType b = dist.beta(); - if(false == beta_detail::check_dist_and_prob( - function, - a, b, p, - &result, Policy())) - { - return result; - } - // Special cases: - if (p == 0) - { - return 0; - } - if (p == 1) - { - return 1; - } - return ibeta_inv(a, b, p, static_cast<RealType*>(0), Policy()); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<beta_distribution<RealType, Policy>, RealType>& c) - { // Complement Quantile or Percent Point beta function . - // Return the number of expected x for a given - // complement of the probability q. - - static const char* function = "boost::math::quantile(beta_distribution<%1%> const&, %1%)"; - - // - // Error checks: - RealType q = c.param; - const beta_distribution<RealType, Policy>& dist = c.dist; - RealType result = 0; - RealType a = dist.alpha(); - RealType b = dist.beta(); - if(false == beta_detail::check_dist_and_prob( - function, - a, - b, - q, - &result, Policy())) - { - return result; - } - // Special cases: - if(q == 1) - { - return 0; - } - if(q == 0) - { - return 1; - } - - return ibetac_inv(a, b, q, static_cast<RealType*>(0), Policy()); - } // Quantile Complement - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#if defined (BOOST_MSVC) -# pragma warning(pop) -#endif - -#endif // BOOST_MATH_DIST_BETA_HPP - -
--- a/any/include/boost/math/distributions/binomial.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,728 +0,0 @@ -// boost\math\distributions\binomial.hpp - -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -// http://en.wikipedia.org/wiki/binomial_distribution - -// Binomial distribution is the discrete probability distribution of -// the number (k) of successes, in a sequence of -// n independent (yes or no, success or failure) Bernoulli trials. - -// It expresses the probability of a number of events occurring in a fixed time -// if these events occur with a known average rate (probability of success), -// and are independent of the time since the last event. - -// The number of cars that pass through a certain point on a road during a given period of time. -// The number of spelling mistakes a secretary makes while typing a single page. -// The number of phone calls at a call center per minute. -// The number of times a web server is accessed per minute. -// The number of light bulbs that burn out in a certain amount of time. -// The number of roadkill found per unit length of road - -// http://en.wikipedia.org/wiki/binomial_distribution - -// Given a sample of N measured values k[i], -// we wish to estimate the value of the parameter x (mean) -// of the binomial population from which the sample was drawn. -// To calculate the maximum likelihood value = 1/N sum i = 1 to N of k[i] - -// Also may want a function for EXACTLY k. - -// And probability that there are EXACTLY k occurrences is -// exp(-x) * pow(x, k) / factorial(k) -// where x is expected occurrences (mean) during the given interval. -// For example, if events occur, on average, every 4 min, -// and we are interested in number of events occurring in 10 min, -// then x = 10/4 = 2.5 - -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366i.htm - -// The binomial distribution is used when there are -// exactly two mutually exclusive outcomes of a trial. -// These outcomes are appropriately labeled "success" and "failure". -// The binomial distribution is used to obtain -// the probability of observing x successes in N trials, -// with the probability of success on a single trial denoted by p. -// The binomial distribution assumes that p is fixed for all trials. - -// P(x, p, n) = n!/(x! * (n-x)!) * p^x * (1-p)^(n-x) - -// http://mathworld.wolfram.com/BinomialCoefficient.html - -// The binomial coefficient (n; k) is the number of ways of picking -// k unordered outcomes from n possibilities, -// also known as a combination or combinatorial number. -// The symbols _nC_k and (n; k) are used to denote a binomial coefficient, -// and are sometimes read as "n choose k." -// (n; k) therefore gives the number of k-subsets possible out of a set of n distinct items. - -// For example: -// The 2-subsets of {1,2,3,4} are the six pairs {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}, so (4; 2)==6. - -// http://functions.wolfram.com/GammaBetaErf/Binomial/ for evaluation. - -// But note that the binomial distribution -// (like others including the poisson, negative binomial & Bernoulli) -// is strictly defined as a discrete function: only integral values of k are envisaged. -// However because of the method of calculation using a continuous gamma function, -// it is convenient to treat it as if a continous function, -// and permit non-integral values of k. -// To enforce the strict mathematical model, users should use floor or ceil functions -// on k outside this function to ensure that k is integral. - -#ifndef BOOST_MATH_SPECIAL_BINOMIAL_HPP -#define BOOST_MATH_SPECIAL_BINOMIAL_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for incomplete beta. -#include <boost/math/distributions/complement.hpp> // complements -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/distributions/detail/inv_discrete_quantile.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. - -#include <utility> - -namespace boost -{ - namespace math - { - - template <class RealType, class Policy> - class binomial_distribution; - - namespace binomial_detail{ - // common error checking routines for binomial distribution functions: - template <class RealType, class Policy> - inline bool check_N(const char* function, const RealType& N, RealType* result, const Policy& pol) - { - if((N < 0) || !(boost::math::isfinite)(N)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Number of Trials argument is %1%, but must be >= 0 !", N, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if((p < 0) || (p > 1) || !(boost::math::isfinite)(p)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& N, const RealType& p, RealType* result, const Policy& pol) - { - return check_success_fraction( - function, p, result, pol) - && check_N( - function, N, result, pol); - } - template <class RealType, class Policy> - inline bool check_dist_and_k(const char* function, const RealType& N, const RealType& p, RealType k, RealType* result, const Policy& pol) - { - if(check_dist(function, N, p, result, pol) == false) - return false; - if((k < 0) || !(boost::math::isfinite)(k)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Number of Successes argument is %1%, but must be >= 0 !", k, pol); - return false; - } - if(k > N) - { - *result = policies::raise_domain_error<RealType>( - function, - "Number of Successes argument is %1%, but must be <= Number of Trials !", k, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, const RealType& N, RealType p, RealType prob, RealType* result, const Policy& pol) - { - if((check_dist(function, N, p, result, pol) && detail::check_probability(function, prob, result, pol)) == false) - return false; - return true; - } - - template <class T, class Policy> - T inverse_binomial_cornish_fisher(T n, T sf, T p, T q, const Policy& pol) - { - BOOST_MATH_STD_USING - // mean: - T m = n * sf; - // standard deviation: - T sigma = sqrt(n * sf * (1 - sf)); - // skewness - T sk = (1 - 2 * sf) / sigma; - // kurtosis: - // T k = (1 - 6 * sf * (1 - sf) ) / (n * sf * (1 - sf)); - // Get the inverse of a std normal distribution: - T x = boost::math::erfc_inv(p > q ? 2 * q : 2 * p, pol) * constants::root_two<T>(); - // Set the sign: - if(p < 0.5) - x = -x; - T x2 = x * x; - // w is correction term due to skewness - T w = x + sk * (x2 - 1) / 6; - /* - // Add on correction due to kurtosis. - // Disabled for now, seems to make things worse? - // - if(n >= 10) - w += k * x * (x2 - 3) / 24 + sk * sk * x * (2 * x2 - 5) / -36; - */ - w = m + sigma * w; - if(w < tools::min_value<T>()) - return sqrt(tools::min_value<T>()); - if(w > n) - return n; - return w; - } - - template <class RealType, class Policy> - RealType quantile_imp(const binomial_distribution<RealType, Policy>& dist, const RealType& p, const RealType& q, bool comp) - { // Quantile or Percent Point Binomial function. - // Return the number of expected successes k, - // for a given probability p. - // - // Error checks: - BOOST_MATH_STD_USING // ADL of std names - RealType result = 0; - RealType trials = dist.trials(); - RealType success_fraction = dist.success_fraction(); - if(false == binomial_detail::check_dist_and_prob( - "boost::math::quantile(binomial_distribution<%1%> const&, %1%)", - trials, - success_fraction, - p, - &result, Policy())) - { - return result; - } - - // Special cases: - // - if(p == 0) - { // There may actually be no answer to this question, - // since the probability of zero successes may be non-zero, - // but zero is the best we can do: - return 0; - } - if(p == 1) - { // Probability of n or fewer successes is always one, - // so n is the most sensible answer here: - return trials; - } - if (p <= pow(1 - success_fraction, trials)) - { // p <= pdf(dist, 0) == cdf(dist, 0) - return 0; // So the only reasonable result is zero. - } // And root finder would fail otherwise. - if(success_fraction == 1) - { // our formulae break down in this case: - return p > 0.5f ? trials : 0; - } - - // Solve for quantile numerically: - // - RealType guess = binomial_detail::inverse_binomial_cornish_fisher(trials, success_fraction, p, q, Policy()); - RealType factor = 8; - if(trials > 100) - factor = 1.01f; // guess is pretty accurate - else if((trials > 10) && (trials - 1 > guess) && (guess > 3)) - factor = 1.15f; // less accurate but OK. - else if(trials < 10) - { - // pretty inaccurate guess in this area: - if(guess > trials / 64) - { - guess = trials / 4; - factor = 2; - } - else - guess = trials / 1024; - } - else - factor = 2; // trials largish, but in far tails. - - typedef typename Policy::discrete_quantile_type discrete_quantile_type; - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - return detail::inverse_discrete_quantile( - dist, - comp ? q : p, - comp, - guess, - factor, - RealType(1), - discrete_quantile_type(), - max_iter); - } // quantile - - } - - template <class RealType = double, class Policy = policies::policy<> > - class binomial_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - binomial_distribution(RealType n = 1, RealType p = 0.5) : m_n(n), m_p(p) - { // Default n = 1 is the Bernoulli distribution - // with equal probability of 'heads' or 'tails. - RealType r; - binomial_detail::check_dist( - "boost::math::binomial_distribution<%1%>::binomial_distribution", - m_n, - m_p, - &r, Policy()); - } // binomial_distribution constructor. - - RealType success_fraction() const - { // Probability. - return m_p; - } - RealType trials() const - { // Total number of trials. - return m_n; - } - - enum interval_type{ - clopper_pearson_exact_interval, - jeffreys_prior_interval - }; - - // - // Estimation of the success fraction parameter. - // The best estimate is actually simply successes/trials, - // these functions are used - // to obtain confidence intervals for the success fraction. - // - static RealType find_lower_bound_on_p( - RealType trials, - RealType successes, - RealType probability, - interval_type t = clopper_pearson_exact_interval) - { - static const char* function = "boost::math::binomial_distribution<%1%>::find_lower_bound_on_p"; - // Error checks: - RealType result = 0; - if(false == binomial_detail::check_dist_and_k( - function, trials, RealType(0), successes, &result, Policy()) - && - binomial_detail::check_dist_and_prob( - function, trials, RealType(0), probability, &result, Policy())) - { return result; } - - if(successes == 0) - return 0; - - // NOTE!!! The Clopper Pearson formula uses "successes" not - // "successes+1" as usual to get the lower bound, - // see http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - return (t == clopper_pearson_exact_interval) ? ibeta_inv(successes, trials - successes + 1, probability, static_cast<RealType*>(0), Policy()) - : ibeta_inv(successes + 0.5f, trials - successes + 0.5f, probability, static_cast<RealType*>(0), Policy()); - } - static RealType find_upper_bound_on_p( - RealType trials, - RealType successes, - RealType probability, - interval_type t = clopper_pearson_exact_interval) - { - static const char* function = "boost::math::binomial_distribution<%1%>::find_upper_bound_on_p"; - // Error checks: - RealType result = 0; - if(false == binomial_detail::check_dist_and_k( - function, trials, RealType(0), successes, &result, Policy()) - && - binomial_detail::check_dist_and_prob( - function, trials, RealType(0), probability, &result, Policy())) - { return result; } - - if(trials == successes) - return 1; - - return (t == clopper_pearson_exact_interval) ? ibetac_inv(successes + 1, trials - successes, probability, static_cast<RealType*>(0), Policy()) - : ibetac_inv(successes + 0.5f, trials - successes + 0.5f, probability, static_cast<RealType*>(0), Policy()); - } - // Estimate number of trials parameter: - // - // "How many trials do I need to be P% sure of seeing k events?" - // or - // "How many trials can I have to be P% sure of seeing fewer than k events?" - // - static RealType find_minimum_number_of_trials( - RealType k, // number of events - RealType p, // success fraction - RealType alpha) // risk level - { - static const char* function = "boost::math::binomial_distribution<%1%>::find_minimum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == binomial_detail::check_dist_and_k( - function, k, p, k, &result, Policy()) - && - binomial_detail::check_dist_and_prob( - function, k, p, alpha, &result, Policy())) - { return result; } - - result = ibetac_invb(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } - - static RealType find_maximum_number_of_trials( - RealType k, // number of events - RealType p, // success fraction - RealType alpha) // risk level - { - static const char* function = "boost::math::binomial_distribution<%1%>::find_maximum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == binomial_detail::check_dist_and_k( - function, k, p, k, &result, Policy()) - && - binomial_detail::check_dist_and_prob( - function, k, p, alpha, &result, Policy())) - { return result; } - - result = ibeta_invb(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } - - private: - RealType m_n; // Not sure if this shouldn't be an int? - RealType m_p; // success_fraction - }; // template <class RealType, class Policy> class binomial_distribution - - typedef binomial_distribution<> binomial; - // typedef binomial_distribution<double> binomial; - // IS now included since no longer a name clash with function binomial. - //typedef binomial_distribution<double> binomial; // Reserved name of type double. - - template <class RealType, class Policy> - const std::pair<RealType, RealType> range(const binomial_distribution<RealType, Policy>& dist) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), dist.trials()); - } - - template <class RealType, class Policy> - const std::pair<RealType, RealType> support(const binomial_distribution<RealType, Policy>& dist) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(static_cast<RealType>(0), dist.trials()); - } - - template <class RealType, class Policy> - inline RealType mean(const binomial_distribution<RealType, Policy>& dist) - { // Mean of Binomial distribution = np. - return dist.trials() * dist.success_fraction(); - } // mean - - template <class RealType, class Policy> - inline RealType variance(const binomial_distribution<RealType, Policy>& dist) - { // Variance of Binomial distribution = np(1-p). - return dist.trials() * dist.success_fraction() * (1 - dist.success_fraction()); - } // variance - - template <class RealType, class Policy> - RealType pdf(const binomial_distribution<RealType, Policy>& dist, const RealType& k) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - - BOOST_MATH_STD_USING // for ADL of std functions - - RealType n = dist.trials(); - - // Error check: - RealType result = 0; // initialization silences some compiler warnings - if(false == binomial_detail::check_dist_and_k( - "boost::math::pdf(binomial_distribution<%1%> const&, %1%)", - n, - dist.success_fraction(), - k, - &result, Policy())) - { - return result; - } - - // Special cases of success_fraction, regardless of k successes and regardless of n trials. - if (dist.success_fraction() == 0) - { // probability of zero successes is 1: - return static_cast<RealType>(k == 0 ? 1 : 0); - } - if (dist.success_fraction() == 1) - { // probability of n successes is 1: - return static_cast<RealType>(k == n ? 1 : 0); - } - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - if (n == 0) - { - return 1; // Probability = 1 = certainty. - } - if (k == 0) - { // binomial coeffic (n 0) = 1, - // n ^ 0 = 1 - return pow(1 - dist.success_fraction(), n); - } - if (k == n) - { // binomial coeffic (n n) = 1, - // n ^ 0 = 1 - return pow(dist.success_fraction(), k); // * pow((1 - dist.success_fraction()), (n - k)) = 1 - } - - // Probability of getting exactly k successes - // if C(n, k) is the binomial coefficient then: - // - // f(k; n,p) = C(n, k) * p^k * (1-p)^(n-k) - // = (n!/(k!(n-k)!)) * p^k * (1-p)^(n-k) - // = (tgamma(n+1) / (tgamma(k+1)*tgamma(n-k+1))) * p^k * (1-p)^(n-k) - // = p^k (1-p)^(n-k) / (beta(k+1, n-k+1) * (n+1)) - // = ibeta_derivative(k+1, n-k+1, p) / (n+1) - // - using boost::math::ibeta_derivative; // a, b, x - return ibeta_derivative(k+1, n-k+1, dist.success_fraction(), Policy()) / (n+1); - - } // pdf - - template <class RealType, class Policy> - inline RealType cdf(const binomial_distribution<RealType, Policy>& dist, const RealType& k) - { // Cumulative Distribution Function Binomial. - // The random variate k is the number of successes in n trials. - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - - // Returns the sum of the terms 0 through k of the Binomial Probability Density/Mass: - // - // i=k - // -- ( n ) i n-i - // > | | p (1-p) - // -- ( i ) - // i=0 - - // The terms are not summed directly instead - // the incomplete beta integral is employed, - // according to the formula: - // P = I[1-p]( n-k, k+1). - // = 1 - I[p](k + 1, n - k) - - BOOST_MATH_STD_USING // for ADL of std functions - - RealType n = dist.trials(); - RealType p = dist.success_fraction(); - - // Error check: - RealType result = 0; - if(false == binomial_detail::check_dist_and_k( - "boost::math::cdf(binomial_distribution<%1%> const&, %1%)", - n, - p, - k, - &result, Policy())) - { - return result; - } - if (k == n) - { - return 1; - } - - // Special cases, regardless of k. - if (p == 0) - { // This need explanation: - // the pdf is zero for all cases except when k == 0. - // For zero p the probability of zero successes is one. - // Therefore the cdf is always 1: - // the probability of k or *fewer* successes is always 1 - // if there are never any successes! - return 1; - } - if (p == 1) - { // This is correct but needs explanation: - // when k = 1 - // all the cdf and pdf values are zero *except* when k == n, - // and that case has been handled above already. - return 0; - } - // - // P = I[1-p](n - k, k + 1) - // = 1 - I[p](k + 1, n - k) - // Use of ibetac here prevents cancellation errors in calculating - // 1-p if p is very small, perhaps smaller than machine epsilon. - // - // Note that we do not use a finite sum here, since the incomplete - // beta uses a finite sum internally for integer arguments, so - // we'll just let it take care of the necessary logic. - // - return ibetac(k + 1, n - k, p, Policy()); - } // binomial cdf - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<binomial_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function Binomial. - // The random variate k is the number of successes in n trials. - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - - // Returns the sum of the terms k+1 through n of the Binomial Probability Density/Mass: - // - // i=n - // -- ( n ) i n-i - // > | | p (1-p) - // -- ( i ) - // i=k+1 - - // The terms are not summed directly instead - // the incomplete beta integral is employed, - // according to the formula: - // Q = 1 -I[1-p]( n-k, k+1). - // = I[p](k + 1, n - k) - - BOOST_MATH_STD_USING // for ADL of std functions - - RealType const& k = c.param; - binomial_distribution<RealType, Policy> const& dist = c.dist; - RealType n = dist.trials(); - RealType p = dist.success_fraction(); - - // Error checks: - RealType result = 0; - if(false == binomial_detail::check_dist_and_k( - "boost::math::cdf(binomial_distribution<%1%> const&, %1%)", - n, - p, - k, - &result, Policy())) - { - return result; - } - - if (k == n) - { // Probability of greater than n successes is necessarily zero: - return 0; - } - - // Special cases, regardless of k. - if (p == 0) - { - // This need explanation: the pdf is zero for all - // cases except when k == 0. For zero p the probability - // of zero successes is one. Therefore the cdf is always - // 1: the probability of *more than* k successes is always 0 - // if there are never any successes! - return 0; - } - if (p == 1) - { - // This needs explanation, when p = 1 - // we always have n successes, so the probability - // of more than k successes is 1 as long as k < n. - // The k == n case has already been handled above. - return 1; - } - // - // Calculate cdf binomial using the incomplete beta function. - // Q = 1 -I[1-p](n - k, k + 1) - // = I[p](k + 1, n - k) - // Use of ibeta here prevents cancellation errors in calculating - // 1-p if p is very small, perhaps smaller than machine epsilon. - // - // Note that we do not use a finite sum here, since the incomplete - // beta uses a finite sum internally for integer arguments, so - // we'll just let it take care of the necessary logic. - // - return ibeta(k + 1, n - k, p, Policy()); - } // binomial cdf - - template <class RealType, class Policy> - inline RealType quantile(const binomial_distribution<RealType, Policy>& dist, const RealType& p) - { - return binomial_detail::quantile_imp(dist, p, RealType(1-p), false); - } // quantile - - template <class RealType, class Policy> - RealType quantile(const complemented2_type<binomial_distribution<RealType, Policy>, RealType>& c) - { - return binomial_detail::quantile_imp(c.dist, RealType(1-c.param), c.param, true); - } // quantile - - template <class RealType, class Policy> - inline RealType mode(const binomial_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // ADL of std functions. - RealType p = dist.success_fraction(); - RealType n = dist.trials(); - return floor(p * (n + 1)); - } - - template <class RealType, class Policy> - inline RealType median(const binomial_distribution<RealType, Policy>& dist) - { // Bounds for the median of the negative binomial distribution - // VAN DE VEN R. ; WEBER N. C. ; - // Univ. Sydney, school mathematics statistics, Sydney N.S.W. 2006, AUSTRALIE - // Metrika (Metrika) ISSN 0026-1335 CODEN MTRKA8 - // 1993, vol. 40, no3-4, pp. 185-189 (4 ref.) - - // Bounds for median and 50 percetage point of binomial and negative binomial distribution - // Metrika, ISSN 0026-1335 (Print) 1435-926X (Online) - // Volume 41, Number 1 / December, 1994, DOI 10.1007/BF01895303 - BOOST_MATH_STD_USING // ADL of std functions. - RealType p = dist.success_fraction(); - RealType n = dist.trials(); - // Wikipedia says one of floor(np) -1, floor (np), floor(np) +1 - return floor(p * n); // Chose the middle value. - } - - template <class RealType, class Policy> - inline RealType skewness(const binomial_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // ADL of std functions. - RealType p = dist.success_fraction(); - RealType n = dist.trials(); - return (1 - 2 * p) / sqrt(n * p * (1 - p)); - } - - template <class RealType, class Policy> - inline RealType kurtosis(const binomial_distribution<RealType, Policy>& dist) - { - RealType p = dist.success_fraction(); - RealType n = dist.trials(); - return 3 - 6 / n + 1 / (n * p * (1 - p)); - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const binomial_distribution<RealType, Policy>& dist) - { - RealType p = dist.success_fraction(); - RealType q = 1 - p; - RealType n = dist.trials(); - return (1 - 6 * p * q) / (n * p * q); - } - - } // namespace math - } // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_SPECIAL_BINOMIAL_HPP - -
--- a/any/include/boost/math/distributions/cauchy.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,362 +0,0 @@ -// Copyright John Maddock 2006, 2007. -// Copyright Paul A. Bristow 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_CAUCHY_HPP -#define BOOST_STATS_CAUCHY_HPP - -#ifdef _MSC_VER -#pragma warning(push) -#pragma warning(disable : 4127) // conditional expression is constant -#endif - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/constants/constants.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/config/no_tr1/cmath.hpp> - -#include <utility> - -namespace boost{ namespace math -{ - -template <class RealType, class Policy> -class cauchy_distribution; - -namespace detail -{ - -template <class RealType, class Policy> -RealType cdf_imp(const cauchy_distribution<RealType, Policy>& dist, const RealType& x, bool complement) -{ - // - // This calculates the cdf of the Cauchy distribution and/or its complement. - // - // The usual formula for the Cauchy cdf is: - // - // cdf = 0.5 + atan(x)/pi - // - // But that suffers from cancellation error as x -> -INF. - // - // Recall that for x < 0: - // - // atan(x) = -pi/2 - atan(1/x) - // - // Substituting into the above we get: - // - // CDF = -atan(1/x) ; x < 0 - // - // So the proceedure is to calculate the cdf for -fabs(x) - // using the above formula, and then subtract from 1 when required - // to get the result. - // - BOOST_MATH_STD_USING // for ADL of std functions - static const char* function = "boost::math::cdf(cauchy<%1%>&, %1%)"; - RealType result = 0; - RealType location = dist.location(); - RealType scale = dist.scale(); - if(false == detail::check_location(function, location, &result, Policy())) - { - return result; - } - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) - { // cdf +infinity is unity. - return static_cast<RealType>((complement) ? 0 : 1); - } - if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) - { // cdf -infinity is zero. - return static_cast<RealType>((complement) ? 1 : 0); - } - if(false == detail::check_x(function, x, &result, Policy())) - { // Catches x == NaN - return result; - } - RealType mx = -fabs((x - location) / scale); // scale is > 0 - if(mx > -tools::epsilon<RealType>() / 8) - { // special case first: x extremely close to location. - return 0.5; - } - result = -atan(1 / mx) / constants::pi<RealType>(); - return (((x > location) != complement) ? 1 - result : result); -} // cdf - -template <class RealType, class Policy> -RealType quantile_imp( - const cauchy_distribution<RealType, Policy>& dist, - const RealType& p, - bool complement) -{ - // This routine implements the quantile for the Cauchy distribution, - // the value p may be the probability, or its complement if complement=true. - // - // The procedure first performs argument reduction on p to avoid error - // when calculating the tangent, then calulates the distance from the - // mid-point of the distribution. This is either added or subtracted - // from the location parameter depending on whether `complement` is true. - // - static const char* function = "boost::math::quantile(cauchy<%1%>&, %1%)"; - BOOST_MATH_STD_USING // for ADL of std functions - - RealType result = 0; - RealType location = dist.location(); - RealType scale = dist.scale(); - if(false == detail::check_location(function, location, &result, Policy())) - { - return result; - } - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(false == detail::check_probability(function, p, &result, Policy())) - { - return result; - } - // Special cases: - if(p == 1) - { - return (complement ? -1 : 1) * policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - if(p == 0) - { - return (complement ? 1 : -1) * policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - - RealType P = p - floor(p); // argument reduction of p: - if(P > 0.5) - { - P = P - 1; - } - if(P == 0.5) // special case: - { - return location; - } - result = -scale / tan(constants::pi<RealType>() * P); - return complement ? RealType(location - result) : RealType(location + result); -} // quantile - -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class cauchy_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - cauchy_distribution(RealType l_location = 0, RealType l_scale = 1) - : m_a(l_location), m_hg(l_scale) - { - static const char* function = "boost::math::cauchy_distribution<%1%>::cauchy_distribution"; - RealType result; - detail::check_location(function, l_location, &result, Policy()); - detail::check_scale(function, l_scale, &result, Policy()); - } // cauchy_distribution - - RealType location()const - { - return m_a; - } - RealType scale()const - { - return m_hg; - } - -private: - RealType m_a; // The location, this is the median of the distribution. - RealType m_hg; // The scale )or shape), this is the half width at half height. -}; - -typedef cauchy_distribution<double> cauchy; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const cauchy_distribution<RealType, Policy>&) -{ // Range of permissible values for random variable x. - if (std::numeric_limits<RealType>::has_infinity) - { - return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. - } - else - { // Can only use max_value. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max. - } -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const cauchy_distribution<RealType, Policy>& ) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - if (std::numeric_limits<RealType>::has_infinity) - { - return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. - } - else - { // Can only use max_value. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max. - } -} - -template <class RealType, class Policy> -inline RealType pdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::pdf(cauchy<%1%>&, %1%)"; - RealType result = 0; - RealType location = dist.location(); - RealType scale = dist.scale(); - if(false == detail::check_scale("boost::math::pdf(cauchy<%1%>&, %1%)", scale, &result, Policy())) - { - return result; - } - if(false == detail::check_location("boost::math::pdf(cauchy<%1%>&, %1%)", location, &result, Policy())) - { - return result; - } - if((boost::math::isinf)(x)) - { - return 0; // pdf + and - infinity is zero. - } - // These produce MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity()) - //{ // pdf + and - infinity is zero. - // return 0; - //} - - if(false == detail::check_x(function, x, &result, Policy())) - { // Catches x = NaN - return result; - } - - RealType xs = (x - location) / scale; - result = 1 / (constants::pi<RealType>() * scale * (1 + xs * xs)); - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const cauchy_distribution<RealType, Policy>& dist, const RealType& x) -{ - return detail::cdf_imp(dist, x, false); -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const cauchy_distribution<RealType, Policy>& dist, const RealType& p) -{ - return detail::quantile_imp(dist, p, false); -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c) -{ - return detail::cdf_imp(c.dist, c.param, true); -} // cdf complement - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<cauchy_distribution<RealType, Policy>, RealType>& c) -{ - return detail::quantile_imp(c.dist, c.param, true); -} // quantile complement - -template <class RealType, class Policy> -inline RealType mean(const cauchy_distribution<RealType, Policy>&) -{ // There is no mean: - typedef typename Policy::assert_undefined_type assert_type; - BOOST_STATIC_ASSERT(assert_type::value == 0); - - return policies::raise_domain_error<RealType>( - "boost::math::mean(cauchy<%1%>&)", - "The Cauchy distribution does not have a mean: " - "the only possible return value is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); -} - -template <class RealType, class Policy> -inline RealType variance(const cauchy_distribution<RealType, Policy>& /*dist*/) -{ - // There is no variance: - typedef typename Policy::assert_undefined_type assert_type; - BOOST_STATIC_ASSERT(assert_type::value == 0); - - return policies::raise_domain_error<RealType>( - "boost::math::variance(cauchy<%1%>&)", - "The Cauchy distribution does not have a variance: " - "the only possible return value is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); -} - -template <class RealType, class Policy> -inline RealType mode(const cauchy_distribution<RealType, Policy>& dist) -{ - return dist.location(); -} - -template <class RealType, class Policy> -inline RealType median(const cauchy_distribution<RealType, Policy>& dist) -{ - return dist.location(); -} -template <class RealType, class Policy> -inline RealType skewness(const cauchy_distribution<RealType, Policy>& /*dist*/) -{ - // There is no skewness: - typedef typename Policy::assert_undefined_type assert_type; - BOOST_STATIC_ASSERT(assert_type::value == 0); - - return policies::raise_domain_error<RealType>( - "boost::math::skewness(cauchy<%1%>&)", - "The Cauchy distribution does not have a skewness: " - "the only possible return value is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity? -} - -template <class RealType, class Policy> -inline RealType kurtosis(const cauchy_distribution<RealType, Policy>& /*dist*/) -{ - // There is no kurtosis: - typedef typename Policy::assert_undefined_type assert_type; - BOOST_STATIC_ASSERT(assert_type::value == 0); - - return policies::raise_domain_error<RealType>( - "boost::math::kurtosis(cauchy<%1%>&)", - "The Cauchy distribution does not have a kurtosis: " - "the only possible return value is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const cauchy_distribution<RealType, Policy>& /*dist*/) -{ - // There is no kurtosis excess: - typedef typename Policy::assert_undefined_type assert_type; - BOOST_STATIC_ASSERT(assert_type::value == 0); - - return policies::raise_domain_error<RealType>( - "boost::math::kurtosis_excess(cauchy<%1%>&)", - "The Cauchy distribution does not have a kurtosis: " - "the only possible return value is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); -} - -} // namespace math -} // namespace boost - -#ifdef _MSC_VER -#pragma warning(pop) -#endif - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_CAUCHY_HPP
--- a/any/include/boost/math/distributions/chi_squared.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,364 +0,0 @@ -// Copyright John Maddock 2006, 2007. -// Copyright Paul A. Bristow 2008, 2010. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP -#define BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/gamma.hpp> // for incomplete beta. -#include <boost/math/distributions/complement.hpp> // complements -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> - -#include <utility> - -namespace boost{ namespace math{ - -template <class RealType = double, class Policy = policies::policy<> > -class chi_squared_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - chi_squared_distribution(RealType i) : m_df(i) - { - RealType result; - detail::check_df( - "boost::math::chi_squared_distribution<%1%>::chi_squared_distribution", m_df, &result, Policy()); - } // chi_squared_distribution - - RealType degrees_of_freedom()const - { - return m_df; - } - - // Parameter estimation: - static RealType find_degrees_of_freedom( - RealType difference_from_variance, - RealType alpha, - RealType beta, - RealType variance, - RealType hint = 100); - -private: - // - // Data member: - // - RealType m_df; // degrees of freedom is a positive real number. -}; // class chi_squared_distribution - -typedef chi_squared_distribution<double> chi_squared; - -#ifdef BOOST_MSVC -#pragma warning(push) -#pragma warning(disable:4127) -#endif - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const chi_squared_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - if (std::numeric_limits<RealType>::has_infinity) - { - return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()); // 0 to + infinity. - } - else - { - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max. - } -} - -#ifdef BOOST_MSVC -#pragma warning(pop) -#endif - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const chi_squared_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity. -} - -template <class RealType, class Policy> -RealType pdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square) -{ - BOOST_MATH_STD_USING // for ADL of std functions - RealType degrees_of_freedom = dist.degrees_of_freedom(); - // Error check: - RealType error_result; - - static const char* function = "boost::math::pdf(const chi_squared_distribution<%1%>&, %1%)"; - - if(false == detail::check_df( - function, degrees_of_freedom, &error_result, Policy())) - return error_result; - - if((chi_square < 0) || !(boost::math::isfinite)(chi_square)) - { - return policies::raise_domain_error<RealType>( - function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy()); - } - - if(chi_square == 0) - { - // Handle special cases: - if(degrees_of_freedom < 2) - { - return policies::raise_overflow_error<RealType>( - function, 0, Policy()); - } - else if(degrees_of_freedom == 2) - { - return 0.5f; - } - else - { - return 0; - } - } - - return gamma_p_derivative(degrees_of_freedom / 2, chi_square / 2, Policy()) / 2; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square) -{ - RealType degrees_of_freedom = dist.degrees_of_freedom(); - // Error check: - RealType error_result; - static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)"; - - if(false == detail::check_df( - function, degrees_of_freedom, &error_result, Policy())) - return error_result; - - if((chi_square < 0) || !(boost::math::isfinite)(chi_square)) - { - return policies::raise_domain_error<RealType>( - function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy()); - } - - return boost::math::gamma_p(degrees_of_freedom / 2, chi_square / 2, Policy()); -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const chi_squared_distribution<RealType, Policy>& dist, const RealType& p) -{ - RealType degrees_of_freedom = dist.degrees_of_freedom(); - static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)"; - // Error check: - RealType error_result; - if(false == - ( - detail::check_df(function, degrees_of_freedom, &error_result, Policy()) - && detail::check_probability(function, p, &error_result, Policy())) - ) - return error_result; - - return 2 * boost::math::gamma_p_inv(degrees_of_freedom / 2, p, Policy()); -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c) -{ - RealType const& degrees_of_freedom = c.dist.degrees_of_freedom(); - RealType const& chi_square = c.param; - static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)"; - // Error check: - RealType error_result; - if(false == detail::check_df( - function, degrees_of_freedom, &error_result, Policy())) - return error_result; - - if((chi_square < 0) || !(boost::math::isfinite)(chi_square)) - { - return policies::raise_domain_error<RealType>( - function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy()); - } - - return boost::math::gamma_q(degrees_of_freedom / 2, chi_square / 2, Policy()); -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c) -{ - RealType const& degrees_of_freedom = c.dist.degrees_of_freedom(); - RealType const& q = c.param; - static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)"; - // Error check: - RealType error_result; - if(false == ( - detail::check_df(function, degrees_of_freedom, &error_result, Policy()) - && detail::check_probability(function, q, &error_result, Policy())) - ) - return error_result; - - return 2 * boost::math::gamma_q_inv(degrees_of_freedom / 2, q, Policy()); -} - -template <class RealType, class Policy> -inline RealType mean(const chi_squared_distribution<RealType, Policy>& dist) -{ // Mean of Chi-Squared distribution = v. - return dist.degrees_of_freedom(); -} // mean - -template <class RealType, class Policy> -inline RealType variance(const chi_squared_distribution<RealType, Policy>& dist) -{ // Variance of Chi-Squared distribution = 2v. - return 2 * dist.degrees_of_freedom(); -} // variance - -template <class RealType, class Policy> -inline RealType mode(const chi_squared_distribution<RealType, Policy>& dist) -{ - RealType df = dist.degrees_of_freedom(); - static const char* function = "boost::math::mode(const chi_squared_distribution<%1%>&)"; - // Most sources only define mode for df >= 2, - // but for 0 <= df <= 2, the pdf maximum actually occurs at random variate = 0; - // So one could extend the definition of mode thus: - //if(df < 0) - //{ - // return policies::raise_domain_error<RealType>( - // function, - // "Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.", - // df, Policy()); - //} - //return (df <= 2) ? 0 : df - 2; - - if(df < 2) - return policies::raise_domain_error<RealType>( - function, - "Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.", - df, Policy()); - return df - 2; -} - -//template <class RealType, class Policy> -//inline RealType median(const chi_squared_distribution<RealType, Policy>& dist) -//{ // Median is given by Quantile[dist, 1/2] -// RealType df = dist.degrees_of_freedom(); -// if(df <= 1) -// return tools::domain_error<RealType>( -// BOOST_CURRENT_FUNCTION, -// "The Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.", -// df); -// return df - RealType(2)/3; -//} -// Now implemented via quantile(half) in derived accessors. - -template <class RealType, class Policy> -inline RealType skewness(const chi_squared_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // For ADL - RealType df = dist.degrees_of_freedom(); - return sqrt (8 / df); // == 2 * sqrt(2 / df); -} - -template <class RealType, class Policy> -inline RealType kurtosis(const chi_squared_distribution<RealType, Policy>& dist) -{ - RealType df = dist.degrees_of_freedom(); - return 3 + 12 / df; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const chi_squared_distribution<RealType, Policy>& dist) -{ - RealType df = dist.degrees_of_freedom(); - return 12 / df; -} - -// -// Parameter estimation comes last: -// -namespace detail -{ - -template <class RealType, class Policy> -struct df_estimator -{ - df_estimator(RealType a, RealType b, RealType variance, RealType delta) - : alpha(a), beta(b), ratio(delta/variance) - { // Constructor - } - - RealType operator()(const RealType& df) - { - if(df <= tools::min_value<RealType>()) - return 1; - chi_squared_distribution<RealType, Policy> cs(df); - - RealType result; - if(ratio > 0) - { - RealType r = 1 + ratio; - result = cdf(cs, quantile(complement(cs, alpha)) / r) - beta; - } - else - { // ratio <= 0 - RealType r = 1 + ratio; - result = cdf(complement(cs, quantile(cs, alpha) / r)) - beta; - } - return result; - } -private: - RealType alpha; - RealType beta; - RealType ratio; // Difference from variance / variance, so fractional. -}; - -} // namespace detail - -template <class RealType, class Policy> -RealType chi_squared_distribution<RealType, Policy>::find_degrees_of_freedom( - RealType difference_from_variance, - RealType alpha, - RealType beta, - RealType variance, - RealType hint) -{ - static const char* function = "boost::math::chi_squared_distribution<%1%>::find_degrees_of_freedom(%1%,%1%,%1%,%1%,%1%)"; - // Check for domain errors: - RealType error_result; - if(false == - detail::check_probability(function, alpha, &error_result, Policy()) - && detail::check_probability(function, beta, &error_result, Policy())) - { // Either probability is outside 0 to 1. - return error_result; - } - - if(hint <= 0) - { // No hint given, so guess df = 1. - hint = 1; - } - - detail::df_estimator<RealType, Policy> f(alpha, beta, variance, difference_from_variance); - tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>()); - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - std::pair<RealType, RealType> r = - tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy()); - RealType result = r.first + (r.second - r.first) / 2; - if(max_iter >= policies::get_max_root_iterations<Policy>()) - { - policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:" - " either there is no answer to how many degrees of freedom are required" - " or the answer is infinite. Current best guess is %1%", result, Policy()); - } - return result; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
--- a/any/include/boost/math/distributions/complement.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,195 +0,0 @@ -// (C) Copyright John Maddock 2006. -// (C) Copyright Paul A. Bristow 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_COMPLEMENT_HPP -#define BOOST_STATS_COMPLEMENT_HPP - -// -// This code really defines our own tuple type. -// It would be nice to reuse boost::math::tuple -// while retaining our own type safety, but it's -// not clear if that's possible. In any case this -// code is *very* lightweight. -// -namespace boost{ namespace math{ - -template <class Dist, class RealType> -struct complemented2_type -{ - complemented2_type( - const Dist& d, - const RealType& p1) - : dist(d), - param(p1) {} - - const Dist& dist; - const RealType& param; - -private: - complemented2_type& operator=(const complemented2_type&); -}; - -template <class Dist, class RealType1, class RealType2> -struct complemented3_type -{ - complemented3_type( - const Dist& d, - const RealType1& p1, - const RealType2& p2) - : dist(d), - param1(p1), - param2(p2) {} - - const Dist& dist; - const RealType1& param1; - const RealType2& param2; -private: - complemented3_type& operator=(const complemented3_type&); -}; - -template <class Dist, class RealType1, class RealType2, class RealType3> -struct complemented4_type -{ - complemented4_type( - const Dist& d, - const RealType1& p1, - const RealType2& p2, - const RealType3& p3) - : dist(d), - param1(p1), - param2(p2), - param3(p3) {} - - const Dist& dist; - const RealType1& param1; - const RealType2& param2; - const RealType3& param3; -private: - complemented4_type& operator=(const complemented4_type&); -}; - -template <class Dist, class RealType1, class RealType2, class RealType3, class RealType4> -struct complemented5_type -{ - complemented5_type( - const Dist& d, - const RealType1& p1, - const RealType2& p2, - const RealType3& p3, - const RealType4& p4) - : dist(d), - param1(p1), - param2(p2), - param3(p3), - param4(p4) {} - - const Dist& dist; - const RealType1& param1; - const RealType2& param2; - const RealType3& param3; - const RealType4& param4; -private: - complemented5_type& operator=(const complemented5_type&); -}; - -template <class Dist, class RealType1, class RealType2, class RealType3, class RealType4, class RealType5> -struct complemented6_type -{ - complemented6_type( - const Dist& d, - const RealType1& p1, - const RealType2& p2, - const RealType3& p3, - const RealType4& p4, - const RealType5& p5) - : dist(d), - param1(p1), - param2(p2), - param3(p3), - param4(p4), - param5(p5) {} - - const Dist& dist; - const RealType1& param1; - const RealType2& param2; - const RealType3& param3; - const RealType4& param4; - const RealType5& param5; -private: - complemented6_type& operator=(const complemented6_type&); -}; - -template <class Dist, class RealType1, class RealType2, class RealType3, class RealType4, class RealType5, class RealType6> -struct complemented7_type -{ - complemented7_type( - const Dist& d, - const RealType1& p1, - const RealType2& p2, - const RealType3& p3, - const RealType4& p4, - const RealType5& p5, - const RealType6& p6) - : dist(d), - param1(p1), - param2(p2), - param3(p3), - param4(p4), - param5(p5), - param6(p6) {} - - const Dist& dist; - const RealType1& param1; - const RealType2& param2; - const RealType3& param3; - const RealType4& param4; - const RealType5& param5; - const RealType6& param6; -private: - complemented7_type& operator=(const complemented7_type&); -}; - -template <class Dist, class RealType> -inline complemented2_type<Dist, RealType> complement(const Dist& d, const RealType& r) -{ - return complemented2_type<Dist, RealType>(d, r); -} - -template <class Dist, class RealType1, class RealType2> -inline complemented3_type<Dist, RealType1, RealType2> complement(const Dist& d, const RealType1& r1, const RealType2& r2) -{ - return complemented3_type<Dist, RealType1, RealType2>(d, r1, r2); -} - -template <class Dist, class RealType1, class RealType2, class RealType3> -inline complemented4_type<Dist, RealType1, RealType2, RealType3> complement(const Dist& d, const RealType1& r1, const RealType2& r2, const RealType3& r3) -{ - return complemented4_type<Dist, RealType1, RealType2, RealType3>(d, r1, r2, r3); -} - -template <class Dist, class RealType1, class RealType2, class RealType3, class RealType4> -inline complemented5_type<Dist, RealType1, RealType2, RealType3, RealType4> complement(const Dist& d, const RealType1& r1, const RealType2& r2, const RealType3& r3, const RealType4& r4) -{ - return complemented5_type<Dist, RealType1, RealType2, RealType3, RealType4>(d, r1, r2, r3, r4); -} - -template <class Dist, class RealType1, class RealType2, class RealType3, class RealType4, class RealType5> -inline complemented6_type<Dist, RealType1, RealType2, RealType3, RealType4, RealType5> complement(const Dist& d, const RealType1& r1, const RealType2& r2, const RealType3& r3, const RealType4& r4, const RealType5& r5) -{ - return complemented6_type<Dist, RealType1, RealType2, RealType3, RealType4, RealType5>(d, r1, r2, r3, r4, r5); -} - -template <class Dist, class RealType1, class RealType2, class RealType3, class RealType4, class RealType5, class RealType6> -inline complemented7_type<Dist, RealType1, RealType2, RealType3, RealType4, RealType5, RealType6> complement(const Dist& d, const RealType1& r1, const RealType2& r2, const RealType3& r3, const RealType4& r4, const RealType5& r5, const RealType6& r6) -{ - return complemented7_type<Dist, RealType1, RealType2, RealType3, RealType4, RealType5, RealType6>(d, r1, r2, r3, r4, r5, r6); -} - -} // namespace math -} // namespace boost - -#endif // BOOST_STATS_COMPLEMENT_HPP -
--- a/any/include/boost/math/distributions/detail/common_error_handling.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,223 +0,0 @@ -// Copyright John Maddock 2006, 2007. -// Copyright Paul A. Bristow 2006, 2007, 2012. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_COMMON_ERROR_HANDLING_HPP -#define BOOST_MATH_DISTRIBUTIONS_COMMON_ERROR_HANDLING_HPP - -#include <boost/math/policies/error_handling.hpp> -#include <boost/math/special_functions/fpclassify.hpp> -// using boost::math::isfinite; -// using boost::math::isnan; - -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable: 4702) // unreachable code (return after domain_error throw). -#endif - -namespace boost{ namespace math{ namespace detail -{ - -template <class RealType, class Policy> -inline bool check_probability(const char* function, RealType const& prob, RealType* result, const Policy& pol) -{ - if((prob < 0) || (prob > 1) || !(boost::math::isfinite)(prob)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Probability argument is %1%, but must be >= 0 and <= 1 !", prob, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_df(const char* function, RealType const& df, RealType* result, const Policy& pol) -{ // df > 0 but NOT +infinity allowed. - if((df <= 0) || !(boost::math::isfinite)(df)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Degrees of freedom argument is %1%, but must be > 0 !", df, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_df_gt0_to_inf(const char* function, RealType const& df, RealType* result, const Policy& pol) -{ // df > 0 or +infinity are allowed. - if( (df <= 0) || (boost::math::isnan)(df) ) - { // is bad df <= 0 or NaN or -infinity. - *result = policies::raise_domain_error<RealType>( - function, - "Degrees of freedom argument is %1%, but must be > 0 !", df, pol); - return false; - } - return true; -} // check_df_gt0_to_inf - - -template <class RealType, class Policy> -inline bool check_scale( - const char* function, - RealType scale, - RealType* result, - const Policy& pol) -{ - if((scale <= 0) || !(boost::math::isfinite)(scale)) - { // Assume scale == 0 is NOT valid for any distribution. - *result = policies::raise_domain_error<RealType>( - function, - "Scale parameter is %1%, but must be > 0 !", scale, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_location( - const char* function, - RealType location, - RealType* result, - const Policy& pol) -{ - if(!(boost::math::isfinite)(location)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Location parameter is %1%, but must be finite!", location, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_x( - const char* function, - RealType x, - RealType* result, - const Policy& pol) -{ - // Note that this test catches both infinity and NaN. - // Some distributions permit x to be infinite, so these must be tested 1st and return, - // leaving this test to catch any NaNs. - // See Normal, Logistic, Laplace and Cauchy for example. - if(!(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate x is %1%, but must be finite!", x, pol); - return false; - } - return true; -} // bool check_x - -template <class RealType, class Policy> -inline bool check_x_not_NaN( - const char* function, - RealType x, - RealType* result, - const Policy& pol) -{ - // Note that this test catches only NaN. - // Some distributions permit x to be infinite, leaving this test to catch any NaNs. - // See Normal, Logistic, Laplace and Cauchy for example. - if ((boost::math::isnan)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate x is %1%, but must be finite or + or - infinity!", x, pol); - return false; - } - return true; -} // bool check_x_not_NaN - -template <class RealType, class Policy> -inline bool check_x_gt0( - const char* function, - RealType x, - RealType* result, - const Policy& pol) -{ - if(x <= 0) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate x is %1%, but must be > 0!", x, pol); - return false; - } - - return true; - // Note that this test catches both infinity and NaN. - // Some special cases permit x to be infinite, so these must be tested 1st, - // leaving this test to catch any NaNs. See Normal and cauchy for example. -} // bool check_x_gt0 - -template <class RealType, class Policy> -inline bool check_positive_x( - const char* function, - RealType x, - RealType* result, - const Policy& pol) -{ - if(!(boost::math::isfinite)(x) || (x < 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate x is %1%, but must be finite and >= 0!", x, pol); - return false; - } - return true; - // Note that this test catches both infinity and NaN. - // Some special cases permit x to be infinite, so these must be tested 1st, - // leaving this test to catch any NaNs. see Normal and cauchy for example. -} - -template <class RealType, class Policy> -inline bool check_non_centrality( - const char* function, - RealType ncp, - RealType* result, - const Policy& pol) -{ - if((ncp < 0) || !(boost::math::isfinite)(ncp)) - { // Assume scale == 0 is NOT valid for any distribution. - *result = policies::raise_domain_error<RealType>( - function, - "Non centrality parameter is %1%, but must be > 0 !", ncp, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_finite( - const char* function, - RealType x, - RealType* result, - const Policy& pol) -{ - if(!(boost::math::isfinite)(x)) - { // Assume scale == 0 is NOT valid for any distribution. - *result = policies::raise_domain_error<RealType>( - function, - "Parameter is %1%, but must be finite !", x, pol); - return false; - } - return true; -} - -} // namespace detail -} // namespace math -} // namespace boost - -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - -#endif // BOOST_MATH_DISTRIBUTIONS_COMMON_ERROR_HANDLING_HPP
--- a/any/include/boost/math/distributions/detail/derived_accessors.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,163 +0,0 @@ -// Copyright John Maddock 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_DERIVED_HPP -#define BOOST_STATS_DERIVED_HPP - -// This file implements various common properties of distributions -// that can be implemented in terms of other properties: -// variance OR standard deviation (see note below), -// hazard, cumulative hazard (chf), coefficient_of_variation. -// -// Note that while both variance and standard_deviation are provided -// here, each distribution MUST SPECIALIZE AT LEAST ONE OF THESE -// otherwise these two versions will just call each other over and over -// until stack space runs out ... - -// Of course there may be more efficient means of implementing these -// that are specific to a particular distribution, but these generic -// versions give these properties "for free" with most distributions. -// -// In order to make use of this header, it must be included AT THE END -// of the distribution header, AFTER the distribution and its core -// property accessors have been defined: this is so that compilers -// that implement 2-phase lookup and early-type-checking of templates -// can find the definitions refered to herein. -// - -#include <boost/type_traits/is_same.hpp> -#include <boost/static_assert.hpp> - -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable: 4723) // potential divide by 0 -// Suppressing spurious warning in coefficient_of_variation -#endif - -namespace boost{ namespace math{ - -template <class Distribution> -typename Distribution::value_type variance(const Distribution& dist); - -template <class Distribution> -inline typename Distribution::value_type standard_deviation(const Distribution& dist) -{ - BOOST_MATH_STD_USING // ADL of sqrt. - return sqrt(variance(dist)); -} - -template <class Distribution> -inline typename Distribution::value_type variance(const Distribution& dist) -{ - typename Distribution::value_type result = standard_deviation(dist); - return result * result; -} - -template <class Distribution, class RealType> -inline typename Distribution::value_type hazard(const Distribution& dist, const RealType& x) -{ // hazard function - // http://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm#HAZ - typedef typename Distribution::value_type value_type; - typedef typename Distribution::policy_type policy_type; - value_type p = cdf(complement(dist, x)); - value_type d = pdf(dist, x); - if(d > p * tools::max_value<value_type>()) - return policies::raise_overflow_error<value_type>( - "boost::math::hazard(const Distribution&, %1%)", 0, policy_type()); - if(d == 0) - { - // This protects against 0/0, but is it the right thing to do? - return 0; - } - return d / p; -} - -template <class Distribution, class RealType> -inline typename Distribution::value_type chf(const Distribution& dist, const RealType& x) -{ // cumulative hazard function. - // http://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm#HAZ - BOOST_MATH_STD_USING - return -log(cdf(complement(dist, x))); -} - -template <class Distribution> -inline typename Distribution::value_type coefficient_of_variation(const Distribution& dist) -{ - typedef typename Distribution::value_type value_type; - typedef typename Distribution::policy_type policy_type; - - using std::abs; - - value_type m = mean(dist); - value_type d = standard_deviation(dist); - if((abs(m) < 1) && (d > abs(m) * tools::max_value<value_type>())) - { // Checks too that m is not zero, - return policies::raise_overflow_error<value_type>("boost::math::coefficient_of_variation(const Distribution&, %1%)", 0, policy_type()); - } - return d / m; // so MSVC warning on zerodivide is spurious, and suppressed. -} -// -// Next follow overloads of some of the standard accessors with mixed -// argument types. We just use a typecast to forward on to the "real" -// implementation with all arguments of the same type: -// -template <class Distribution, class RealType> -inline typename Distribution::value_type pdf(const Distribution& dist, const RealType& x) -{ - typedef typename Distribution::value_type value_type; - return pdf(dist, static_cast<value_type>(x)); -} -template <class Distribution, class RealType> -inline typename Distribution::value_type cdf(const Distribution& dist, const RealType& x) -{ - typedef typename Distribution::value_type value_type; - return cdf(dist, static_cast<value_type>(x)); -} -template <class Distribution, class RealType> -inline typename Distribution::value_type quantile(const Distribution& dist, const RealType& x) -{ - typedef typename Distribution::value_type value_type; - return quantile(dist, static_cast<value_type>(x)); -} -/* -template <class Distribution, class RealType> -inline typename Distribution::value_type chf(const Distribution& dist, const RealType& x) -{ - typedef typename Distribution::value_type value_type; - return chf(dist, static_cast<value_type>(x)); -} -*/ -template <class Distribution, class RealType> -inline typename Distribution::value_type cdf(const complemented2_type<Distribution, RealType>& c) -{ - typedef typename Distribution::value_type value_type; - return cdf(complement(c.dist, static_cast<value_type>(c.param))); -} - -template <class Distribution, class RealType> -inline typename Distribution::value_type quantile(const complemented2_type<Distribution, RealType>& c) -{ - typedef typename Distribution::value_type value_type; - return quantile(complement(c.dist, static_cast<value_type>(c.param))); -} - -template <class Dist> -inline typename Dist::value_type median(const Dist& d) -{ // median - default definition for those distributions for which a - // simple closed form is not known, - // and for which a domain_error and/or NaN generating function is NOT defined. - typedef typename Dist::value_type value_type; - return quantile(d, static_cast<value_type>(0.5f)); -} - -} // namespace math -} // namespace boost - - -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - -#endif // BOOST_STATS_DERIVED_HPP
--- a/any/include/boost/math/distributions/detail/generic_mode.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,149 +0,0 @@ -// Copyright John Maddock 2008. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_MODE_HPP -#define BOOST_MATH_DISTRIBUTIONS_DETAIL_MODE_HPP - -#include <boost/math/tools/minima.hpp> // function minimization for mode -#include <boost/math/policies/error_handling.hpp> -#include <boost/math/distributions/fwd.hpp> - -namespace boost{ namespace math{ namespace detail{ - -template <class Dist> -struct pdf_minimizer -{ - pdf_minimizer(const Dist& d) - : dist(d) {} - - typename Dist::value_type operator()(const typename Dist::value_type& x) - { - return -pdf(dist, x); - } -private: - Dist dist; -}; - -template <class Dist> -typename Dist::value_type generic_find_mode(const Dist& dist, typename Dist::value_type guess, const char* function, typename Dist::value_type step = 0) -{ - BOOST_MATH_STD_USING - typedef typename Dist::value_type value_type; - typedef typename Dist::policy_type policy_type; - // - // Need to begin by bracketing the maxima of the PDF: - // - value_type maxval; - value_type upper_bound = guess; - value_type lower_bound; - value_type v = pdf(dist, guess); - if(v == 0) - { - // - // Oops we don't know how to handle this, or even in which - // direction we should move in, treat as an evaluation error: - // - return policies::raise_evaluation_error( - function, - "Could not locate a starting location for the search for the mode, original guess was %1%", guess, policy_type()); - } - do - { - maxval = v; - if(step != 0) - upper_bound += step; - else - upper_bound *= 2; - v = pdf(dist, upper_bound); - }while(maxval < v); - - lower_bound = upper_bound; - do - { - maxval = v; - if(step != 0) - lower_bound -= step; - else - lower_bound /= 2; - v = pdf(dist, lower_bound); - }while(maxval < v); - - boost::uintmax_t max_iter = policies::get_max_root_iterations<policy_type>(); - - value_type result = tools::brent_find_minima( - pdf_minimizer<Dist>(dist), - lower_bound, - upper_bound, - policies::digits<value_type, policy_type>(), - max_iter).first; - if(max_iter >= policies::get_max_root_iterations<policy_type>()) - { - return policies::raise_evaluation_error<value_type>( - function, - "Unable to locate solution in a reasonable time:" - " either there is no answer to the mode of the distribution" - " or the answer is infinite. Current best guess is %1%", result, policy_type()); - } - return result; -} -// -// As above,but confined to the interval [0,1]: -// -template <class Dist> -typename Dist::value_type generic_find_mode_01(const Dist& dist, typename Dist::value_type guess, const char* function) -{ - BOOST_MATH_STD_USING - typedef typename Dist::value_type value_type; - typedef typename Dist::policy_type policy_type; - // - // Need to begin by bracketing the maxima of the PDF: - // - value_type maxval; - value_type upper_bound = guess; - value_type lower_bound; - value_type v = pdf(dist, guess); - do - { - maxval = v; - upper_bound = 1 - (1 - upper_bound) / 2; - if(upper_bound == 1) - return 1; - v = pdf(dist, upper_bound); - }while(maxval < v); - - lower_bound = upper_bound; - do - { - maxval = v; - lower_bound /= 2; - if(lower_bound < tools::min_value<value_type>()) - return 0; - v = pdf(dist, lower_bound); - }while(maxval < v); - - boost::uintmax_t max_iter = policies::get_max_root_iterations<policy_type>(); - - value_type result = tools::brent_find_minima( - pdf_minimizer<Dist>(dist), - lower_bound, - upper_bound, - policies::digits<value_type, policy_type>(), - max_iter).first; - if(max_iter >= policies::get_max_root_iterations<policy_type>()) - { - return policies::raise_evaluation_error<value_type>( - function, - "Unable to locate solution in a reasonable time:" - " either there is no answer to the mode of the distribution" - " or the answer is infinite. Current best guess is %1%", result, policy_type()); - } - return result; -} - -}}} // namespaces - -#endif // BOOST_MATH_DISTRIBUTIONS_DETAIL_MODE_HPP
--- a/any/include/boost/math/distributions/detail/generic_quantile.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,91 +0,0 @@ -// Copyright John Maddock 2008. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTIBUTIONS_DETAIL_GENERIC_QUANTILE_HPP -#define BOOST_MATH_DISTIBUTIONS_DETAIL_GENERIC_QUANTILE_HPP - -namespace boost{ namespace math{ namespace detail{ - -template <class Dist> -struct generic_quantile_finder -{ - typedef typename Dist::value_type value_type; - typedef typename Dist::policy_type policy_type; - - generic_quantile_finder(const Dist& d, value_type t, bool c) - : dist(d), target(t), comp(c) {} - - value_type operator()(const value_type& x) - { - return comp ? - value_type(target - cdf(complement(dist, x))) - : value_type(cdf(dist, x) - target); - } - -private: - Dist dist; - value_type target; - bool comp; -}; - -template <class T, class Policy> -inline T check_range_result(const T& x, const Policy& pol, const char* function) -{ - if((x >= 0) && (x < tools::min_value<T>())) - return policies::raise_underflow_error<T>(function, 0, pol); - if(x <= -tools::max_value<T>()) - return -policies::raise_overflow_error<T>(function, 0, pol); - if(x >= tools::max_value<T>()) - return policies::raise_overflow_error<T>(function, 0, pol); - return x; -} - -template <class Dist> -typename Dist::value_type generic_quantile(const Dist& dist, const typename Dist::value_type& p, const typename Dist::value_type& guess, bool comp, const char* function) -{ - typedef typename Dist::value_type value_type; - typedef typename Dist::policy_type policy_type; - typedef typename policies::normalise< - policy_type, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - // - // Special cases first: - // - if(p == 0) - { - return comp - ? check_range_result(range(dist).second, forwarding_policy(), function) - : check_range_result(range(dist).first, forwarding_policy(), function); - } - if(p == 1) - { - return !comp - ? check_range_result(range(dist).second, forwarding_policy(), function) - : check_range_result(range(dist).first, forwarding_policy(), function); - } - - generic_quantile_finder<Dist> f(dist, p, comp); - tools::eps_tolerance<value_type> tol(policies::digits<value_type, forwarding_policy>() - 3); - boost::uintmax_t max_iter = policies::get_max_root_iterations<forwarding_policy>(); - std::pair<value_type, value_type> ir = tools::bracket_and_solve_root( - f, guess, value_type(2), true, tol, max_iter, forwarding_policy()); - value_type result = ir.first + (ir.second - ir.first) / 2; - if(max_iter >= policies::get_max_root_iterations<forwarding_policy>()) - { - return policies::raise_evaluation_error<value_type>(function, "Unable to locate solution in a reasonable time:" - " either there is no answer to quantile" - " or the answer is infinite. Current best guess is %1%", result, forwarding_policy()); - } - return result; -} - -}}} // namespaces - -#endif // BOOST_MATH_DISTIBUTIONS_DETAIL_GENERIC_QUANTILE_HPP -
--- a/any/include/boost/math/distributions/detail/hypergeometric_cdf.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,100 +0,0 @@ -// Copyright 2008 John Maddock -// -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_CDF_HPP -#define BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_CDF_HPP - -#include <boost/math/policies/error_handling.hpp> -#include <boost/math/distributions/detail/hypergeometric_pdf.hpp> - -namespace boost{ namespace math{ namespace detail{ - - template <class T, class Policy> - T hypergeometric_cdf_imp(unsigned x, unsigned r, unsigned n, unsigned N, bool invert, const Policy& pol) - { -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable:4267) -#endif - BOOST_MATH_STD_USING - T result = 0; - T mode = floor(T(r + 1) * T(n + 1) / (N + 2)); - if(x < mode) - { - result = hypergeometric_pdf<T>(x, r, n, N, pol); - T diff = result; - unsigned lower_limit = static_cast<unsigned>((std::max)(0, (int)(n + r) - (int)(N))); - while(diff > (invert ? T(1) : result) * tools::epsilon<T>()) - { - diff = T(x) * T((N + x) - n - r) * diff / (T(1 + n - x) * T(1 + r - x)); - result += diff; - BOOST_MATH_INSTRUMENT_VARIABLE(x); - BOOST_MATH_INSTRUMENT_VARIABLE(diff); - BOOST_MATH_INSTRUMENT_VARIABLE(result); - if(x == lower_limit) - break; - --x; - } - } - else - { - invert = !invert; - unsigned upper_limit = (std::min)(r, n); - if(x != upper_limit) - { - ++x; - result = hypergeometric_pdf<T>(x, r, n, N, pol); - T diff = result; - while((x <= upper_limit) && (diff > (invert ? T(1) : result) * tools::epsilon<T>())) - { - diff = T(n - x) * T(r - x) * diff / (T(x + 1) * T((N + x + 1) - n - r)); - result += diff; - ++x; - BOOST_MATH_INSTRUMENT_VARIABLE(x); - BOOST_MATH_INSTRUMENT_VARIABLE(diff); - BOOST_MATH_INSTRUMENT_VARIABLE(result); - } - } - } - if(invert) - result = 1 - result; - return result; -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - } - - template <class T, class Policy> - inline T hypergeometric_cdf(unsigned x, unsigned r, unsigned n, unsigned N, bool invert, const Policy&) - { - BOOST_FPU_EXCEPTION_GUARD - typedef typename tools::promote_args<T>::type result_type; - typedef typename policies::evaluation<result_type, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - value_type result; - result = detail::hypergeometric_cdf_imp<value_type>(x, r, n, N, invert, forwarding_policy()); - if(result > 1) - { - result = 1; - } - if(result < 0) - { - result = 0; - } - return policies::checked_narrowing_cast<result_type, forwarding_policy>(result, "boost::math::hypergeometric_cdf<%1%>(%1%,%1%,%1%,%1%)"); - } - -}}} // namespaces - -#endif -
--- a/any/include/boost/math/distributions/detail/hypergeometric_pdf.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,488 +0,0 @@ -// Copyright 2008 Gautam Sewani -// Copyright 2008 John Maddock -// -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_PDF_HPP -#define BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_PDF_HPP - -#include <boost/math/constants/constants.hpp> -#include <boost/math/special_functions/lanczos.hpp> -#include <boost/math/special_functions/gamma.hpp> -#include <boost/math/special_functions/pow.hpp> -#include <boost/math/special_functions/prime.hpp> -#include <boost/math/policies/error_handling.hpp> - -#ifdef BOOST_MATH_INSTRUMENT -#include <typeinfo> -#endif - -namespace boost{ namespace math{ namespace detail{ - -template <class T, class Func> -void bubble_down_one(T* first, T* last, Func f) -{ - using std::swap; - T* next = first; - ++next; - while((next != last) && (!f(*first, *next))) - { - swap(*first, *next); - ++first; - ++next; - } -} - -template <class T> -struct sort_functor -{ - sort_functor(const T* exponents) : m_exponents(exponents){} - bool operator()(int i, int j) - { - return m_exponents[i] > m_exponents[j]; - } -private: - const T* m_exponents; -}; - -template <class T, class Lanczos, class Policy> -T hypergeometric_pdf_lanczos_imp(T /*dummy*/, unsigned x, unsigned r, unsigned n, unsigned N, const Lanczos&, const Policy&) -{ - BOOST_MATH_STD_USING - - BOOST_MATH_INSTRUMENT_FPU - BOOST_MATH_INSTRUMENT_VARIABLE(x); - BOOST_MATH_INSTRUMENT_VARIABLE(r); - BOOST_MATH_INSTRUMENT_VARIABLE(n); - BOOST_MATH_INSTRUMENT_VARIABLE(N); - BOOST_MATH_INSTRUMENT_VARIABLE(typeid(Lanczos).name()); - - T bases[9] = { - T(n) + static_cast<T>(Lanczos::g()) + 0.5f, - T(r) + static_cast<T>(Lanczos::g()) + 0.5f, - T(N - n) + static_cast<T>(Lanczos::g()) + 0.5f, - T(N - r) + static_cast<T>(Lanczos::g()) + 0.5f, - 1 / (T(N) + static_cast<T>(Lanczos::g()) + 0.5f), - 1 / (T(x) + static_cast<T>(Lanczos::g()) + 0.5f), - 1 / (T(n - x) + static_cast<T>(Lanczos::g()) + 0.5f), - 1 / (T(r - x) + static_cast<T>(Lanczos::g()) + 0.5f), - 1 / (T(N - n - r + x) + static_cast<T>(Lanczos::g()) + 0.5f) - }; - T exponents[9] = { - n + T(0.5f), - r + T(0.5f), - N - n + T(0.5f), - N - r + T(0.5f), - N + T(0.5f), - x + T(0.5f), - n - x + T(0.5f), - r - x + T(0.5f), - N - n - r + x + T(0.5f) - }; - int base_e_factors[9] = { - -1, -1, -1, -1, 1, 1, 1, 1, 1 - }; - int sorted_indexes[9] = { - 0, 1, 2, 3, 4, 5, 6, 7, 8 - }; -#ifdef BOOST_MATH_INSTRUMENT - BOOST_MATH_INSTRUMENT_FPU - for(unsigned i = 0; i < 9; ++i) - { - BOOST_MATH_INSTRUMENT_VARIABLE(i); - BOOST_MATH_INSTRUMENT_VARIABLE(bases[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(exponents[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(base_e_factors[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(sorted_indexes[i]); - } -#endif - std::sort(sorted_indexes, sorted_indexes + 9, sort_functor<T>(exponents)); -#ifdef BOOST_MATH_INSTRUMENT - BOOST_MATH_INSTRUMENT_FPU - for(unsigned i = 0; i < 9; ++i) - { - BOOST_MATH_INSTRUMENT_VARIABLE(i); - BOOST_MATH_INSTRUMENT_VARIABLE(bases[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(exponents[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(base_e_factors[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(sorted_indexes[i]); - } -#endif - - do{ - exponents[sorted_indexes[0]] -= exponents[sorted_indexes[1]]; - bases[sorted_indexes[1]] *= bases[sorted_indexes[0]]; - if((bases[sorted_indexes[1]] < tools::min_value<T>()) && (exponents[sorted_indexes[1]] != 0)) - { - return 0; - } - base_e_factors[sorted_indexes[1]] += base_e_factors[sorted_indexes[0]]; - bubble_down_one(sorted_indexes, sorted_indexes + 9, sort_functor<T>(exponents)); - -#ifdef BOOST_MATH_INSTRUMENT - for(unsigned i = 0; i < 9; ++i) - { - BOOST_MATH_INSTRUMENT_VARIABLE(i); - BOOST_MATH_INSTRUMENT_VARIABLE(bases[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(exponents[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(base_e_factors[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(sorted_indexes[i]); - } -#endif - }while(exponents[sorted_indexes[1]] > 1); - - // - // Combine equal powers: - // - int j = 8; - while(exponents[sorted_indexes[j]] == 0) --j; - while(j) - { - while(j && (exponents[sorted_indexes[j-1]] == exponents[sorted_indexes[j]])) - { - bases[sorted_indexes[j-1]] *= bases[sorted_indexes[j]]; - exponents[sorted_indexes[j]] = 0; - base_e_factors[sorted_indexes[j-1]] += base_e_factors[sorted_indexes[j]]; - bubble_down_one(sorted_indexes + j, sorted_indexes + 9, sort_functor<T>(exponents)); - --j; - } - --j; - -#ifdef BOOST_MATH_INSTRUMENT - BOOST_MATH_INSTRUMENT_VARIABLE(j); - for(unsigned i = 0; i < 9; ++i) - { - BOOST_MATH_INSTRUMENT_VARIABLE(i); - BOOST_MATH_INSTRUMENT_VARIABLE(bases[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(exponents[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(base_e_factors[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(sorted_indexes[i]); - } -#endif - } - -#ifdef BOOST_MATH_INSTRUMENT - BOOST_MATH_INSTRUMENT_FPU - for(unsigned i = 0; i < 9; ++i) - { - BOOST_MATH_INSTRUMENT_VARIABLE(i); - BOOST_MATH_INSTRUMENT_VARIABLE(bases[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(exponents[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(base_e_factors[i]); - BOOST_MATH_INSTRUMENT_VARIABLE(sorted_indexes[i]); - } -#endif - - T result; - BOOST_MATH_INSTRUMENT_VARIABLE(bases[sorted_indexes[0]] * exp(static_cast<T>(base_e_factors[sorted_indexes[0]]))); - BOOST_MATH_INSTRUMENT_VARIABLE(exponents[sorted_indexes[0]]); - { - BOOST_FPU_EXCEPTION_GUARD - result = pow(bases[sorted_indexes[0]] * exp(static_cast<T>(base_e_factors[sorted_indexes[0]])), exponents[sorted_indexes[0]]); - } - BOOST_MATH_INSTRUMENT_VARIABLE(result); - for(unsigned i = 1; (i < 9) && (exponents[sorted_indexes[i]] > 0); ++i) - { - BOOST_FPU_EXCEPTION_GUARD - if(result < tools::min_value<T>()) - return 0; // short circuit further evaluation - if(exponents[sorted_indexes[i]] == 1) - result *= bases[sorted_indexes[i]] * exp(static_cast<T>(base_e_factors[sorted_indexes[i]])); - else if(exponents[sorted_indexes[i]] == 0.5f) - result *= sqrt(bases[sorted_indexes[i]] * exp(static_cast<T>(base_e_factors[sorted_indexes[i]]))); - else - result *= pow(bases[sorted_indexes[i]] * exp(static_cast<T>(base_e_factors[sorted_indexes[i]])), exponents[sorted_indexes[i]]); - - BOOST_MATH_INSTRUMENT_VARIABLE(result); - } - - result *= Lanczos::lanczos_sum_expG_scaled(static_cast<T>(n + 1)) - * Lanczos::lanczos_sum_expG_scaled(static_cast<T>(r + 1)) - * Lanczos::lanczos_sum_expG_scaled(static_cast<T>(N - n + 1)) - * Lanczos::lanczos_sum_expG_scaled(static_cast<T>(N - r + 1)) - / - ( Lanczos::lanczos_sum_expG_scaled(static_cast<T>(N + 1)) - * Lanczos::lanczos_sum_expG_scaled(static_cast<T>(x + 1)) - * Lanczos::lanczos_sum_expG_scaled(static_cast<T>(n - x + 1)) - * Lanczos::lanczos_sum_expG_scaled(static_cast<T>(r - x + 1)) - * Lanczos::lanczos_sum_expG_scaled(static_cast<T>(N - n - r + x + 1))); - - BOOST_MATH_INSTRUMENT_VARIABLE(result); - return result; -} - -template <class T, class Policy> -T hypergeometric_pdf_lanczos_imp(T /*dummy*/, unsigned x, unsigned r, unsigned n, unsigned N, const boost::math::lanczos::undefined_lanczos&, const Policy& pol) -{ - BOOST_MATH_STD_USING - return exp( - boost::math::lgamma(T(n + 1), pol) - + boost::math::lgamma(T(r + 1), pol) - + boost::math::lgamma(T(N - n + 1), pol) - + boost::math::lgamma(T(N - r + 1), pol) - - boost::math::lgamma(T(N + 1), pol) - - boost::math::lgamma(T(x + 1), pol) - - boost::math::lgamma(T(n - x + 1), pol) - - boost::math::lgamma(T(r - x + 1), pol) - - boost::math::lgamma(T(N - n - r + x + 1), pol)); -} - -template <class T> -inline T integer_power(const T& x, int ex) -{ - if(ex < 0) - return 1 / integer_power(x, -ex); - switch(ex) - { - case 0: - return 1; - case 1: - return x; - case 2: - return x * x; - case 3: - return x * x * x; - case 4: - return boost::math::pow<4>(x); - case 5: - return boost::math::pow<5>(x); - case 6: - return boost::math::pow<6>(x); - case 7: - return boost::math::pow<7>(x); - case 8: - return boost::math::pow<8>(x); - } - BOOST_MATH_STD_USING -#ifdef __SUNPRO_CC - return pow(x, T(ex)); -#else - return pow(x, ex); -#endif -} -template <class T> -struct hypergeometric_pdf_prime_loop_result_entry -{ - T value; - const hypergeometric_pdf_prime_loop_result_entry* next; -}; - -#ifdef BOOST_MSVC -#pragma warning(push) -#pragma warning(disable:4510 4512 4610) -#endif - -struct hypergeometric_pdf_prime_loop_data -{ - const unsigned x; - const unsigned r; - const unsigned n; - const unsigned N; - unsigned prime_index; - unsigned current_prime; -}; - -#ifdef BOOST_MSVC -#pragma warning(pop) -#endif - -template <class T> -T hypergeometric_pdf_prime_loop_imp(hypergeometric_pdf_prime_loop_data& data, hypergeometric_pdf_prime_loop_result_entry<T>& result) -{ - while(data.current_prime <= data.N) - { - unsigned base = data.current_prime; - int prime_powers = 0; - while(base <= data.N) - { - prime_powers += data.n / base; - prime_powers += data.r / base; - prime_powers += (data.N - data.n) / base; - prime_powers += (data.N - data.r) / base; - prime_powers -= data.N / base; - prime_powers -= data.x / base; - prime_powers -= (data.n - data.x) / base; - prime_powers -= (data.r - data.x) / base; - prime_powers -= (data.N - data.n - data.r + data.x) / base; - base *= data.current_prime; - } - if(prime_powers) - { - T p = integer_power<T>(static_cast<T>(data.current_prime), prime_powers); - if((p > 1) && (tools::max_value<T>() / p < result.value)) - { - // - // The next calculation would overflow, use recursion - // to sidestep the issue: - // - hypergeometric_pdf_prime_loop_result_entry<T> t = { p, &result }; - data.current_prime = prime(++data.prime_index); - return hypergeometric_pdf_prime_loop_imp<T>(data, t); - } - if((p < 1) && (tools::min_value<T>() / p > result.value)) - { - // - // The next calculation would underflow, use recursion - // to sidestep the issue: - // - hypergeometric_pdf_prime_loop_result_entry<T> t = { p, &result }; - data.current_prime = prime(++data.prime_index); - return hypergeometric_pdf_prime_loop_imp<T>(data, t); - } - result.value *= p; - } - data.current_prime = prime(++data.prime_index); - } - // - // When we get to here we have run out of prime factors, - // the overall result is the product of all the partial - // results we have accumulated on the stack so far, these - // are in a linked list starting with "data.head" and ending - // with "result". - // - // All that remains is to multiply them together, taking - // care not to overflow or underflow. - // - // Enumerate partial results >= 1 in variable i - // and partial results < 1 in variable j: - // - hypergeometric_pdf_prime_loop_result_entry<T> const *i, *j; - i = &result; - while(i && i->value < 1) - i = i->next; - j = &result; - while(j && j->value >= 1) - j = j->next; - - T prod = 1; - - while(i || j) - { - while(i && ((prod <= 1) || (j == 0))) - { - prod *= i->value; - i = i->next; - while(i && i->value < 1) - i = i->next; - } - while(j && ((prod >= 1) || (i == 0))) - { - prod *= j->value; - j = j->next; - while(j && j->value >= 1) - j = j->next; - } - } - - return prod; -} - -template <class T, class Policy> -inline T hypergeometric_pdf_prime_imp(unsigned x, unsigned r, unsigned n, unsigned N, const Policy&) -{ - hypergeometric_pdf_prime_loop_result_entry<T> result = { 1, 0 }; - hypergeometric_pdf_prime_loop_data data = { x, r, n, N, 0, prime(0) }; - return hypergeometric_pdf_prime_loop_imp<T>(data, result); -} - -template <class T, class Policy> -T hypergeometric_pdf_factorial_imp(unsigned x, unsigned r, unsigned n, unsigned N, const Policy&) -{ - BOOST_MATH_STD_USING - BOOST_ASSERT(N <= boost::math::max_factorial<T>::value); - T result = boost::math::unchecked_factorial<T>(n); - T num[3] = { - boost::math::unchecked_factorial<T>(r), - boost::math::unchecked_factorial<T>(N - n), - boost::math::unchecked_factorial<T>(N - r) - }; - T denom[5] = { - boost::math::unchecked_factorial<T>(N), - boost::math::unchecked_factorial<T>(x), - boost::math::unchecked_factorial<T>(n - x), - boost::math::unchecked_factorial<T>(r - x), - boost::math::unchecked_factorial<T>(N - n - r + x) - }; - int i = 0; - int j = 0; - while((i < 3) || (j < 5)) - { - while((j < 5) && ((result >= 1) || (i >= 3))) - { - result /= denom[j]; - ++j; - } - while((i < 3) && ((result <= 1) || (j >= 5))) - { - result *= num[i]; - ++i; - } - } - return result; -} - - -template <class T, class Policy> -inline typename tools::promote_args<T>::type - hypergeometric_pdf(unsigned x, unsigned r, unsigned n, unsigned N, const Policy&) -{ - BOOST_FPU_EXCEPTION_GUARD - typedef typename tools::promote_args<T>::type result_type; - typedef typename policies::evaluation<result_type, Policy>::type value_type; - typedef typename lanczos::lanczos<value_type, Policy>::type evaluation_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - value_type result; - if(N <= boost::math::max_factorial<value_type>::value) - { - // - // If N is small enough then we can evaluate the PDF via the factorials - // directly: table lookup of the factorials gives the best performance - // of the methods available: - // - result = detail::hypergeometric_pdf_factorial_imp<value_type>(x, r, n, N, forwarding_policy()); - } - else if(N <= boost::math::prime(boost::math::max_prime - 1)) - { - // - // If N is no larger than the largest prime number in our lookup table - // (104729) then we can use prime factorisation to evaluate the PDF, - // this is slow but accurate: - // - result = detail::hypergeometric_pdf_prime_imp<value_type>(x, r, n, N, forwarding_policy()); - } - else - { - // - // Catch all case - use the lanczos approximation - where available - - // to evaluate the ratio of factorials. This is reasonably fast - // (almost as quick as using logarithmic evaluation in terms of lgamma) - // but only a few digits better in accuracy than using lgamma: - // - result = detail::hypergeometric_pdf_lanczos_imp(value_type(), x, r, n, N, evaluation_type(), forwarding_policy()); - } - - if(result > 1) - { - result = 1; - } - if(result < 0) - { - result = 0; - } - - return policies::checked_narrowing_cast<result_type, forwarding_policy>(result, "boost::math::hypergeometric_pdf<%1%>(%1%,%1%,%1%,%1%)"); -} - -}}} // namespaces - -#endif -
--- a/any/include/boost/math/distributions/detail/hypergeometric_quantile.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,245 +0,0 @@ -// Copyright 2008 John Maddock -// -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_QUANTILE_HPP -#define BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_QUANTILE_HPP - -#include <boost/math/policies/error_handling.hpp> -#include <boost/math/distributions/detail/hypergeometric_pdf.hpp> - -namespace boost{ namespace math{ namespace detail{ - -template <class T> -inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&) -{ - if((p < cum * fudge_factor) && (x != lbound)) - { - BOOST_MATH_INSTRUMENT_VARIABLE(x-1); - return --x; - } - return x; -} - -template <class T> -inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned /*lbound*/, unsigned ubound, const policies::discrete_quantile<policies::integer_round_up>&) -{ - if((cum < p * fudge_factor) && (x != ubound)) - { - BOOST_MATH_INSTRUMENT_VARIABLE(x+1); - return ++x; - } - return x; -} - -template <class T> -inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_inwards>&) -{ - if(p >= 0.5) - return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>()); - return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>()); -} - -template <class T> -inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_outwards>&) -{ - if(p >= 0.5) - return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>()); - return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>()); -} - -template <class T> -inline unsigned round_x_from_p(unsigned x, T /*p*/, T /*cum*/, T /*fudge_factor*/, unsigned /*lbound*/, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&) -{ - return x; -} - -template <class T> -inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&) -{ - if((q * fudge_factor > cum) && (x != lbound)) - { - BOOST_MATH_INSTRUMENT_VARIABLE(x-1); - return --x; - } - return x; -} - -template <class T> -inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned /*lbound*/, unsigned ubound, const policies::discrete_quantile<policies::integer_round_up>&) -{ - if((q < cum * fudge_factor) && (x != ubound)) - { - BOOST_MATH_INSTRUMENT_VARIABLE(x+1); - return ++x; - } - return x; -} - -template <class T> -inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_inwards>&) -{ - if(q < 0.5) - return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>()); - return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>()); -} - -template <class T> -inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_outwards>&) -{ - if(q >= 0.5) - return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>()); - return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>()); -} - -template <class T> -inline unsigned round_x_from_q(unsigned x, T /*q*/, T /*cum*/, T /*fudge_factor*/, unsigned /*lbound*/, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&) -{ - return x; -} - -template <class T, class Policy> -unsigned hypergeometric_quantile_imp(T p, T q, unsigned r, unsigned n, unsigned N, const Policy& pol) -{ -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable:4267) -#endif - typedef typename Policy::discrete_quantile_type discrete_quantile_type; - BOOST_MATH_STD_USING - BOOST_FPU_EXCEPTION_GUARD - T result; - T fudge_factor = 1 + tools::epsilon<T>() * ((N <= boost::math::prime(boost::math::max_prime - 1)) ? 50 : 2 * N); - unsigned base = static_cast<unsigned>((std::max)(0, (int)(n + r) - (int)(N))); - unsigned lim = (std::min)(r, n); - - BOOST_MATH_INSTRUMENT_VARIABLE(p); - BOOST_MATH_INSTRUMENT_VARIABLE(q); - BOOST_MATH_INSTRUMENT_VARIABLE(r); - BOOST_MATH_INSTRUMENT_VARIABLE(n); - BOOST_MATH_INSTRUMENT_VARIABLE(N); - BOOST_MATH_INSTRUMENT_VARIABLE(fudge_factor); - BOOST_MATH_INSTRUMENT_VARIABLE(base); - BOOST_MATH_INSTRUMENT_VARIABLE(lim); - - if(p <= 0.5) - { - unsigned x = base; - result = hypergeometric_pdf<T>(x, r, n, N, pol); - T diff = result; - if (diff == 0) - { - ++x; - // We want to skip through x values as fast as we can until we start getting non-zero values, - // otherwise we're just making lots of expensive PDF calls: - T log_pdf = boost::math::lgamma(static_cast<T>(n + 1), pol) - + boost::math::lgamma(static_cast<T>(r + 1), pol) - + boost::math::lgamma(static_cast<T>(N - n + 1), pol) - + boost::math::lgamma(static_cast<T>(N - r + 1), pol) - - boost::math::lgamma(static_cast<T>(N + 1), pol) - - boost::math::lgamma(static_cast<T>(x + 1), pol) - - boost::math::lgamma(static_cast<T>(n - x + 1), pol) - - boost::math::lgamma(static_cast<T>(r - x + 1), pol) - - boost::math::lgamma(static_cast<T>(N - n - r + x + 1), pol); - while (log_pdf < tools::log_min_value<T>()) - { - log_pdf += -log(static_cast<T>(x + 1)) + log(static_cast<T>(n - x)) + log(static_cast<T>(r - x)) - log(static_cast<T>(N - n - r + x + 1)); - ++x; - } - // By the time we get here, log_pdf may be fairly inaccurate due to - // roundoff errors, get a fresh PDF calculation before proceding: - diff = hypergeometric_pdf<T>(x, r, n, N, pol); - } - while(result < p) - { - diff = (diff > tools::min_value<T>() * 8) - ? T(n - x) * T(r - x) * diff / (T(x + 1) * T(N + x + 1 - n - r)) - : hypergeometric_pdf<T>(x + 1, r, n, N, pol); - if(result + diff / 2 > p) - break; - ++x; - result += diff; -#ifdef BOOST_MATH_INSTRUMENT - if(diff != 0) - { - BOOST_MATH_INSTRUMENT_VARIABLE(x); - BOOST_MATH_INSTRUMENT_VARIABLE(diff); - BOOST_MATH_INSTRUMENT_VARIABLE(result); - } -#endif - } - return round_x_from_p(x, p, result, fudge_factor, base, lim, discrete_quantile_type()); - } - else - { - unsigned x = lim; - result = 0; - T diff = hypergeometric_pdf<T>(x, r, n, N, pol); - if (diff == 0) - { - // We want to skip through x values as fast as we can until we start getting non-zero values, - // otherwise we're just making lots of expensive PDF calls: - --x; - T log_pdf = boost::math::lgamma(static_cast<T>(n + 1), pol) - + boost::math::lgamma(static_cast<T>(r + 1), pol) - + boost::math::lgamma(static_cast<T>(N - n + 1), pol) - + boost::math::lgamma(static_cast<T>(N - r + 1), pol) - - boost::math::lgamma(static_cast<T>(N + 1), pol) - - boost::math::lgamma(static_cast<T>(x + 1), pol) - - boost::math::lgamma(static_cast<T>(n - x + 1), pol) - - boost::math::lgamma(static_cast<T>(r - x + 1), pol) - - boost::math::lgamma(static_cast<T>(N - n - r + x + 1), pol); - while (log_pdf < tools::log_min_value<T>()) - { - log_pdf += log(static_cast<T>(x)) - log(static_cast<T>(n - x + 1)) - log(static_cast<T>(r - x + 1)) + log(static_cast<T>(N - n - r + x)); - --x; - } - // By the time we get here, log_pdf may be fairly inaccurate due to - // roundoff errors, get a fresh PDF calculation before proceding: - diff = hypergeometric_pdf<T>(x, r, n, N, pol); - } - while(result + diff / 2 < q) - { - result += diff; - diff = (diff > tools::min_value<T>() * 8) - ? x * T(N + x - n - r) * diff / (T(1 + n - x) * T(1 + r - x)) - : hypergeometric_pdf<T>(x - 1, r, n, N, pol); - --x; -#ifdef BOOST_MATH_INSTRUMENT - if(diff != 0) - { - BOOST_MATH_INSTRUMENT_VARIABLE(x); - BOOST_MATH_INSTRUMENT_VARIABLE(diff); - BOOST_MATH_INSTRUMENT_VARIABLE(result); - } -#endif - } - return round_x_from_q(x, q, result, fudge_factor, base, lim, discrete_quantile_type()); - } -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif -} - -template <class T, class Policy> -inline unsigned hypergeometric_quantile(T p, T q, unsigned r, unsigned n, unsigned N, const Policy&) -{ - BOOST_FPU_EXCEPTION_GUARD - typedef typename tools::promote_args<T>::type result_type; - typedef typename policies::evaluation<result_type, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::assert_undefined<> >::type forwarding_policy; - - return detail::hypergeometric_quantile_imp<value_type>(p, q, r, n, N, forwarding_policy()); -} - -}}} // namespaces - -#endif -
--- a/any/include/boost/math/distributions/detail/inv_discrete_quantile.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,571 +0,0 @@ -// Copyright John Maddock 2007. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_INV_DISCRETE_QUANTILE -#define BOOST_MATH_DISTRIBUTIONS_DETAIL_INV_DISCRETE_QUANTILE - -#include <algorithm> - -namespace boost{ namespace math{ namespace detail{ - -// -// Functor for root finding algorithm: -// -template <class Dist> -struct distribution_quantile_finder -{ - typedef typename Dist::value_type value_type; - typedef typename Dist::policy_type policy_type; - - distribution_quantile_finder(const Dist d, value_type p, bool c) - : dist(d), target(p), comp(c) {} - - value_type operator()(value_type const& x) - { - return comp ? value_type(target - cdf(complement(dist, x))) : value_type(cdf(dist, x) - target); - } - -private: - Dist dist; - value_type target; - bool comp; -}; -// -// The purpose of adjust_bounds, is to toggle the last bit of the -// range so that both ends round to the same integer, if possible. -// If they do both round the same then we terminate the search -// for the root *very* quickly when finding an integer result. -// At the point that this function is called we know that "a" is -// below the root and "b" above it, so this change can not result -// in the root no longer being bracketed. -// -template <class Real, class Tol> -void adjust_bounds(Real& /* a */, Real& /* b */, Tol const& /* tol */){} - -template <class Real> -void adjust_bounds(Real& /* a */, Real& b, tools::equal_floor const& /* tol */) -{ - BOOST_MATH_STD_USING - b -= tools::epsilon<Real>() * b; -} - -template <class Real> -void adjust_bounds(Real& a, Real& /* b */, tools::equal_ceil const& /* tol */) -{ - BOOST_MATH_STD_USING - a += tools::epsilon<Real>() * a; -} - -template <class Real> -void adjust_bounds(Real& a, Real& b, tools::equal_nearest_integer const& /* tol */) -{ - BOOST_MATH_STD_USING - a += tools::epsilon<Real>() * a; - b -= tools::epsilon<Real>() * b; -} -// -// This is where all the work is done: -// -template <class Dist, class Tolerance> -typename Dist::value_type - do_inverse_discrete_quantile( - const Dist& dist, - const typename Dist::value_type& p, - bool comp, - typename Dist::value_type guess, - const typename Dist::value_type& multiplier, - typename Dist::value_type adder, - const Tolerance& tol, - boost::uintmax_t& max_iter) -{ - typedef typename Dist::value_type value_type; - typedef typename Dist::policy_type policy_type; - - static const char* function = "boost::math::do_inverse_discrete_quantile<%1%>"; - - BOOST_MATH_STD_USING - - distribution_quantile_finder<Dist> f(dist, p, comp); - // - // Max bounds of the distribution: - // - value_type min_bound, max_bound; - boost::math::tie(min_bound, max_bound) = support(dist); - - if(guess > max_bound) - guess = max_bound; - if(guess < min_bound) - guess = min_bound; - - value_type fa = f(guess); - boost::uintmax_t count = max_iter - 1; - value_type fb(fa), a(guess), b =0; // Compiler warning C4701: potentially uninitialized local variable 'b' used - - if(fa == 0) - return guess; - - // - // For small expected results, just use a linear search: - // - if(guess < 10) - { - b = a; - while((a < 10) && (fa * fb >= 0)) - { - if(fb <= 0) - { - a = b; - b = a + 1; - if(b > max_bound) - b = max_bound; - fb = f(b); - --count; - if(fb == 0) - return b; - if(a == b) - return b; // can't go any higher! - } - else - { - b = a; - a = (std::max)(value_type(b - 1), value_type(0)); - if(a < min_bound) - a = min_bound; - fa = f(a); - --count; - if(fa == 0) - return a; - if(a == b) - return a; // We can't go any lower than this! - } - } - } - // - // Try and bracket using a couple of additions first, - // we're assuming that "guess" is likely to be accurate - // to the nearest int or so: - // - else if(adder != 0) - { - // - // If we're looking for a large result, then bump "adder" up - // by a bit to increase our chances of bracketing the root: - // - //adder = (std::max)(adder, 0.001f * guess); - if(fa < 0) - { - b = a + adder; - if(b > max_bound) - b = max_bound; - } - else - { - b = (std::max)(value_type(a - adder), value_type(0)); - if(b < min_bound) - b = min_bound; - } - fb = f(b); - --count; - if(fb == 0) - return b; - if(count && (fa * fb >= 0)) - { - // - // We didn't bracket the root, try - // once more: - // - a = b; - fa = fb; - if(fa < 0) - { - b = a + adder; - if(b > max_bound) - b = max_bound; - } - else - { - b = (std::max)(value_type(a - adder), value_type(0)); - if(b < min_bound) - b = min_bound; - } - fb = f(b); - --count; - } - if(a > b) - { - using std::swap; - swap(a, b); - swap(fa, fb); - } - } - // - // If the root hasn't been bracketed yet, try again - // using the multiplier this time: - // - if((boost::math::sign)(fb) == (boost::math::sign)(fa)) - { - if(fa < 0) - { - // - // Zero is to the right of x2, so walk upwards - // until we find it: - // - while(((boost::math::sign)(fb) == (boost::math::sign)(fa)) && (a != b)) - { - if(count == 0) - return policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", b, policy_type()); - a = b; - fa = fb; - b *= multiplier; - if(b > max_bound) - b = max_bound; - fb = f(b); - --count; - BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count); - } - } - else - { - // - // Zero is to the left of a, so walk downwards - // until we find it: - // - while(((boost::math::sign)(fb) == (boost::math::sign)(fa)) && (a != b)) - { - if(fabs(a) < tools::min_value<value_type>()) - { - // Escape route just in case the answer is zero! - max_iter -= count; - max_iter += 1; - return 0; - } - if(count == 0) - return policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", a, policy_type()); - b = a; - fb = fa; - a /= multiplier; - if(a < min_bound) - a = min_bound; - fa = f(a); - --count; - BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count); - } - } - } - max_iter -= count; - if(fa == 0) - return a; - if(fb == 0) - return b; - if(a == b) - return b; // Ran out of bounds trying to bracket - there is no answer! - // - // Adjust bounds so that if we're looking for an integer - // result, then both ends round the same way: - // - adjust_bounds(a, b, tol); - // - // We don't want zero or denorm lower bounds: - // - if(a < tools::min_value<value_type>()) - a = tools::min_value<value_type>(); - // - // Go ahead and find the root: - // - std::pair<value_type, value_type> r = toms748_solve(f, a, b, fa, fb, tol, count, policy_type()); - max_iter += count; - BOOST_MATH_INSTRUMENT_CODE("max_iter = " << max_iter << " count = " << count); - return (r.first + r.second) / 2; -} -// -// Some special routine for rounding up and down: -// We want to check and see if we are very close to an integer, and if so test to see if -// that integer is an exact root of the cdf. We do this because our root finder only -// guarantees to find *a root*, and there can sometimes be many consecutive floating -// point values which are all roots. This is especially true if the target probability -// is very close 1. -// -template <class Dist> -inline typename Dist::value_type round_to_floor(const Dist& d, typename Dist::value_type result, typename Dist::value_type p, bool c) -{ - BOOST_MATH_STD_USING - typename Dist::value_type cc = ceil(result); - typename Dist::value_type pp = cc <= support(d).second ? c ? cdf(complement(d, cc)) : cdf(d, cc) : 1; - if(pp == p) - result = cc; - else - result = floor(result); - // - // Now find the smallest integer <= result for which we get an exact root: - // - while(result != 0) - { - cc = result - 1; - if(cc < support(d).first) - break; - pp = c ? cdf(complement(d, cc)) : cdf(d, cc); - if(pp == p) - result = cc; - else if(c ? pp > p : pp < p) - break; - result -= 1; - } - - return result; -} - -#ifdef BOOST_MSVC -#pragma warning(push) -#pragma warning(disable:4127) -#endif - -template <class Dist> -inline typename Dist::value_type round_to_ceil(const Dist& d, typename Dist::value_type result, typename Dist::value_type p, bool c) -{ - BOOST_MATH_STD_USING - typename Dist::value_type cc = floor(result); - typename Dist::value_type pp = cc >= support(d).first ? c ? cdf(complement(d, cc)) : cdf(d, cc) : 0; - if(pp == p) - result = cc; - else - result = ceil(result); - // - // Now find the largest integer >= result for which we get an exact root: - // - while(true) - { - cc = result + 1; - if(cc > support(d).second) - break; - pp = c ? cdf(complement(d, cc)) : cdf(d, cc); - if(pp == p) - result = cc; - else if(c ? pp < p : pp > p) - break; - result += 1; - } - - return result; -} - -#ifdef BOOST_MSVC -#pragma warning(pop) -#endif -// -// Now finally are the public API functions. -// There is one overload for each policy, -// each one is responsible for selecting the correct -// termination condition, and rounding the result -// to an int where required. -// -template <class Dist> -inline typename Dist::value_type - inverse_discrete_quantile( - const Dist& dist, - typename Dist::value_type p, - bool c, - const typename Dist::value_type& guess, - const typename Dist::value_type& multiplier, - const typename Dist::value_type& adder, - const policies::discrete_quantile<policies::real>&, - boost::uintmax_t& max_iter) -{ - if(p > 0.5) - { - p = 1 - p; - c = !c; - } - typename Dist::value_type pp = c ? 1 - p : p; - if(pp <= pdf(dist, 0)) - return 0; - return do_inverse_discrete_quantile( - dist, - p, - c, - guess, - multiplier, - adder, - tools::eps_tolerance<typename Dist::value_type>(policies::digits<typename Dist::value_type, typename Dist::policy_type>()), - max_iter); -} - -template <class Dist> -inline typename Dist::value_type - inverse_discrete_quantile( - const Dist& dist, - const typename Dist::value_type& p, - bool c, - const typename Dist::value_type& guess, - const typename Dist::value_type& multiplier, - const typename Dist::value_type& adder, - const policies::discrete_quantile<policies::integer_round_outwards>&, - boost::uintmax_t& max_iter) -{ - typedef typename Dist::value_type value_type; - BOOST_MATH_STD_USING - typename Dist::value_type pp = c ? 1 - p : p; - if(pp <= pdf(dist, 0)) - return 0; - // - // What happens next depends on whether we're looking for an - // upper or lower quantile: - // - if(pp < 0.5f) - return round_to_floor(dist, do_inverse_discrete_quantile( - dist, - p, - c, - (guess < 1 ? value_type(1) : (value_type)floor(guess)), - multiplier, - adder, - tools::equal_floor(), - max_iter), p, c); - // else: - return round_to_ceil(dist, do_inverse_discrete_quantile( - dist, - p, - c, - (value_type)ceil(guess), - multiplier, - adder, - tools::equal_ceil(), - max_iter), p, c); -} - -template <class Dist> -inline typename Dist::value_type - inverse_discrete_quantile( - const Dist& dist, - const typename Dist::value_type& p, - bool c, - const typename Dist::value_type& guess, - const typename Dist::value_type& multiplier, - const typename Dist::value_type& adder, - const policies::discrete_quantile<policies::integer_round_inwards>&, - boost::uintmax_t& max_iter) -{ - typedef typename Dist::value_type value_type; - BOOST_MATH_STD_USING - typename Dist::value_type pp = c ? 1 - p : p; - if(pp <= pdf(dist, 0)) - return 0; - // - // What happens next depends on whether we're looking for an - // upper or lower quantile: - // - if(pp < 0.5f) - return round_to_ceil(dist, do_inverse_discrete_quantile( - dist, - p, - c, - ceil(guess), - multiplier, - adder, - tools::equal_ceil(), - max_iter), p, c); - // else: - return round_to_floor(dist, do_inverse_discrete_quantile( - dist, - p, - c, - (guess < 1 ? value_type(1) : floor(guess)), - multiplier, - adder, - tools::equal_floor(), - max_iter), p, c); -} - -template <class Dist> -inline typename Dist::value_type - inverse_discrete_quantile( - const Dist& dist, - const typename Dist::value_type& p, - bool c, - const typename Dist::value_type& guess, - const typename Dist::value_type& multiplier, - const typename Dist::value_type& adder, - const policies::discrete_quantile<policies::integer_round_down>&, - boost::uintmax_t& max_iter) -{ - typedef typename Dist::value_type value_type; - BOOST_MATH_STD_USING - typename Dist::value_type pp = c ? 1 - p : p; - if(pp <= pdf(dist, 0)) - return 0; - return round_to_floor(dist, do_inverse_discrete_quantile( - dist, - p, - c, - (guess < 1 ? value_type(1) : floor(guess)), - multiplier, - adder, - tools::equal_floor(), - max_iter), p, c); -} - -template <class Dist> -inline typename Dist::value_type - inverse_discrete_quantile( - const Dist& dist, - const typename Dist::value_type& p, - bool c, - const typename Dist::value_type& guess, - const typename Dist::value_type& multiplier, - const typename Dist::value_type& adder, - const policies::discrete_quantile<policies::integer_round_up>&, - boost::uintmax_t& max_iter) -{ - BOOST_MATH_STD_USING - typename Dist::value_type pp = c ? 1 - p : p; - if(pp <= pdf(dist, 0)) - return 0; - return round_to_ceil(dist, do_inverse_discrete_quantile( - dist, - p, - c, - ceil(guess), - multiplier, - adder, - tools::equal_ceil(), - max_iter), p, c); -} - -template <class Dist> -inline typename Dist::value_type - inverse_discrete_quantile( - const Dist& dist, - const typename Dist::value_type& p, - bool c, - const typename Dist::value_type& guess, - const typename Dist::value_type& multiplier, - const typename Dist::value_type& adder, - const policies::discrete_quantile<policies::integer_round_nearest>&, - boost::uintmax_t& max_iter) -{ - typedef typename Dist::value_type value_type; - BOOST_MATH_STD_USING - typename Dist::value_type pp = c ? 1 - p : p; - if(pp <= pdf(dist, 0)) - return 0; - // - // Note that we adjust the guess to the nearest half-integer: - // this increase the chances that we will bracket the root - // with two results that both round to the same integer quickly. - // - return round_to_floor(dist, do_inverse_discrete_quantile( - dist, - p, - c, - (guess < 0.5f ? value_type(1.5f) : floor(guess + 0.5f) + 0.5f), - multiplier, - adder, - tools::equal_nearest_integer(), - max_iter) + 0.5f, p, c); -} - -}}} // namespaces - -#endif // BOOST_MATH_DISTRIBUTIONS_DETAIL_INV_DISCRETE_QUANTILE -
--- a/any/include/boost/math/distributions/exponential.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,275 +0,0 @@ -// Copyright John Maddock 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_EXPONENTIAL_HPP -#define BOOST_STATS_EXPONENTIAL_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/constants/constants.hpp> -#include <boost/math/special_functions/log1p.hpp> -#include <boost/math/special_functions/expm1.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/config/no_tr1/cmath.hpp> - -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable: 4127) // conditional expression is constant -# pragma warning(disable: 4702) // unreachable code (return after domain_error throw). -#endif - -#include <utility> - -namespace boost{ namespace math{ - -namespace detail{ -// -// Error check: -// -template <class RealType, class Policy> -inline bool verify_lambda(const char* function, RealType l, RealType* presult, const Policy& pol) -{ - if((l <= 0) || !(boost::math::isfinite)(l)) - { - *presult = policies::raise_domain_error<RealType>( - function, - "The scale parameter \"lambda\" must be > 0, but was: %1%.", l, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool verify_exp_x(const char* function, RealType x, RealType* presult, const Policy& pol) -{ - if((x < 0) || (boost::math::isnan)(x)) - { - *presult = policies::raise_domain_error<RealType>( - function, - "The random variable must be >= 0, but was: %1%.", x, pol); - return false; - } - return true; -} - -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class exponential_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - exponential_distribution(RealType l_lambda = 1) - : m_lambda(l_lambda) - { - RealType err; - detail::verify_lambda("boost::math::exponential_distribution<%1%>::exponential_distribution", l_lambda, &err, Policy()); - } // exponential_distribution - - RealType lambda()const { return m_lambda; } - -private: - RealType m_lambda; -}; - -typedef exponential_distribution<double> exponential; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const exponential_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - if (std::numeric_limits<RealType>::has_infinity) - { - return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()); // 0 to + infinity. - } - else - { - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max - } -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const exponential_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - using boost::math::tools::min_value; - return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>()); - // min_value<RealType>() to avoid a discontinuity at x = 0. -} - -template <class RealType, class Policy> -inline RealType pdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::pdf(const exponential_distribution<%1%>&, %1%)"; - - RealType lambda = dist.lambda(); - RealType result = 0; - if(0 == detail::verify_lambda(function, lambda, &result, Policy())) - return result; - if(0 == detail::verify_exp_x(function, x, &result, Policy())) - return result; - // Workaround for VC11/12 bug: - if ((boost::math::isinf)(x)) - return 0; - result = lambda * exp(-lambda * x); - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)"; - - RealType result = 0; - RealType lambda = dist.lambda(); - if(0 == detail::verify_lambda(function, lambda, &result, Policy())) - return result; - if(0 == detail::verify_exp_x(function, x, &result, Policy())) - return result; - result = -boost::math::expm1(-x * lambda, Policy()); - - return result; -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const exponential_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)"; - - RealType result = 0; - RealType lambda = dist.lambda(); - if(0 == detail::verify_lambda(function, lambda, &result, Policy())) - return result; - if(0 == detail::check_probability(function, p, &result, Policy())) - return result; - - if(p == 0) - return 0; - if(p == 1) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = -boost::math::log1p(-p, Policy()) / lambda; - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)"; - - RealType result = 0; - RealType lambda = c.dist.lambda(); - if(0 == detail::verify_lambda(function, lambda, &result, Policy())) - return result; - if(0 == detail::verify_exp_x(function, c.param, &result, Policy())) - return result; - // Workaround for VC11/12 bug: - if (c.param >= tools::max_value<RealType>()) - return 0; - result = exp(-c.param * lambda); - - return result; -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)"; - - RealType result = 0; - RealType lambda = c.dist.lambda(); - if(0 == detail::verify_lambda(function, lambda, &result, Policy())) - return result; - - RealType q = c.param; - if(0 == detail::check_probability(function, q, &result, Policy())) - return result; - - if(q == 1) - return 0; - if(q == 0) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = -log(q) / lambda; - return result; -} - -template <class RealType, class Policy> -inline RealType mean(const exponential_distribution<RealType, Policy>& dist) -{ - RealType result = 0; - RealType lambda = dist.lambda(); - if(0 == detail::verify_lambda("boost::math::mean(const exponential_distribution<%1%>&)", lambda, &result, Policy())) - return result; - return 1 / lambda; -} - -template <class RealType, class Policy> -inline RealType standard_deviation(const exponential_distribution<RealType, Policy>& dist) -{ - RealType result = 0; - RealType lambda = dist.lambda(); - if(0 == detail::verify_lambda("boost::math::standard_deviation(const exponential_distribution<%1%>&)", lambda, &result, Policy())) - return result; - return 1 / lambda; -} - -template <class RealType, class Policy> -inline RealType mode(const exponential_distribution<RealType, Policy>& /*dist*/) -{ - return 0; -} - -template <class RealType, class Policy> -inline RealType median(const exponential_distribution<RealType, Policy>& dist) -{ - using boost::math::constants::ln_two; - return ln_two<RealType>() / dist.lambda(); // ln(2) / lambda -} - -template <class RealType, class Policy> -inline RealType skewness(const exponential_distribution<RealType, Policy>& /*dist*/) -{ - return 2; -} - -template <class RealType, class Policy> -inline RealType kurtosis(const exponential_distribution<RealType, Policy>& /*dist*/) -{ - return 9; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const exponential_distribution<RealType, Policy>& /*dist*/) -{ - return 6; -} - -} // namespace math -} // namespace boost - -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_EXPONENTIAL_HPP
--- a/any/include/boost/math/distributions/extreme_value.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,300 +0,0 @@ -// Copyright John Maddock 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_EXTREME_VALUE_HPP -#define BOOST_STATS_EXTREME_VALUE_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/constants/constants.hpp> -#include <boost/math/special_functions/log1p.hpp> -#include <boost/math/special_functions/expm1.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/config/no_tr1/cmath.hpp> - -// -// This is the maximum extreme value distribution, see -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm -// and http://mathworld.wolfram.com/ExtremeValueDistribution.html -// Also known as a Fisher-Tippett distribution, a log-Weibull -// distribution or a Gumbel distribution. - -#include <utility> - -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable: 4702) // unreachable code (return after domain_error throw). -#endif - -namespace boost{ namespace math{ - -namespace detail{ -// -// Error check: -// -template <class RealType, class Policy> -inline bool verify_scale_b(const char* function, RealType b, RealType* presult, const Policy& pol) -{ - if((b <= 0) || !(boost::math::isfinite)(b)) - { - *presult = policies::raise_domain_error<RealType>( - function, - "The scale parameter \"b\" must be finite and > 0, but was: %1%.", b, pol); - return false; - } - return true; -} - -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class extreme_value_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - extreme_value_distribution(RealType a = 0, RealType b = 1) - : m_a(a), m_b(b) - { - RealType err; - detail::verify_scale_b("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", b, &err, Policy()); - detail::check_finite("boost::math::extreme_value_distribution<%1%>::extreme_value_distribution", a, &err, Policy()); - } // extreme_value_distribution - - RealType location()const { return m_a; } - RealType scale()const { return m_b; } - -private: - RealType m_a, m_b; -}; - -typedef extreme_value_distribution<double> extreme_value; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const extreme_value_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>( - std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), - std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>()); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const extreme_value_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline RealType pdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::pdf(const extreme_value_distribution<%1%>&, %1%)"; - - RealType a = dist.location(); - RealType b = dist.scale(); - RealType result = 0; - if(0 == detail::verify_scale_b(function, b, &result, Policy())) - return result; - if(0 == detail::check_finite(function, a, &result, Policy())) - return result; - if((boost::math::isinf)(x)) - return 0.0f; - if(0 == detail::check_x(function, x, &result, Policy())) - return result; - RealType e = (a - x) / b; - if(e < tools::log_max_value<RealType>()) - result = exp(e) * exp(-exp(e)) / b; - // else.... result *must* be zero since exp(e) is infinite... - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const extreme_value_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)"; - - if((boost::math::isinf)(x)) - return x < 0 ? 0.0f : 1.0f; - RealType a = dist.location(); - RealType b = dist.scale(); - RealType result = 0; - if(0 == detail::verify_scale_b(function, b, &result, Policy())) - return result; - if(0 == detail::check_finite(function, a, &result, Policy())) - return result; - if(0 == detail::check_finite(function, a, &result, Policy())) - return result; - if(0 == detail::check_x("boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)", x, &result, Policy())) - return result; - - result = exp(-exp((a-x)/b)); - - return result; -} // cdf - -template <class RealType, class Policy> -RealType quantile(const extreme_value_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)"; - - RealType a = dist.location(); - RealType b = dist.scale(); - RealType result = 0; - if(0 == detail::verify_scale_b(function, b, &result, Policy())) - return result; - if(0 == detail::check_finite(function, a, &result, Policy())) - return result; - if(0 == detail::check_probability(function, p, &result, Policy())) - return result; - - if(p == 0) - return -policies::raise_overflow_error<RealType>(function, 0, Policy()); - if(p == 1) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = a - log(-log(p)) * b; - - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const extreme_value_distribution<%1%>&, %1%)"; - - if((boost::math::isinf)(c.param)) - return c.param < 0 ? 1.0f : 0.0f; - RealType a = c.dist.location(); - RealType b = c.dist.scale(); - RealType result = 0; - if(0 == detail::verify_scale_b(function, b, &result, Policy())) - return result; - if(0 == detail::check_finite(function, a, &result, Policy())) - return result; - if(0 == detail::check_x(function, c.param, &result, Policy())) - return result; - - result = -boost::math::expm1(-exp((a-c.param)/b), Policy()); - - return result; -} - -template <class RealType, class Policy> -RealType quantile(const complemented2_type<extreme_value_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const extreme_value_distribution<%1%>&, %1%)"; - - RealType a = c.dist.location(); - RealType b = c.dist.scale(); - RealType q = c.param; - RealType result = 0; - if(0 == detail::verify_scale_b(function, b, &result, Policy())) - return result; - if(0 == detail::check_finite(function, a, &result, Policy())) - return result; - if(0 == detail::check_probability(function, q, &result, Policy())) - return result; - - if(q == 0) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - if(q == 1) - return -policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = a - log(-boost::math::log1p(-q, Policy())) * b; - - return result; -} - -template <class RealType, class Policy> -inline RealType mean(const extreme_value_distribution<RealType, Policy>& dist) -{ - RealType a = dist.location(); - RealType b = dist.scale(); - RealType result = 0; - if(0 == detail::verify_scale_b("boost::math::mean(const extreme_value_distribution<%1%>&)", b, &result, Policy())) - return result; - if (0 == detail::check_finite("boost::math::mean(const extreme_value_distribution<%1%>&)", a, &result, Policy())) - return result; - return a + constants::euler<RealType>() * b; -} - -template <class RealType, class Policy> -inline RealType standard_deviation(const extreme_value_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions. - - RealType b = dist.scale(); - RealType result = 0; - if(0 == detail::verify_scale_b("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", b, &result, Policy())) - return result; - if(0 == detail::check_finite("boost::math::standard_deviation(const extreme_value_distribution<%1%>&)", dist.location(), &result, Policy())) - return result; - return constants::pi<RealType>() * b / sqrt(static_cast<RealType>(6)); -} - -template <class RealType, class Policy> -inline RealType mode(const extreme_value_distribution<RealType, Policy>& dist) -{ - return dist.location(); -} - -template <class RealType, class Policy> -inline RealType median(const extreme_value_distribution<RealType, Policy>& dist) -{ - using constants::ln_ln_two; - return dist.location() - dist.scale() * ln_ln_two<RealType>(); -} - -template <class RealType, class Policy> -inline RealType skewness(const extreme_value_distribution<RealType, Policy>& /*dist*/) -{ - // - // This is 12 * sqrt(6) * zeta(3) / pi^3: - // See http://mathworld.wolfram.com/ExtremeValueDistribution.html - // - return static_cast<RealType>(1.1395470994046486574927930193898461120875997958366L); -} - -template <class RealType, class Policy> -inline RealType kurtosis(const extreme_value_distribution<RealType, Policy>& /*dist*/) -{ - // See http://mathworld.wolfram.com/ExtremeValueDistribution.html - return RealType(27) / 5; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const extreme_value_distribution<RealType, Policy>& /*dist*/) -{ - // See http://mathworld.wolfram.com/ExtremeValueDistribution.html - return RealType(12) / 5; -} - - -} // namespace math -} // namespace boost - -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_EXTREME_VALUE_HPP
--- a/any/include/boost/math/distributions/find_location.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,146 +0,0 @@ -// Copyright John Maddock 2007. -// Copyright Paul A. Bristow 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_FIND_LOCATION_HPP -#define BOOST_STATS_FIND_LOCATION_HPP - -#include <boost/math/distributions/fwd.hpp> // for all distribution signatures. -#include <boost/math/distributions/complement.hpp> -#include <boost/math/policies/policy.hpp> -#include <boost/math/tools/traits.hpp> -#include <boost/static_assert.hpp> -#include <boost/math/special_functions/fpclassify.hpp> -#include <boost/math/policies/error_handling.hpp> -// using boost::math::policies::policy; -// using boost::math::complement; // will be needed by users who want complement, -// but NOT placed here to avoid putting it in global scope. - -namespace boost -{ - namespace math - { - // Function to find location of random variable z - // to give probability p (given scale) - // Applies to normal, lognormal, extreme value, Cauchy, (and symmetrical triangular), - // enforced by BOOST_STATIC_ASSERT below. - - template <class Dist, class Policy> - inline - typename Dist::value_type find_location( // For example, normal mean. - typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. - // For example, a nominal minimum acceptable z, so that p * 100 % are > z - typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. - typename Dist::value_type scale, // scale parameter, for example, normal standard deviation. - const Policy& pol - ) - { -#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590)) - // Will fail to compile here if try to use with a distribution without scale & location, - // for example pareto, and many others. These tests are disabled by the pp-logic - // above if the compiler doesn't support the SFINAE tricks used in the traits class. - BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); - BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); -#endif - static const char* function = "boost::math::find_location<Dist, Policy>&, %1%)"; - - if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, pol); - } - if(!(boost::math::isfinite)(z)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "z parameter was %1%, but must be finite!", z, pol); - } - if(!(boost::math::isfinite)(scale)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "scale parameter was %1%, but must be finite!", scale, pol); - } - - //cout << "z " << z << ", p " << p << ", quantile(Dist(), p) " - // << quantile(Dist(), p) << ", quan * scale " << quantile(Dist(), p) * scale << endl; - return z - (quantile(Dist(), p) * scale); - } // find_location - - template <class Dist> - inline // with default policy. - typename Dist::value_type find_location( // For example, normal mean. - typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. - // For example, a nominal minimum acceptable z, so that p * 100 % are > z - typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. - typename Dist::value_type scale) // scale parameter, for example, normal standard deviation. - { // Forward to find_location with default policy. - return (find_location<Dist>(z, p, scale, policies::policy<>())); - } // find_location - - // So the user can start from the complement q = (1 - p) of the probability p, - // for example, l = find_location<normal>(complement(z, q, sd)); - - template <class Dist, class Real1, class Real2, class Real3> - inline typename Dist::value_type find_location( // Default policy. - complemented3_type<Real1, Real2, Real3> const& c) - { - static const char* function = "boost::math::find_location<Dist, Policy>&, %1%)"; - - typename Dist::value_type p = c.param1; - if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, policies::policy<>()); - } - typename Dist::value_type z = c.dist; - if(!(boost::math::isfinite)(z)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "z parameter was %1%, but must be finite!", z, policies::policy<>()); - } - typename Dist::value_type scale = c.param2; - if(!(boost::math::isfinite)(scale)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "scale parameter was %1%, but must be finite!", scale, policies::policy<>()); - } - // cout << "z " << c.dist << ", quantile (Dist(), " << c.param1 << ") * scale " << c.param2 << endl; - return z - quantile(Dist(), p) * scale; - } // find_location complement - - - template <class Dist, class Real1, class Real2, class Real3, class Real4> - inline typename Dist::value_type find_location( // Explicit policy. - complemented4_type<Real1, Real2, Real3, Real4> const& c) - { - static const char* function = "boost::math::find_location<Dist, Policy>&, %1%)"; - - typename Dist::value_type p = c.param1; - if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, c.param3); - } - typename Dist::value_type z = c.dist; - if(!(boost::math::isfinite)(z)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "z parameter was %1%, but must be finite!", z, c.param3); - } - typename Dist::value_type scale = c.param2; - if(!(boost::math::isfinite)(scale)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "scale parameter was %1%, but must be finite!", scale, c.param3); - } - // cout << "z " << c.dist << ", quantile (Dist(), " << c.param1 << ") * scale " << c.param2 << endl; - return z - quantile(Dist(), p) * scale; - } // find_location complement - - } // namespace boost -} // namespace math - -#endif // BOOST_STATS_FIND_LOCATION_HPP -
--- a/any/include/boost/math/distributions/find_scale.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,211 +0,0 @@ -// Copyright John Maddock 2007. -// Copyright Paul A. Bristow 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_FIND_SCALE_HPP -#define BOOST_STATS_FIND_SCALE_HPP - -#include <boost/math/distributions/fwd.hpp> // for all distribution signatures. -#include <boost/math/distributions/complement.hpp> -#include <boost/math/policies/policy.hpp> -// using boost::math::policies::policy; -#include <boost/math/tools/traits.hpp> -#include <boost/static_assert.hpp> -#include <boost/math/special_functions/fpclassify.hpp> -#include <boost/math/policies/error_handling.hpp> -// using boost::math::complement; // will be needed by users who want complement, -// but NOT placed here to avoid putting it in global scope. - -namespace boost -{ - namespace math - { - // Function to find location of random variable z - // to give probability p (given scale) - // Applies to normal, lognormal, extreme value, Cauchy, (and symmetrical triangular), - // distributions that have scale. - // BOOST_STATIC_ASSERTs, see below, are used to enforce this. - - template <class Dist, class Policy> - inline - typename Dist::value_type find_scale( // For example, normal mean. - typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. - // For example, a nominal minimum acceptable weight z, so that p * 100 % are > z - typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. - typename Dist::value_type location, // location parameter, for example, normal distribution mean. - const Policy& pol - ) - { -#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590)) - BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); - BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); -#endif - static const char* function = "boost::math::find_scale<Dist, Policy>(%1%, %1%, %1%, Policy)"; - - if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "Probability parameter was %1%, but must be >= 0 and <= 1!", p, pol); - } - if(!(boost::math::isfinite)(z)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "find_scale z parameter was %1%, but must be finite!", z, pol); - } - if(!(boost::math::isfinite)(location)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "find_scale location parameter was %1%, but must be finite!", location, pol); - } - - //cout << "z " << z << ", p " << p << ", quantile(Dist(), p) " - //<< quantile(Dist(), p) << ", z - mean " << z - location - //<<", sd " << (z - location) / quantile(Dist(), p) << endl; - - //quantile(N01, 0.001) -3.09023 - //quantile(N01, 0.01) -2.32635 - //quantile(N01, 0.05) -1.64485 - //quantile(N01, 0.333333) -0.430728 - //quantile(N01, 0.5) 0 - //quantile(N01, 0.666667) 0.430728 - //quantile(N01, 0.9) 1.28155 - //quantile(N01, 0.95) 1.64485 - //quantile(N01, 0.99) 2.32635 - //quantile(N01, 0.999) 3.09023 - - typename Dist::value_type result = - (z - location) // difference between desired x and current location. - / quantile(Dist(), p); // standard distribution. - - if (result <= 0) - { // If policy isn't to throw, return the scale <= 0. - policies::raise_evaluation_error<typename Dist::value_type>(function, - "Computed scale (%1%) is <= 0!" " Was the complement intended?", - result, Policy()); - } - return result; - } // template <class Dist, class Policy> find_scale - - template <class Dist> - inline // with default policy. - typename Dist::value_type find_scale( // For example, normal mean. - typename Dist::value_type z, // location of random variable z to give probability, P(X > z) == p. - // For example, a nominal minimum acceptable z, so that p * 100 % are > z - typename Dist::value_type p, // probability value desired at x, say 0.95 for 95% > z. - typename Dist::value_type location) // location parameter, for example, mean. - { // Forward to find_scale using the default policy. - return (find_scale<Dist>(z, p, location, policies::policy<>())); - } // find_scale - - template <class Dist, class Real1, class Real2, class Real3, class Policy> - inline typename Dist::value_type find_scale( - complemented4_type<Real1, Real2, Real3, Policy> const& c) - { - //cout << "cparam1 q " << c.param1 // q - // << ", c.dist z " << c.dist // z - // << ", c.param2 l " << c.param2 // l - // << ", quantile (Dist(), c.param1 = q) " - // << quantile(Dist(), c.param1) //q - // << endl; - -#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590)) - BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); - BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); -#endif - static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))"; - - // Checks on arguments, as not complemented version, - // Explicit policy. - typename Dist::value_type q = c.param1; - if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, c.param3); - } - typename Dist::value_type z = c.dist; - if(!(boost::math::isfinite)(z)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "find_scale z parameter was %1%, but must be finite!", z, c.param3); - } - typename Dist::value_type location = c.param2; - if(!(boost::math::isfinite)(location)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "find_scale location parameter was %1%, but must be finite!", location, c.param3); - } - - typename Dist::value_type result = - (c.dist - c.param2) // difference between desired x and current location. - / quantile(complement(Dist(), c.param1)); - // ( z - location) / (quantile(complement(Dist(), q)) - if (result <= 0) - { // If policy isn't to throw, return the scale <= 0. - policies::raise_evaluation_error<typename Dist::value_type>(function, - "Computed scale (%1%) is <= 0!" " Was the complement intended?", - result, Policy()); - } - return result; - } // template <class Dist, class Policy, class Real1, class Real2, class Real3> typename Dist::value_type find_scale - - // So the user can start from the complement q = (1 - p) of the probability p, - // for example, s = find_scale<normal>(complement(z, q, l)); - - template <class Dist, class Real1, class Real2, class Real3> - inline typename Dist::value_type find_scale( - complemented3_type<Real1, Real2, Real3> const& c) - { - //cout << "cparam1 q " << c.param1 // q - // << ", c.dist z " << c.dist // z - // << ", c.param2 l " << c.param2 // l - // << ", quantile (Dist(), c.param1 = q) " - // << quantile(Dist(), c.param1) //q - // << endl; - -#if !defined(BOOST_NO_SFINAE) && !BOOST_WORKAROUND(__SUNPRO_CC, BOOST_TESTED_AT(0x590)) - BOOST_STATIC_ASSERT(::boost::math::tools::is_distribution<Dist>::value); - BOOST_STATIC_ASSERT(::boost::math::tools::is_scaled_distribution<Dist>::value); -#endif - static const char* function = "boost::math::find_scale<Dist, Policy>(complement(%1%, %1%, %1%, Policy))"; - - // Checks on arguments, as not complemented version, - // default policy policies::policy<>(). - typename Dist::value_type q = c.param1; - if(!(boost::math::isfinite)(q) || (q < 0) || (q > 1)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "Probability parameter was %1%, but must be >= 0 and <= 1!", q, policies::policy<>()); - } - typename Dist::value_type z = c.dist; - if(!(boost::math::isfinite)(z)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "find_scale z parameter was %1%, but must be finite!", z, policies::policy<>()); - } - typename Dist::value_type location = c.param2; - if(!(boost::math::isfinite)(location)) - { - return policies::raise_domain_error<typename Dist::value_type>( - function, "find_scale location parameter was %1%, but must be finite!", location, policies::policy<>()); - } - - typename Dist::value_type result = - (z - location) // difference between desired x and current location. - / quantile(complement(Dist(), q)); - // ( z - location) / (quantile(complement(Dist(), q)) - if (result <= 0) - { // If policy isn't to throw, return the scale <= 0. - policies::raise_evaluation_error<typename Dist::value_type>(function, - "Computed scale (%1%) is <= 0!" " Was the complement intended?", - result, policies::policy<>()); // This is only the default policy - also Want a version with Policy here. - } - return result; - } // template <class Dist, class Real1, class Real2, class Real3> typename Dist::value_type find_scale - - } // namespace boost -} // namespace math - -#endif // BOOST_STATS_FIND_SCALE_HPP
--- a/any/include/boost/math/distributions/fisher_f.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,387 +0,0 @@ -// Copyright John Maddock 2006. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP -#define BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for incomplete beta. -#include <boost/math/distributions/complement.hpp> // complements -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> - -#include <utility> - -namespace boost{ namespace math{ - -template <class RealType = double, class Policy = policies::policy<> > -class fisher_f_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - fisher_f_distribution(const RealType& i, const RealType& j) : m_df1(i), m_df2(j) - { - static const char* function = "fisher_f_distribution<%1%>::fisher_f_distribution"; - RealType result; - detail::check_df( - function, m_df1, &result, Policy()); - detail::check_df( - function, m_df2, &result, Policy()); - } // fisher_f_distribution - - RealType degrees_of_freedom1()const - { - return m_df1; - } - RealType degrees_of_freedom2()const - { - return m_df2; - } - -private: - // - // Data members: - // - RealType m_df1; // degrees of freedom are a real number. - RealType m_df2; // degrees of freedom are a real number. -}; - -typedef fisher_f_distribution<double> fisher_f; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const fisher_f_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const fisher_f_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -RealType pdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - static const char* function = "boost::math::pdf(fisher_f_distribution<%1%> const&, %1%)"; - if(false == (detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy()))) - return error_result; - - if((x < 0) || !(boost::math::isfinite)(x)) - { - return policies::raise_domain_error<RealType>( - function, "Random variable parameter was %1%, but must be > 0 !", x, Policy()); - } - - if(x == 0) - { - // special cases: - if(df1 < 2) - return policies::raise_overflow_error<RealType>( - function, 0, Policy()); - else if(df1 == 2) - return 1; - else - return 0; - } - - // - // You reach this formula by direct differentiation of the - // cdf expressed in terms of the incomplete beta. - // - // There are two versions so we don't pass a value of z - // that is very close to 1 to ibeta_derivative: for some values - // of df1 and df2, all the change takes place in this area. - // - RealType v1x = df1 * x; - RealType result; - if(v1x > df2) - { - result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x)); - result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy()); - } - else - { - result = df2 + df1 * x; - result = (result * df1 - x * df1 * df1) / (result * result); - result *= ibeta_derivative(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy()); - } - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x) -{ - static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)"; - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - if(false == detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy())) - return error_result; - - if((x < 0) || !(boost::math::isfinite)(x)) - { - return policies::raise_domain_error<RealType>( - function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy()); - } - - RealType v1x = df1 * x; - // - // There are two equivalent formulas used here, the aim is - // to prevent the final argument to the incomplete beta - // from being too close to 1: for some values of df1 and df2 - // the rate of change can be arbitrarily large in this area, - // whilst the value we're passing will have lost information - // content as a result of being 0.999999something. Better - // to switch things around so we're passing 1-z instead. - // - return v1x > df2 - ? boost::math::ibetac(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy()) - : boost::math::ibeta(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy()); -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const fisher_f_distribution<RealType, Policy>& dist, const RealType& p) -{ - static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)"; - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - if(false == (detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy()) - && detail::check_probability( - function, p, &error_result, Policy()))) - return error_result; - - // With optimizations turned on, gcc wrongly warns about y being used - // uninitializated unless we initialize it to something: - RealType x, y(0); - - x = boost::math::ibeta_inv(df1 / 2, df2 / 2, p, &y, Policy()); - - return df2 * x / (df1 * y); -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c) -{ - static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)"; - RealType df1 = c.dist.degrees_of_freedom1(); - RealType df2 = c.dist.degrees_of_freedom2(); - RealType x = c.param; - // Error check: - RealType error_result = 0; - if(false == detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy())) - return error_result; - - if((x < 0) || !(boost::math::isfinite)(x)) - { - return policies::raise_domain_error<RealType>( - function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy()); - } - - RealType v1x = df1 * x; - // - // There are two equivalent formulas used here, the aim is - // to prevent the final argument to the incomplete beta - // from being too close to 1: for some values of df1 and df2 - // the rate of change can be arbitrarily large in this area, - // whilst the value we're passing will have lost information - // content as a result of being 0.999999something. Better - // to switch things around so we're passing 1-z instead. - // - return v1x > df2 - ? boost::math::ibeta(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy()) - : boost::math::ibetac(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy()); -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c) -{ - static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)"; - RealType df1 = c.dist.degrees_of_freedom1(); - RealType df2 = c.dist.degrees_of_freedom2(); - RealType p = c.param; - // Error check: - RealType error_result = 0; - if(false == (detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy()) - && detail::check_probability( - function, p, &error_result, Policy()))) - return error_result; - - RealType x, y; - - x = boost::math::ibetac_inv(df1 / 2, df2 / 2, p, &y, Policy()); - - return df2 * x / (df1 * y); -} - -template <class RealType, class Policy> -inline RealType mean(const fisher_f_distribution<RealType, Policy>& dist) -{ // Mean of F distribution = v. - static const char* function = "boost::math::mean(fisher_f_distribution<%1%> const&)"; - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - if(false == detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy())) - return error_result; - if(df2 <= 2) - { - return policies::raise_domain_error<RealType>( - function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mean.", df2, Policy()); - } - return df2 / (df2 - 2); -} // mean - -template <class RealType, class Policy> -inline RealType variance(const fisher_f_distribution<RealType, Policy>& dist) -{ // Variance of F distribution. - static const char* function = "boost::math::variance(fisher_f_distribution<%1%> const&)"; - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - if(false == detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy())) - return error_result; - if(df2 <= 4) - { - return policies::raise_domain_error<RealType>( - function, "Second degree of freedom was %1% but must be > 4 in order for the distribution to have a valid variance.", df2, Policy()); - } - return 2 * df2 * df2 * (df1 + df2 - 2) / (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4)); -} // variance - -template <class RealType, class Policy> -inline RealType mode(const fisher_f_distribution<RealType, Policy>& dist) -{ - static const char* function = "boost::math::mode(fisher_f_distribution<%1%> const&)"; - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - if(false == detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy())) - return error_result; - if(df2 <= 2) - { - return policies::raise_domain_error<RealType>( - function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mode.", df2, Policy()); - } - return df2 * (df1 - 2) / (df1 * (df2 + 2)); -} - -//template <class RealType, class Policy> -//inline RealType median(const fisher_f_distribution<RealType, Policy>& dist) -//{ // Median of Fisher F distribution is not defined. -// return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); -// } // median - -// Now implemented via quantile(half) in derived accessors. - -template <class RealType, class Policy> -inline RealType skewness(const fisher_f_distribution<RealType, Policy>& dist) -{ - static const char* function = "boost::math::skewness(fisher_f_distribution<%1%> const&)"; - BOOST_MATH_STD_USING // ADL of std names - // See http://mathworld.wolfram.com/F-Distribution.html - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - if(false == detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy())) - return error_result; - if(df2 <= 6) - { - return policies::raise_domain_error<RealType>( - function, "Second degree of freedom was %1% but must be > 6 in order for the distribution to have a skewness.", df2, Policy()); - } - return 2 * (df2 + 2 * df1 - 2) * sqrt((2 * df2 - 8) / (df1 * (df2 + df1 - 2))) / (df2 - 6); -} - -template <class RealType, class Policy> -RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist); - -template <class RealType, class Policy> -inline RealType kurtosis(const fisher_f_distribution<RealType, Policy>& dist) -{ - return 3 + kurtosis_excess(dist); -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist) -{ - static const char* function = "boost::math::kurtosis_excess(fisher_f_distribution<%1%> const&)"; - // See http://mathworld.wolfram.com/F-Distribution.html - RealType df1 = dist.degrees_of_freedom1(); - RealType df2 = dist.degrees_of_freedom2(); - // Error check: - RealType error_result = 0; - if(false == detail::check_df( - function, df1, &error_result, Policy()) - && detail::check_df( - function, df2, &error_result, Policy())) - return error_result; - if(df2 <= 8) - { - return policies::raise_domain_error<RealType>( - function, "Second degree of freedom was %1% but must be > 8 in order for the distribution to have a kutosis.", df2, Policy()); - } - RealType df2_2 = df2 * df2; - RealType df1_2 = df1 * df1; - RealType n = -16 + 20 * df2 - 8 * df2_2 + df2_2 * df2 + 44 * df1 - 32 * df2 * df1 + 5 * df2_2 * df1 - 22 * df1_2 + 5 * df2 * df1_2; - n *= 12; - RealType d = df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2); - return n / d; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP
--- a/any/include/boost/math/distributions/fwd.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,153 +0,0 @@ -// fwd.hpp Forward declarations of Boost.Math distributions. - -// Copyright Paul A. Bristow 2007, 2010, 2012, 2014. -// Copyright John Maddock 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_FWD_HPP -#define BOOST_MATH_DISTRIBUTIONS_FWD_HPP - -// 33 distributions at Boost 1.9.1 after adding hyperexpon and arcsine - -namespace boost{ namespace math{ - -template <class RealType, class Policy> -class arcsine_distribution; - -template <class RealType, class Policy> -class bernoulli_distribution; - -template <class RealType, class Policy> -class beta_distribution; - -template <class RealType, class Policy> -class binomial_distribution; - -template <class RealType, class Policy> -class cauchy_distribution; - -template <class RealType, class Policy> -class chi_squared_distribution; - -template <class RealType, class Policy> -class exponential_distribution; - -template <class RealType, class Policy> -class extreme_value_distribution; - -template <class RealType, class Policy> -class fisher_f_distribution; - -template <class RealType, class Policy> -class gamma_distribution; - -template <class RealType, class Policy> -class geometric_distribution; - -template <class RealType, class Policy> -class hyperexponential_distribution; - -template <class RealType, class Policy> -class hypergeometric_distribution; - -template <class RealType, class Policy> -class inverse_chi_squared_distribution; - -template <class RealType, class Policy> -class inverse_gamma_distribution; - -template <class RealType, class Policy> -class inverse_gaussian_distribution; - -template <class RealType, class Policy> -class laplace_distribution; - -template <class RealType, class Policy> -class logistic_distribution; - -template <class RealType, class Policy> -class lognormal_distribution; - -template <class RealType, class Policy> -class negative_binomial_distribution; - -template <class RealType, class Policy> -class non_central_beta_distribution; - -template <class RealType, class Policy> -class non_central_chi_squared_distribution; - -template <class RealType, class Policy> -class non_central_f_distribution; - -template <class RealType, class Policy> -class non_central_t_distribution; - -template <class RealType, class Policy> -class normal_distribution; - -template <class RealType, class Policy> -class pareto_distribution; - -template <class RealType, class Policy> -class poisson_distribution; - -template <class RealType, class Policy> -class rayleigh_distribution; - -template <class RealType, class Policy> -class skew_normal_distribution; - -template <class RealType, class Policy> -class students_t_distribution; - -template <class RealType, class Policy> -class triangular_distribution; - -template <class RealType, class Policy> -class uniform_distribution; - -template <class RealType, class Policy> -class weibull_distribution; - -}} // namespaces - -#define BOOST_MATH_DECLARE_DISTRIBUTIONS(Type, Policy)\ - typedef boost::math::arcsine_distribution<Type, Policy> arcsine;\ - typedef boost::math::bernoulli_distribution<Type, Policy> bernoulli;\ - typedef boost::math::beta_distribution<Type, Policy> beta;\ - typedef boost::math::binomial_distribution<Type, Policy> binomial;\ - typedef boost::math::cauchy_distribution<Type, Policy> cauchy;\ - typedef boost::math::chi_squared_distribution<Type, Policy> chi_squared;\ - typedef boost::math::exponential_distribution<Type, Policy> exponential;\ - typedef boost::math::extreme_value_distribution<Type, Policy> extreme_value;\ - typedef boost::math::fisher_f_distribution<Type, Policy> fisher_f;\ - typedef boost::math::gamma_distribution<Type, Policy> gamma;\ - typedef boost::math::geometric_distribution<Type, Policy> geometric;\ - typedef boost::math::hypergeometric_distribution<Type, Policy> hypergeometric;\ - typedef boost::math::inverse_chi_squared_distribution<Type, Policy> inverse_chi_squared;\ - typedef boost::math::inverse_gaussian_distribution<Type, Policy> inverse_gaussian;\ - typedef boost::math::inverse_gamma_distribution<Type, Policy> inverse_gamma;\ - typedef boost::math::laplace_distribution<Type, Policy> laplace;\ - typedef boost::math::logistic_distribution<Type, Policy> logistic;\ - typedef boost::math::lognormal_distribution<Type, Policy> lognormal;\ - typedef boost::math::negative_binomial_distribution<Type, Policy> negative_binomial;\ - typedef boost::math::non_central_beta_distribution<Type, Policy> non_central_beta;\ - typedef boost::math::non_central_chi_squared_distribution<Type, Policy> non_central_chi_squared;\ - typedef boost::math::non_central_f_distribution<Type, Policy> non_central_f;\ - typedef boost::math::non_central_t_distribution<Type, Policy> non_central_t;\ - typedef boost::math::normal_distribution<Type, Policy> normal;\ - typedef boost::math::pareto_distribution<Type, Policy> pareto;\ - typedef boost::math::poisson_distribution<Type, Policy> poisson;\ - typedef boost::math::rayleigh_distribution<Type, Policy> rayleigh;\ - typedef boost::math::skew_normal_distribution<Type, Policy> skew_normal;\ - typedef boost::math::students_t_distribution<Type, Policy> students_t;\ - typedef boost::math::triangular_distribution<Type, Policy> triangular;\ - typedef boost::math::uniform_distribution<Type, Policy> uniform;\ - typedef boost::math::weibull_distribution<Type, Policy> weibull; - -#endif // BOOST_MATH_DISTRIBUTIONS_FWD_HPP
--- a/any/include/boost/math/distributions/gamma.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,349 +0,0 @@ -// Copyright John Maddock 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_GAMMA_HPP -#define BOOST_STATS_GAMMA_HPP - -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm -// http://mathworld.wolfram.com/GammaDistribution.html -// http://en.wikipedia.org/wiki/Gamma_distribution - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/gamma.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> - -#include <utility> - -namespace boost{ namespace math -{ -namespace detail -{ - -template <class RealType, class Policy> -inline bool check_gamma_shape( - const char* function, - RealType shape, - RealType* result, const Policy& pol) -{ - if((shape <= 0) || !(boost::math::isfinite)(shape)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but must be > 0 !", shape, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_gamma_x( - const char* function, - RealType const& x, - RealType* result, const Policy& pol) -{ - if((x < 0) || !(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate is %1% but must be >= 0 !", x, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_gamma( - const char* function, - RealType scale, - RealType shape, - RealType* result, const Policy& pol) -{ - return check_scale(function, scale, result, pol) && check_gamma_shape(function, shape, result, pol); -} - -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class gamma_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - gamma_distribution(RealType l_shape, RealType l_scale = 1) - : m_shape(l_shape), m_scale(l_scale) - { - RealType result; - detail::check_gamma("boost::math::gamma_distribution<%1%>::gamma_distribution", l_scale, l_shape, &result, Policy()); - } - - RealType shape()const - { - return m_shape; - } - - RealType scale()const - { - return m_scale; - } -private: - // - // Data members: - // - RealType m_shape; // distribution shape - RealType m_scale; // distribution scale -}; - -// NO typedef because of clash with name of gamma function. - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const gamma_distribution<RealType, Policy>& /* dist */) -{ // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const gamma_distribution<RealType, Policy>& /* dist */) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - using boost::math::tools::min_value; - return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline RealType pdf(const gamma_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::pdf(const gamma_distribution<%1%>&, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_gamma_x(function, x, &result, Policy())) - return result; - - if(x == 0) - { - return 0; - } - result = gamma_p_derivative(shape, x / scale, Policy()) / scale; - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const gamma_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const gamma_distribution<%1%>&, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_gamma_x(function, x, &result, Policy())) - return result; - - result = boost::math::gamma_p(shape, x / scale, Policy()); - return result; -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const gamma_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - - if(p == 1) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = gamma_p_inv(shape, p, Policy()) * scale; - - return result; -} - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<gamma_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)"; - - RealType shape = c.dist.shape(); - RealType scale = c.dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_gamma_x(function, c.param, &result, Policy())) - return result; - - result = gamma_q(shape, c.param / scale, Policy()); - - return result; -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<gamma_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)"; - - RealType shape = c.dist.shape(); - RealType scale = c.dist.scale(); - RealType q = c.param; - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_probability(function, q, &result, Policy())) - return result; - - if(q == 0) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = gamma_q_inv(shape, q, Policy()) * scale; - - return result; -} - -template <class RealType, class Policy> -inline RealType mean(const gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::mean(const gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - - result = shape * scale; - return result; -} - -template <class RealType, class Policy> -inline RealType variance(const gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::variance(const gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - - result = shape * scale * scale; - return result; -} - -template <class RealType, class Policy> -inline RealType mode(const gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::mode(const gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - - if(shape < 1) - return policies::raise_domain_error<RealType>( - function, - "The mode of the gamma distribution is only defined for values of the shape parameter >= 1, but got %1%.", - shape, Policy()); - - result = (shape - 1) * scale; - return result; -} - -//template <class RealType, class Policy> -//inline RealType median(const gamma_distribution<RealType, Policy>& dist) -//{ // Rely on default definition in derived accessors. -//} - -template <class RealType, class Policy> -inline RealType skewness(const gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::skewness(const gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - - result = 2 / sqrt(shape); - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::kurtosis_excess(const gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_gamma(function, scale, shape, &result, Policy())) - return result; - - result = 6 / shape; - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis(const gamma_distribution<RealType, Policy>& dist) -{ - return kurtosis_excess(dist) + 3; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_GAMMA_HPP - -
--- a/any/include/boost/math/distributions/geometric.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,516 +0,0 @@ -// boost\math\distributions\geometric.hpp - -// Copyright John Maddock 2010. -// Copyright Paul A. Bristow 2010. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -// geometric distribution is a discrete probability distribution. -// It expresses the probability distribution of the number (k) of -// events, occurrences, failures or arrivals before the first success. -// supported on the set {0, 1, 2, 3...} - -// Note that the set includes zero (unlike some definitions that start at one). - -// The random variate k is the number of events, occurrences or arrivals. -// k argument may be integral, signed, or unsigned, or floating point. -// If necessary, it has already been promoted from an integral type. - -// Note that the geometric distribution -// (like others including the binomial, geometric & Bernoulli) -// is strictly defined as a discrete function: -// only integral values of k are envisaged. -// However because the method of calculation uses a continuous gamma function, -// it is convenient to treat it as if a continous function, -// and permit non-integral values of k. -// To enforce the strict mathematical model, users should use floor or ceil functions -// on k outside this function to ensure that k is integral. - -// See http://en.wikipedia.org/wiki/geometric_distribution -// http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html -// http://mathworld.wolfram.com/GeometricDistribution.html - -#ifndef BOOST_MATH_SPECIAL_GEOMETRIC_HPP -#define BOOST_MATH_SPECIAL_GEOMETRIC_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b). -#include <boost/math/distributions/complement.hpp> // complement. -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error. -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. -#include <boost/math/distributions/detail/inv_discrete_quantile.hpp> - -#include <boost/type_traits/is_floating_point.hpp> -#include <boost/type_traits/is_integral.hpp> -#include <boost/type_traits/is_same.hpp> -#include <boost/mpl/if.hpp> - -#include <limits> // using std::numeric_limits; -#include <utility> - -#if defined (BOOST_MSVC) -# pragma warning(push) -// This believed not now necessary, so commented out. -//# pragma warning(disable: 4702) // unreachable code. -// in domain_error_imp in error_handling. -#endif - -namespace boost -{ - namespace math - { - namespace geometric_detail - { - // Common error checking routines for geometric distribution function: - template <class RealType, class Policy> - inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) ) - { - *result = policies::raise_domain_error<RealType>( - function, - "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } - - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - return check_success_fraction(function, p, result, pol); - } - - template <class RealType, class Policy> - inline bool check_dist_and_k(const char* function, const RealType& p, RealType k, RealType* result, const Policy& pol) - { - if(check_dist(function, p, result, pol) == false) - { - return false; - } - if( !(boost::math::isfinite)(k) || (k < 0) ) - { // Check k failures. - *result = policies::raise_domain_error<RealType>( - function, - "Number of failures argument is %1%, but must be >= 0 !", k, pol); - return false; - } - return true; - } // Check_dist_and_k - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, RealType p, RealType prob, RealType* result, const Policy& pol) - { - if((check_dist(function, p, result, pol) && detail::check_probability(function, prob, result, pol)) == false) - { - return false; - } - return true; - } // check_dist_and_prob - } // namespace geometric_detail - - template <class RealType = double, class Policy = policies::policy<> > - class geometric_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - geometric_distribution(RealType p) : m_p(p) - { // Constructor stores success_fraction p. - RealType result; - geometric_detail::check_dist( - "geometric_distribution<%1%>::geometric_distribution", - m_p, // Check success_fraction 0 <= p <= 1. - &result, Policy()); - } // geometric_distribution constructor. - - // Private data getter class member functions. - RealType success_fraction() const - { // Probability of success as fraction in range 0 to 1. - return m_p; - } - RealType successes() const - { // Total number of successes r = 1 (for compatibility with negative binomial?). - return 1; - } - - // Parameter estimation. - // (These are copies of negative_binomial distribution with successes = 1). - static RealType find_lower_bound_on_p( - RealType trials, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::geometric<%1%>::find_lower_bound_on_p"; - RealType result = 0; // of error checks. - RealType successes = 1; - RealType failures = trials - successes; - if(false == detail::check_probability(function, alpha, &result, Policy()) - && geometric_detail::check_dist_and_k( - function, RealType(0), failures, &result, Policy())) - { - return result; - } - // Use complement ibeta_inv function for lower bound. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy()); - } // find_lower_bound_on_p - - static RealType find_upper_bound_on_p( - RealType trials, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::geometric<%1%>::find_upper_bound_on_p"; - RealType result = 0; // of error checks. - RealType successes = 1; - RealType failures = trials - successes; - if(false == geometric_detail::check_dist_and_k( - function, RealType(0), failures, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - if(failures == 0) - { - return 1; - }// Use complement ibetac_inv function for upper bound. - // Note adjusted failures value: *not* failures+1 as usual. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. Krishnamoorthy - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy()); - } // find_upper_bound_on_p - - // Estimate number of trials : - // "How many trials do I need to be P% sure of seeing k or fewer failures?" - - static RealType find_minimum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::geometric<%1%>::find_minimum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - result = ibeta_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_failures - - static RealType find_maximum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::geometric<%1%>::find_maximum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - result = ibetac_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_trials complemented - - private: - //RealType m_r; // successes fixed at unity. - RealType m_p; // success_fraction - }; // template <class RealType, class Policy> class geometric_distribution - - typedef geometric_distribution<double> geometric; // Reserved name of type double. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const geometric_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const geometric_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline RealType mean(const geometric_distribution<RealType, Policy>& dist) - { // Mean of geometric distribution = (1-p)/p. - return (1 - dist.success_fraction() ) / dist.success_fraction(); - } // mean - - // median implemented via quantile(half) in derived accessors. - - template <class RealType, class Policy> - inline RealType mode(const geometric_distribution<RealType, Policy>&) - { // Mode of geometric distribution = zero. - BOOST_MATH_STD_USING // ADL of std functions. - return 0; - } // mode - - template <class RealType, class Policy> - inline RealType variance(const geometric_distribution<RealType, Policy>& dist) - { // Variance of Binomial distribution = (1-p) / p^2. - return (1 - dist.success_fraction()) - / (dist.success_fraction() * dist.success_fraction()); - } // variance - - template <class RealType, class Policy> - inline RealType skewness(const geometric_distribution<RealType, Policy>& dist) - { // skewness of geometric distribution = 2-p / (sqrt(r(1-p)) - BOOST_MATH_STD_USING // ADL of std functions. - RealType p = dist.success_fraction(); - return (2 - p) / sqrt(1 - p); - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis(const geometric_distribution<RealType, Policy>& dist) - { // kurtosis of geometric distribution - // http://en.wikipedia.org/wiki/geometric is kurtosis_excess so add 3 - RealType p = dist.success_fraction(); - return 3 + (p*p - 6*p + 6) / (1 - p); - } // kurtosis - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const geometric_distribution<RealType, Policy>& dist) - { // kurtosis excess of geometric distribution - // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess - RealType p = dist.success_fraction(); - return (p*p - 6*p + 6) / (1 - p); - } // kurtosis_excess - - // RealType standard_deviation(const geometric_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - // RealType hazard(const geometric_distribution<RealType, Policy>& dist) - // hazard of geometric distribution provided by derived accessors. - // RealType chf(const geometric_distribution<RealType, Policy>& dist) - // chf of geometric distribution provided by derived accessors. - - template <class RealType, class Policy> - inline RealType pdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - BOOST_MATH_STD_USING // For ADL of math functions. - static const char* function = "boost::math::pdf(const geometric_distribution<%1%>&, %1%)"; - - RealType p = dist.success_fraction(); - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, - p, - k, - &result, Policy())) - { - return result; - } - if (k == 0) - { - return p; // success_fraction - } - RealType q = 1 - p; // Inaccurate for small p? - // So try to avoid inaccuracy for large or small p. - // but has little effect > last significant bit. - //cout << "p * pow(q, k) " << result << endl; // seems best whatever p - //cout << "exp(p * k * log1p(-p)) " << p * exp(k * log1p(-p)) << endl; - //if (p < 0.5) - //{ - // result = p * pow(q, k); - //} - //else - //{ - // result = p * exp(k * log1p(-p)); - //} - result = p * pow(q, k); - return result; - } // geometric_pdf - - template <class RealType, class Policy> - inline RealType cdf(const geometric_distribution<RealType, Policy>& dist, const RealType& k) - { // Cumulative Distribution Function of geometric. - static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)"; - - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType p = dist.success_fraction(); - // Error check: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, - p, - k, - &result, Policy())) - { - return result; - } - if(k == 0) - { - return p; // success_fraction - } - //RealType q = 1 - p; // Bad for small p - //RealType probability = 1 - std::pow(q, k+1); - - RealType z = boost::math::log1p(-p, Policy()) * (k + 1); - RealType probability = -boost::math::expm1(z, Policy()); - - return probability; - } // cdf Cumulative Distribution Function geometric. - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function geometric. - BOOST_MATH_STD_USING - static const char* function = "boost::math::cdf(const geometric_distribution<%1%>&, %1%)"; - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType const& k = c.param; - geometric_distribution<RealType, Policy> const& dist = c.dist; - RealType p = dist.success_fraction(); - // Error check: - RealType result = 0; - if(false == geometric_detail::check_dist_and_k( - function, - p, - k, - &result, Policy())) - { - return result; - } - RealType z = boost::math::log1p(-p, Policy()) * (k+1); - RealType probability = exp(z); - return probability; - } // cdf Complemented Cumulative Distribution Function geometric. - - template <class RealType, class Policy> - inline RealType quantile(const geometric_distribution<RealType, Policy>& dist, const RealType& x) - { // Quantile, percentile/100 or Percent Point geometric function. - // Return the number of expected failures k for a given probability p. - - // Inverse cumulative Distribution Function or Quantile (percentile / 100) of geometric Probability. - // k argument may be integral, signed, or unsigned, or floating point. - - static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING // ADL of std functions. - - RealType success_fraction = dist.success_fraction(); - // Check dist and x. - RealType result = 0; - if(false == geometric_detail::check_dist_and_prob - (function, success_fraction, x, &result, Policy())) - { - return result; - } - - // Special cases. - if (x == 1) - { // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument is 1, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - if (x == 0) - { // No failures are expected if P = 0. - return 0; // Total trials will be just dist.successes. - } - // if (P <= pow(dist.success_fraction(), 1)) - if (x <= success_fraction) - { // p <= pdf(dist, 0) == cdf(dist, 0) - return 0; - } - if (x == 1) - { - return 0; - } - - // log(1-x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small - result = boost::math::log1p(-x, Policy()) / boost::math::log1p(-success_fraction, Policy()) - 1; - // Subtract a few epsilons here too? - // to make sure it doesn't slip over, so ceil would be one too many. - return result; - } // RealType quantile(const geometric_distribution dist, p) - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<geometric_distribution<RealType, Policy>, RealType>& c) - { // Quantile or Percent Point Binomial function. - // Return the number of expected failures k for a given - // complement of the probability Q = 1 - P. - static const char* function = "boost::math::quantile(const geometric_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING - // Error checks: - RealType x = c.param; - const geometric_distribution<RealType, Policy>& dist = c.dist; - RealType success_fraction = dist.success_fraction(); - RealType result = 0; - if(false == geometric_detail::check_dist_and_prob( - function, - success_fraction, - x, - &result, Policy())) - { - return result; - } - - // Special cases: - if(x == 1) - { // There may actually be no answer to this question, - // since the probability of zero failures may be non-zero, - return 0; // but zero is the best we can do: - } - if (-x <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy())) - { // q <= cdf(complement(dist, 0)) == pdf(dist, 0) - return 0; // - } - if(x == 0) - { // Probability 1 - Q == 1 so infinite failures to achieve certainty. - // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument complement is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - // log(x) /log(1-success_fraction) -1; but use log1p in case success_fraction is small - result = log(x) / boost::math::log1p(-success_fraction, Policy()) - 1; - return result; - - } // quantile complement - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#if defined (BOOST_MSVC) -# pragma warning(pop) -#endif - -#endif // BOOST_MATH_SPECIAL_GEOMETRIC_HPP
--- a/any/include/boost/math/distributions/hyperexponential.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,634 +0,0 @@ -// Copyright 2014 Marco Guazzone (marco.guazzone@gmail.com) -// -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -// -// This module implements the Hyper-Exponential distribution. -// -// References: -// - "Queueing Theory in Manufacturing Systems Analysis and Design" by H.T. Papadopolous, C. Heavey and J. Browne (Chapman & Hall/CRC, 1993) -// - http://reference.wolfram.com/language/ref/HyperexponentialDistribution.html -// - http://en.wikipedia.org/wiki/Hyperexponential_distribution -// - -#ifndef BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL_HPP -#define BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL_HPP - - -#include <boost/config.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/exponential.hpp> -#include <boost/math/policies/policy.hpp> -#include <boost/math/special_functions/fpclassify.hpp> -#include <boost/math/tools/precision.hpp> -#include <boost/math/tools/roots.hpp> -#include <boost/range/begin.hpp> -#include <boost/range/end.hpp> -#include <boost/range/size.hpp> -#include <boost/type_traits/has_pre_increment.hpp> -#include <cstddef> -#include <iterator> -#include <limits> -#include <numeric> -#include <utility> -#include <vector> - -#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) -# include <initializer_list> -#endif - -#ifdef _MSC_VER -# pragma warning (push) -# pragma warning(disable:4127) // conditional expression is constant -# pragma warning(disable:4389) // '==' : signed/unsigned mismatch in test_tools -#endif // _MSC_VER - -namespace boost { namespace math { - -namespace detail { - -template <typename Dist> -typename Dist::value_type generic_quantile(const Dist& dist, const typename Dist::value_type& p, const typename Dist::value_type& guess, bool comp, const char* function); - -} // Namespace detail - - -template <typename RealT, typename PolicyT> -class hyperexponential_distribution; - - -namespace /*<unnamed>*/ { namespace hyperexp_detail { - -template <typename T> -void normalize(std::vector<T>& v) -{ - if(!v.size()) - return; // Our error handlers will get this later - const T sum = std::accumulate(v.begin(), v.end(), static_cast<T>(0)); - T final_sum = 0; - const typename std::vector<T>::iterator end = --v.end(); - for (typename std::vector<T>::iterator it = v.begin(); - it != end; - ++it) - { - *it /= sum; - final_sum += *it; - } - *end = 1 - final_sum; // avoids round off errors, ensures the probs really do sum to 1. -} - -template <typename RealT, typename PolicyT> -bool check_probabilities(char const* function, std::vector<RealT> const& probabilities, RealT* presult, PolicyT const& pol) -{ - BOOST_MATH_STD_USING - const std::size_t n = probabilities.size(); - RealT sum = 0; - for (std::size_t i = 0; i < n; ++i) - { - if (probabilities[i] < 0 - || probabilities[i] > 1 - || !(boost::math::isfinite)(probabilities[i])) - { - *presult = policies::raise_domain_error<RealT>(function, - "The elements of parameter \"probabilities\" must be >= 0 and <= 1, but at least one of them was: %1%.", - probabilities[i], - pol); - return false; - } - sum += probabilities[i]; - } - - // - // We try to keep phase probabilities correctly normalized in the distribution constructors, - // however in practice we have to allow for a very slight divergence from a sum of exactly 1: - // - if (fabs(sum - 1) > tools::epsilon<RealT>() * 2) - { - *presult = policies::raise_domain_error<RealT>(function, - "The elements of parameter \"probabilities\" must sum to 1, but their sum is: %1%.", - sum, - pol); - return false; - } - - return true; -} - -template <typename RealT, typename PolicyT> -bool check_rates(char const* function, std::vector<RealT> const& rates, RealT* presult, PolicyT const& pol) -{ - const std::size_t n = rates.size(); - for (std::size_t i = 0; i < n; ++i) - { - if (rates[i] <= 0 - || !(boost::math::isfinite)(rates[i])) - { - *presult = policies::raise_domain_error<RealT>(function, - "The elements of parameter \"rates\" must be > 0, but at least one of them is: %1%.", - rates[i], - pol); - return false; - } - } - return true; -} - -template <typename RealT, typename PolicyT> -bool check_dist(char const* function, std::vector<RealT> const& probabilities, std::vector<RealT> const& rates, RealT* presult, PolicyT const& pol) -{ - BOOST_MATH_STD_USING - if (probabilities.size() != rates.size()) - { - *presult = policies::raise_domain_error<RealT>(function, - "The parameters \"probabilities\" and \"rates\" must have the same length, but their size differ by: %1%.", - fabs(static_cast<RealT>(probabilities.size())-static_cast<RealT>(rates.size())), - pol); - return false; - } - - return check_probabilities(function, probabilities, presult, pol) - && check_rates(function, rates, presult, pol); -} - -template <typename RealT, typename PolicyT> -bool check_x(char const* function, RealT x, RealT* presult, PolicyT const& pol) -{ - if (x < 0 || (boost::math::isnan)(x)) - { - *presult = policies::raise_domain_error<RealT>(function, "The random variable must be >= 0, but is: %1%.", x, pol); - return false; - } - return true; -} - -template <typename RealT, typename PolicyT> -bool check_probability(char const* function, RealT p, RealT* presult, PolicyT const& pol) -{ - if (p < 0 || p > 1 || (boost::math::isnan)(p)) - { - *presult = policies::raise_domain_error<RealT>(function, "The probability be >= 0 and <= 1, but is: %1%.", p, pol); - return false; - } - return true; -} - -template <typename RealT, typename PolicyT> -RealT quantile_impl(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& p, bool comp) -{ - // Don't have a closed form so try to numerically solve the inverse CDF... - - typedef typename policies::evaluation<RealT, PolicyT>::type value_type; - typedef typename policies::normalise<PolicyT, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - static const char* function = comp ? "boost::math::quantile(const boost::math::complemented2_type<boost::math::hyperexponential_distribution<%1%>, %1%>&)" - : "boost::math::quantile(const boost::math::hyperexponential_distribution<%1%>&, %1%)"; - - RealT result = 0; - - if (!check_probability(function, p, &result, PolicyT())) - { - return result; - } - - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - // A possible (but inaccurate) approximation is given below, where the - // quantile is given by the weighted sum of exponential quantiles: - RealT guess = 0; - if (comp) - { - for (std::size_t i = 0; i < n; ++i) - { - const exponential_distribution<RealT,PolicyT> exp(rates[i]); - - guess += probs[i]*quantile(complement(exp, p)); - } - } - else - { - for (std::size_t i = 0; i < n; ++i) - { - const exponential_distribution<RealT,PolicyT> exp(rates[i]); - - guess += probs[i]*quantile(exp, p); - } - } - - // Fast return in case the Hyper-Exponential is essentially an Exponential - if (n == 1) - { - return guess; - } - - value_type q; - q = detail::generic_quantile(hyperexponential_distribution<RealT,forwarding_policy>(probs, rates), - p, - guess, - comp, - function); - - result = policies::checked_narrowing_cast<RealT,forwarding_policy>(q, function); - - return result; -} - -}} // Namespace <unnamed>::hyperexp_detail - - -template <typename RealT = double, typename PolicyT = policies::policy<> > -class hyperexponential_distribution -{ - public: typedef RealT value_type; - public: typedef PolicyT policy_type; - - - public: hyperexponential_distribution() - : probs_(1, 1), - rates_(1, 1) - { - RealT err; - hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", - probs_, - rates_, - &err, - PolicyT()); - } - - // Four arg constructor: no ambiguity here, the arguments must be two pairs of iterators: - public: template <typename ProbIterT, typename RateIterT> - hyperexponential_distribution(ProbIterT prob_first, ProbIterT prob_last, - RateIterT rate_first, RateIterT rate_last) - : probs_(prob_first, prob_last), - rates_(rate_first, rate_last) - { - hyperexp_detail::normalize(probs_); - RealT err; - hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", - probs_, - rates_, - &err, - PolicyT()); - } - - // Two arg constructor from 2 ranges, we SFINAE this out of existance if - // either argument type is incrementable as in that case the type is - // probably an iterator: - public: template <typename ProbRangeT, typename RateRangeT> - hyperexponential_distribution(ProbRangeT const& prob_range, - RateRangeT const& rate_range, - typename boost::disable_if_c<boost::has_pre_increment<ProbRangeT>::value || boost::has_pre_increment<RateRangeT>::value>::type* = 0) - : probs_(boost::begin(prob_range), boost::end(prob_range)), - rates_(boost::begin(rate_range), boost::end(rate_range)) - { - hyperexp_detail::normalize(probs_); - - RealT err; - hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", - probs_, - rates_, - &err, - PolicyT()); - } - - // Two arg constructor for a pair of iterators: we SFINAE this out of - // existance if neither argument types are incrementable. - // Note that we allow different argument types here to allow for - // construction from an array plus a pointer into that array. - public: template <typename RateIterT, typename RateIterT2> - hyperexponential_distribution(RateIterT const& rate_first, - RateIterT2 const& rate_last, - typename boost::enable_if_c<boost::has_pre_increment<RateIterT>::value || boost::has_pre_increment<RateIterT2>::value>::type* = 0) - : probs_(std::distance(rate_first, rate_last), 1), // will be normalized below - rates_(rate_first, rate_last) - { - hyperexp_detail::normalize(probs_); - - RealT err; - hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", - probs_, - rates_, - &err, - PolicyT()); - } - -#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) - // Initializer list constructor: allows for construction from array literals: -public: hyperexponential_distribution(std::initializer_list<RealT> l1, std::initializer_list<RealT> l2) - : probs_(l1.begin(), l1.end()), - rates_(l2.begin(), l2.end()) - { - hyperexp_detail::normalize(probs_); - - RealT err; - hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", - probs_, - rates_, - &err, - PolicyT()); - } - -public: hyperexponential_distribution(std::initializer_list<RealT> l1) - : probs_(l1.size(), 1), - rates_(l1.begin(), l1.end()) - { - hyperexp_detail::normalize(probs_); - - RealT err; - hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", - probs_, - rates_, - &err, - PolicyT()); - } -#endif // !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) - - // Single argument constructor: argument must be a range. - public: template <typename RateRangeT> - hyperexponential_distribution(RateRangeT const& rate_range) - : probs_(boost::size(rate_range), 1), // will be normalized below - rates_(boost::begin(rate_range), boost::end(rate_range)) - { - hyperexp_detail::normalize(probs_); - - RealT err; - hyperexp_detail::check_dist("boost::math::hyperexponential_distribution<%1%>::hyperexponential_distribution", - probs_, - rates_, - &err, - PolicyT()); - } - - public: std::vector<RealT> probabilities() const - { - return probs_; - } - - public: std::vector<RealT> rates() const - { - return rates_; - } - - public: std::size_t num_phases() const - { - return rates_.size(); - } - - - private: std::vector<RealT> probs_; - private: std::vector<RealT> rates_; -}; // class hyperexponential_distribution - - -// Convenient type synonym for double. -typedef hyperexponential_distribution<double> hyperexponential; - - -// Range of permissible values for random variable x -template <typename RealT, typename PolicyT> -std::pair<RealT,RealT> range(hyperexponential_distribution<RealT,PolicyT> const&) -{ - if (std::numeric_limits<RealT>::has_infinity) - { - return std::make_pair(static_cast<RealT>(0), std::numeric_limits<RealT>::infinity()); // 0 to +inf. - } - - return std::make_pair(static_cast<RealT>(0), tools::max_value<RealT>()); // 0 to +<max value> -} - -// Range of supported values for random variable x. -// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. -template <typename RealT, typename PolicyT> -std::pair<RealT,RealT> support(hyperexponential_distribution<RealT,PolicyT> const&) -{ - return std::make_pair(tools::min_value<RealT>(), tools::max_value<RealT>()); // <min value> to +<max value>. -} - -template <typename RealT, typename PolicyT> -RealT pdf(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& x) -{ - BOOST_MATH_STD_USING - RealT result = 0; - - if (!hyperexp_detail::check_x("boost::math::pdf(const boost::math::hyperexponential_distribution<%1%>&, %1%)", x, &result, PolicyT())) - { - return result; - } - - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - for (std::size_t i = 0; i < n; ++i) - { - const exponential_distribution<RealT,PolicyT> exp(rates[i]); - - result += probs[i]*pdf(exp, x); - //result += probs[i]*rates[i]*exp(-rates[i]*x); - } - - return result; -} - -template <typename RealT, typename PolicyT> -RealT cdf(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& x) -{ - RealT result = 0; - - if (!hyperexp_detail::check_x("boost::math::cdf(const boost::math::hyperexponential_distribution<%1%>&, %1%)", x, &result, PolicyT())) - { - return result; - } - - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - for (std::size_t i = 0; i < n; ++i) - { - const exponential_distribution<RealT,PolicyT> exp(rates[i]); - - result += probs[i]*cdf(exp, x); - } - - return result; -} - -template <typename RealT, typename PolicyT> -RealT quantile(hyperexponential_distribution<RealT, PolicyT> const& dist, RealT const& p) -{ - return hyperexp_detail::quantile_impl(dist, p , false); -} - -template <typename RealT, typename PolicyT> -RealT cdf(complemented2_type<hyperexponential_distribution<RealT,PolicyT>, RealT> const& c) -{ - RealT const& x = c.param; - hyperexponential_distribution<RealT,PolicyT> const& dist = c.dist; - - RealT result = 0; - - if (!hyperexp_detail::check_x("boost::math::cdf(boost::math::complemented2_type<const boost::math::hyperexponential_distribution<%1%>&, %1%>)", x, &result, PolicyT())) - { - return result; - } - - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - for (std::size_t i = 0; i < n; ++i) - { - const exponential_distribution<RealT,PolicyT> exp(rates[i]); - - result += probs[i]*cdf(complement(exp, x)); - } - - return result; -} - - -template <typename RealT, typename PolicyT> -RealT quantile(complemented2_type<hyperexponential_distribution<RealT, PolicyT>, RealT> const& c) -{ - RealT const& p = c.param; - hyperexponential_distribution<RealT,PolicyT> const& dist = c.dist; - - return hyperexp_detail::quantile_impl(dist, p , true); -} - -template <typename RealT, typename PolicyT> -RealT mean(hyperexponential_distribution<RealT, PolicyT> const& dist) -{ - RealT result = 0; - - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - for (std::size_t i = 0; i < n; ++i) - { - const exponential_distribution<RealT,PolicyT> exp(rates[i]); - - result += probs[i]*mean(exp); - } - - return result; -} - -template <typename RealT, typename PolicyT> -RealT variance(hyperexponential_distribution<RealT, PolicyT> const& dist) -{ - RealT result = 0; - - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - for (std::size_t i = 0; i < n; ++i) - { - result += probs[i]/(rates[i]*rates[i]); - } - - const RealT mean = boost::math::mean(dist); - - result = 2*result-mean*mean; - - return result; -} - -template <typename RealT, typename PolicyT> -RealT skewness(hyperexponential_distribution<RealT,PolicyT> const& dist) -{ - BOOST_MATH_STD_USING - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - RealT s1 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i} - RealT s2 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^2} - RealT s3 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^3} - for (std::size_t i = 0; i < n; ++i) - { - const RealT p = probs[i]; - const RealT r = rates[i]; - const RealT r2 = r*r; - const RealT r3 = r2*r; - - s1 += p/r; - s2 += p/r2; - s3 += p/r3; - } - - const RealT s1s1 = s1*s1; - - const RealT num = (6*s3 - (3*(2*s2 - s1s1) + s1s1)*s1); - const RealT den = (2*s2 - s1s1); - - return num / pow(den, static_cast<RealT>(1.5)); -} - -template <typename RealT, typename PolicyT> -RealT kurtosis(hyperexponential_distribution<RealT,PolicyT> const& dist) -{ - const std::size_t n = dist.num_phases(); - const std::vector<RealT> probs = dist.probabilities(); - const std::vector<RealT> rates = dist.rates(); - - RealT s1 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i} - RealT s2 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^2} - RealT s3 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^3} - RealT s4 = 0; // \sum_{i=1}^n \frac{p_i}{\lambda_i^4} - for (std::size_t i = 0; i < n; ++i) - { - const RealT p = probs[i]; - const RealT r = rates[i]; - const RealT r2 = r*r; - const RealT r3 = r2*r; - const RealT r4 = r3*r; - - s1 += p/r; - s2 += p/r2; - s3 += p/r3; - s4 += p/r4; - } - - const RealT s1s1 = s1*s1; - - const RealT num = (24*s4 - 24*s3*s1 + 3*(2*(2*s2 - s1s1) + s1s1)*s1s1); - const RealT den = (2*s2 - s1s1); - - return num/(den*den); -} - -template <typename RealT, typename PolicyT> -RealT kurtosis_excess(hyperexponential_distribution<RealT,PolicyT> const& dist) -{ - return kurtosis(dist) - 3; -} - -template <typename RealT, typename PolicyT> -RealT mode(hyperexponential_distribution<RealT,PolicyT> const& /*dist*/) -{ - return 0; -} - -}} // namespace boost::math - -#ifdef BOOST_MSVC -#pragma warning (pop) -#endif -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> -#include <boost/math/distributions/detail/generic_quantile.hpp> - -#endif // BOOST_MATH_DISTRIBUTIONS_HYPEREXPONENTIAL
--- a/any/include/boost/math/distributions/hypergeometric.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,293 +0,0 @@ -// Copyright 2008 Gautam Sewani -// Copyright 2008 John Maddock -// -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_HYPERGEOMETRIC_HPP -#define BOOST_MATH_DISTRIBUTIONS_HYPERGEOMETRIC_HPP - -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/hypergeometric_pdf.hpp> -#include <boost/math/distributions/detail/hypergeometric_cdf.hpp> -#include <boost/math/distributions/detail/hypergeometric_quantile.hpp> -#include <boost/math/special_functions/fpclassify.hpp> - - -namespace boost { namespace math { - - template <class RealType = double, class Policy = policies::policy<> > - class hypergeometric_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - hypergeometric_distribution(unsigned r, unsigned n, unsigned N) // Constructor. - : m_n(n), m_N(N), m_r(r) - { - static const char* function = "boost::math::hypergeometric_distribution<%1%>::hypergeometric_distribution"; - RealType ret; - check_params(function, &ret); - } - // Accessor functions. - unsigned total()const - { - return m_N; - } - - unsigned defective()const - { - return m_r; - } - - unsigned sample_count()const - { - return m_n; - } - - bool check_params(const char* function, RealType* result)const - { - if(m_r > m_N) - { - *result = boost::math::policies::raise_domain_error<RealType>( - function, "Parameter r out of range: must be <= N but got %1%", static_cast<RealType>(m_r), Policy()); - return false; - } - if(m_n > m_N) - { - *result = boost::math::policies::raise_domain_error<RealType>( - function, "Parameter n out of range: must be <= N but got %1%", static_cast<RealType>(m_n), Policy()); - return false; - } - return true; - } - bool check_x(unsigned x, const char* function, RealType* result)const - { - if(x < static_cast<unsigned>((std::max)(0, (int)(m_n + m_r) - (int)(m_N)))) - { - *result = boost::math::policies::raise_domain_error<RealType>( - function, "Random variable out of range: must be > 0 and > m + r - N but got %1%", static_cast<RealType>(x), Policy()); - return false; - } - if(x > (std::min)(m_r, m_n)) - { - *result = boost::math::policies::raise_domain_error<RealType>( - function, "Random variable out of range: must be less than both n and r but got %1%", static_cast<RealType>(x), Policy()); - return false; - } - return true; - } - - private: - // Data members: - unsigned m_n; // number of items picked - unsigned m_N; // number of "total" items - unsigned m_r; // number of "defective" items - - }; // class hypergeometric_distribution - - typedef hypergeometric_distribution<double> hypergeometric; - - template <class RealType, class Policy> - inline const std::pair<unsigned, unsigned> range(const hypergeometric_distribution<RealType, Policy>& dist) - { // Range of permissible values for random variable x. -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable:4267) -#endif - unsigned r = dist.defective(); - unsigned n = dist.sample_count(); - unsigned N = dist.total(); - unsigned l = static_cast<unsigned>((std::max)(0, (int)(n + r) - (int)(N))); - unsigned u = (std::min)(r, n); - return std::pair<unsigned, unsigned>(l, u); -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - } - - template <class RealType, class Policy> - inline const std::pair<unsigned, unsigned> support(const hypergeometric_distribution<RealType, Policy>& d) - { - return range(d); - } - - template <class RealType, class Policy> - inline RealType pdf(const hypergeometric_distribution<RealType, Policy>& dist, const unsigned& x) - { - static const char* function = "boost::math::pdf(const hypergeometric_distribution<%1%>&, const %1%&)"; - RealType result = 0; - if(!dist.check_params(function, &result)) - return result; - if(!dist.check_x(x, function, &result)) - return result; - - return boost::math::detail::hypergeometric_pdf<RealType>( - x, dist.defective(), dist.sample_count(), dist.total(), Policy()); - } - - template <class RealType, class Policy, class U> - inline RealType pdf(const hypergeometric_distribution<RealType, Policy>& dist, const U& x) - { - BOOST_MATH_STD_USING - static const char* function = "boost::math::pdf(const hypergeometric_distribution<%1%>&, const %1%&)"; - RealType r = static_cast<RealType>(x); - unsigned u = itrunc(r, typename policies::normalise<Policy, policies::rounding_error<policies::ignore_error> >::type()); - if(u != r) - { - return boost::math::policies::raise_domain_error<RealType>( - function, "Random variable out of range: must be an integer but got %1%", r, Policy()); - } - return pdf(dist, u); - } - - template <class RealType, class Policy> - inline RealType cdf(const hypergeometric_distribution<RealType, Policy>& dist, const unsigned& x) - { - static const char* function = "boost::math::cdf(const hypergeometric_distribution<%1%>&, const %1%&)"; - RealType result = 0; - if(!dist.check_params(function, &result)) - return result; - if(!dist.check_x(x, function, &result)) - return result; - - return boost::math::detail::hypergeometric_cdf<RealType>( - x, dist.defective(), dist.sample_count(), dist.total(), false, Policy()); - } - - template <class RealType, class Policy, class U> - inline RealType cdf(const hypergeometric_distribution<RealType, Policy>& dist, const U& x) - { - BOOST_MATH_STD_USING - static const char* function = "boost::math::cdf(const hypergeometric_distribution<%1%>&, const %1%&)"; - RealType r = static_cast<RealType>(x); - unsigned u = itrunc(r, typename policies::normalise<Policy, policies::rounding_error<policies::ignore_error> >::type()); - if(u != r) - { - return boost::math::policies::raise_domain_error<RealType>( - function, "Random variable out of range: must be an integer but got %1%", r, Policy()); - } - return cdf(dist, u); - } - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<hypergeometric_distribution<RealType, Policy>, unsigned>& c) - { - static const char* function = "boost::math::cdf(const hypergeometric_distribution<%1%>&, const %1%&)"; - RealType result = 0; - if(!c.dist.check_params(function, &result)) - return result; - if(!c.dist.check_x(c.param, function, &result)) - return result; - - return boost::math::detail::hypergeometric_cdf<RealType>( - c.param, c.dist.defective(), c.dist.sample_count(), c.dist.total(), true, Policy()); - } - - template <class RealType, class Policy, class U> - inline RealType cdf(const complemented2_type<hypergeometric_distribution<RealType, Policy>, U>& c) - { - BOOST_MATH_STD_USING - static const char* function = "boost::math::cdf(const hypergeometric_distribution<%1%>&, const %1%&)"; - RealType r = static_cast<RealType>(c.param); - unsigned u = itrunc(r, typename policies::normalise<Policy, policies::rounding_error<policies::ignore_error> >::type()); - if(u != r) - { - return boost::math::policies::raise_domain_error<RealType>( - function, "Random variable out of range: must be an integer but got %1%", r, Policy()); - } - return cdf(complement(c.dist, u)); - } - - template <class RealType, class Policy> - inline RealType quantile(const hypergeometric_distribution<RealType, Policy>& dist, const RealType& p) - { - BOOST_MATH_STD_USING // for ADL of std functions - - // Checking function argument - RealType result = 0; - const char* function = "boost::math::quantile(const hypergeometric_distribution<%1%>&, %1%)"; - if (false == dist.check_params(function, &result)) return result; - if(false == detail::check_probability(function, p, &result, Policy())) return result; - - return static_cast<RealType>(detail::hypergeometric_quantile(p, RealType(1 - p), dist.defective(), dist.sample_count(), dist.total(), Policy())); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<hypergeometric_distribution<RealType, Policy>, RealType>& c) - { - BOOST_MATH_STD_USING // for ADL of std functions - - // Checking function argument - RealType result = 0; - const char* function = "quantile(const complemented2_type<hypergeometric_distribution<%1%>, %1%>&)"; - if (false == c.dist.check_params(function, &result)) return result; - if(false == detail::check_probability(function, c.param, &result, Policy())) return result; - - return static_cast<RealType>(detail::hypergeometric_quantile(RealType(1 - c.param), c.param, c.dist.defective(), c.dist.sample_count(), c.dist.total(), Policy())); - } // quantile - - template <class RealType, class Policy> - inline RealType mean(const hypergeometric_distribution<RealType, Policy>& dist) - { - return static_cast<RealType>(dist.defective() * dist.sample_count()) / dist.total(); - } // RealType mean(const hypergeometric_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType variance(const hypergeometric_distribution<RealType, Policy>& dist) - { - RealType r = static_cast<RealType>(dist.defective()); - RealType n = static_cast<RealType>(dist.sample_count()); - RealType N = static_cast<RealType>(dist.total()); - return n * r * (N - r) * (N - n) / (N * N * (N - 1)); - } // RealType variance(const hypergeometric_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType mode(const hypergeometric_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING - RealType r = static_cast<RealType>(dist.defective()); - RealType n = static_cast<RealType>(dist.sample_count()); - RealType N = static_cast<RealType>(dist.total()); - return floor((r + 1) * (n + 1) / (N + 2)); - } - - template <class RealType, class Policy> - inline RealType skewness(const hypergeometric_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING - RealType r = static_cast<RealType>(dist.defective()); - RealType n = static_cast<RealType>(dist.sample_count()); - RealType N = static_cast<RealType>(dist.total()); - return (N - 2 * r) * sqrt(N - 1) * (N - 2 * n) / (sqrt(n * r * (N - r) * (N - n)) * (N - 2)); - } // RealType skewness(const hypergeometric_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const hypergeometric_distribution<RealType, Policy>& dist) - { - RealType r = static_cast<RealType>(dist.defective()); - RealType n = static_cast<RealType>(dist.sample_count()); - RealType N = static_cast<RealType>(dist.total()); - RealType t1 = N * N * (N - 1) / (r * (N - 2) * (N - 3) * (N - r)); - RealType t2 = (N * (N + 1) - 6 * N * (N - r)) / (n * (N - n)) - + 3 * r * (N - r) * (N + 6) / (N * N) - 6; - return t1 * t2; - } // RealType kurtosis_excess(const hypergeometric_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis(const hypergeometric_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist) + 3; - } // RealType kurtosis_excess(const hypergeometric_distribution<RealType, Policy>& dist) -}} // namespaces - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // include guard
--- a/any/include/boost/math/distributions/inverse_chi_squared.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,391 +0,0 @@ -// Copyright John Maddock 2010. -// Copyright Paul A. Bristow 2010. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP -#define BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/gamma.hpp> // for incomplete beta. -#include <boost/math/distributions/complement.hpp> // for complements. -#include <boost/math/distributions/detail/common_error_handling.hpp> // for error checks. -#include <boost/math/special_functions/fpclassify.hpp> // for isfinite - -// See http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution -// for definitions of this scaled version. -// See http://en.wikipedia.org/wiki/Inverse-chi-square_distribution -// for unscaled version. - -// http://reference.wolfram.com/mathematica/ref/InverseChiSquareDistribution.html -// Weisstein, Eric W. "Inverse Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. -// http://mathworld.wolfram.com/InverseChi-SquaredDistribution.html - -#include <utility> - -namespace boost{ namespace math{ - -namespace detail -{ - template <class RealType, class Policy> - inline bool check_inverse_chi_squared( // Check both distribution parameters. - const char* function, - RealType degrees_of_freedom, // degrees_of_freedom (aka nu). - RealType scale, // scale (aka sigma^2) - RealType* result, - const Policy& pol) - { - return check_scale(function, scale, result, pol) - && check_df(function, degrees_of_freedom, - result, pol); - } // bool check_inverse_chi_squared -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class inverse_chi_squared_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - inverse_chi_squared_distribution(RealType df, RealType l_scale) : m_df(df), m_scale (l_scale) - { - RealType result; - detail::check_df( - "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", - m_df, &result, Policy()) - && detail::check_scale( -"boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", - m_scale, &result, Policy()); - } // inverse_chi_squared_distribution constructor - - inverse_chi_squared_distribution(RealType df = 1) : m_df(df) - { - RealType result; - m_scale = 1 / m_df ; // Default scale = 1 / degrees of freedom (Wikipedia definition 1). - detail::check_df( - "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", - m_df, &result, Policy()); - } // inverse_chi_squared_distribution - - RealType degrees_of_freedom()const - { - return m_df; // aka nu - } - RealType scale()const - { - return m_scale; // aka xi - } - - // Parameter estimation: NOT implemented yet. - //static RealType find_degrees_of_freedom( - // RealType difference_from_variance, - // RealType alpha, - // RealType beta, - // RealType variance, - // RealType hint = 100); - -private: - // Data members: - RealType m_df; // degrees of freedom are treated as a real number. - RealType m_scale; // distribution scale. - -}; // class chi_squared_distribution - -typedef inverse_chi_squared_distribution<double> inverse_chi_squared; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const inverse_chi_squared_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + infinity. -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const inverse_chi_squared_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity. -} - -template <class RealType, class Policy> -RealType pdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions. - RealType df = dist.degrees_of_freedom(); - RealType scale = dist.scale(); - RealType error_result; - - static const char* function = "boost::math::pdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; - - if(false == detail::check_inverse_chi_squared - (function, df, scale, &error_result, Policy()) - ) - { // Bad distribution. - return error_result; - } - if((x < 0) || !(boost::math::isfinite)(x)) - { // Bad x. - return policies::raise_domain_error<RealType>( - function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy()); - } - - if(x == 0) - { // Treat as special case. - return 0; - } - // Wikipedia scaled inverse chi sq (df, scale) related to inv gamma (df/2, df * scale /2) - // so use inverse gamma pdf with shape = df/2, scale df * scale /2 - // RealType shape = df /2; // inv_gamma shape - // RealType scale = df * scale/2; // inv_gamma scale - // RealType result = gamma_p_derivative(shape, scale / x, Policy()) * scale / (x * x); - RealType result = df * scale/2 / x; - if(result < tools::min_value<RealType>()) - return 0; // Random variable is near enough infinite. - result = gamma_p_derivative(df/2, result, Policy()) * df * scale/2; - if(result != 0) // prevent 0 / 0, gamma_p_derivative -> 0 faster than x^2 - result /= (x * x); - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) -{ - static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; - RealType df = dist.degrees_of_freedom(); - RealType scale = dist.scale(); - RealType error_result; - - if(false == - detail::check_inverse_chi_squared(function, df, scale, &error_result, Policy()) - ) - { // Bad distribution. - return error_result; - } - if((x < 0) || !(boost::math::isfinite)(x)) - { // Bad x. - return policies::raise_domain_error<RealType>( - function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy()); - } - if (x == 0) - { // Treat zero as a special case. - return 0; - } - // RealType shape = df /2; // inv_gamma shape, - // RealType scale = df * scale/2; // inv_gamma scale, - // result = boost::math::gamma_q(shape, scale / x, Policy()); // inverse_gamma code. - return boost::math::gamma_q(df / 2, (df * (scale / 2)) / x, Policy()); -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& p) -{ - using boost::math::gamma_q_inv; - RealType df = dist.degrees_of_freedom(); - RealType scale = dist.scale(); - - static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)"; - // Error check: - RealType error_result; - if(false == detail::check_df( - function, df, &error_result, Policy()) - && detail::check_probability( - function, p, &error_result, Policy())) - { - return error_result; - } - if(false == detail::check_probability( - function, p, &error_result, Policy())) - { - return error_result; - } - // RealType shape = df /2; // inv_gamma shape, - // RealType scale = df * scale/2; // inv_gamma scale, - // result = scale / gamma_q_inv(shape, p, Policy()); - RealType result = gamma_q_inv(df /2, p, Policy()); - if(result == 0) - return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy()); - result = df * (scale / 2) / result; - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c) -{ - using boost::math::gamma_q_inv; - RealType const& df = c.dist.degrees_of_freedom(); - RealType const& scale = c.dist.scale(); - RealType const& x = c.param; - static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; - // Error check: - RealType error_result; - if(false == detail::check_df( - function, df, &error_result, Policy())) - { - return error_result; - } - if (x == 0) - { // Treat zero as a special case. - return 1; - } - if((x < 0) || !(boost::math::isfinite)(x)) - { - return policies::raise_domain_error<RealType>( - function, "inverse Chi Square parameter was %1%, but must be > 0 !", x, Policy()); - } - // RealType shape = df /2; // inv_gamma shape, - // RealType scale = df * scale/2; // inv_gamma scale, - // result = gamma_p(shape, scale/c.param, Policy()); use inv_gamma. - - return gamma_p(df / 2, (df * scale/2) / x, Policy()); // OK -} // cdf(complemented - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c) -{ - using boost::math::gamma_q_inv; - - RealType const& df = c.dist.degrees_of_freedom(); - RealType const& scale = c.dist.scale(); - RealType const& q = c.param; - static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)"; - // Error check: - RealType error_result; - if(false == detail::check_df(function, df, &error_result, Policy())) - { - return error_result; - } - if(false == detail::check_probability(function, q, &error_result, Policy())) - { - return error_result; - } - // RealType shape = df /2; // inv_gamma shape, - // RealType scale = df * scale/2; // inv_gamma scale, - // result = scale / gamma_p_inv(shape, q, Policy()); // using inv_gamma. - RealType result = gamma_p_inv(df/2, q, Policy()); - if(result == 0) - return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy()); - result = (df * scale / 2) / result; - return result; -} // quantile(const complement - -template <class RealType, class Policy> -inline RealType mean(const inverse_chi_squared_distribution<RealType, Policy>& dist) -{ // Mean of inverse Chi-Squared distribution. - RealType df = dist.degrees_of_freedom(); - RealType scale = dist.scale(); - - static const char* function = "boost::math::mean(const inverse_chi_squared_distribution<%1%>&)"; - if(df <= 2) - return policies::raise_domain_error<RealType>( - function, - "inverse Chi-Squared distribution only has a mode for degrees of freedom > 2, but got degrees of freedom = %1%.", - df, Policy()); - return (df * scale) / (df - 2); -} // mean - -template <class RealType, class Policy> -inline RealType variance(const inverse_chi_squared_distribution<RealType, Policy>& dist) -{ // Variance of inverse Chi-Squared distribution. - RealType df = dist.degrees_of_freedom(); - RealType scale = dist.scale(); - static const char* function = "boost::math::variance(const inverse_chi_squared_distribution<%1%>&)"; - if(df <= 4) - { - return policies::raise_domain_error<RealType>( - function, - "inverse Chi-Squared distribution only has a variance for degrees of freedom > 4, but got degrees of freedom = %1%.", - df, Policy()); - } - return 2 * df * df * scale * scale / ((df - 2)*(df - 2) * (df - 4)); -} // variance - -template <class RealType, class Policy> -inline RealType mode(const inverse_chi_squared_distribution<RealType, Policy>& dist) -{ // mode is not defined in Mathematica. - // See Discussion section http://en.wikipedia.org/wiki/Talk:Scaled-inverse-chi-square_distribution - // for origin of the formula used below. - - RealType df = dist.degrees_of_freedom(); - RealType scale = dist.scale(); - static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)"; - if(df < 0) - return policies::raise_domain_error<RealType>( - function, - "inverse Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.", - df, Policy()); - return (df * scale) / (df + 2); -} - -//template <class RealType, class Policy> -//inline RealType median(const inverse_chi_squared_distribution<RealType, Policy>& dist) -//{ // Median is given by Quantile[dist, 1/2] -// RealType df = dist.degrees_of_freedom(); -// if(df <= 1) -// return tools::domain_error<RealType>( -// BOOST_CURRENT_FUNCTION, -// "The inverse_Chi-Squared distribution only has a median for degrees of freedom >= 0, but got degrees of freedom = %1%.", -// df); -// return df; -//} -// Now implemented via quantile(half) in derived accessors. - -template <class RealType, class Policy> -inline RealType skewness(const inverse_chi_squared_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // For ADL - RealType df = dist.degrees_of_freedom(); - static const char* function = "boost::math::skewness(const inverse_chi_squared_distribution<%1%>&)"; - if(df <= 6) - return policies::raise_domain_error<RealType>( - function, - "inverse Chi-Squared distribution only has a skewness for degrees of freedom > 6, but got degrees of freedom = %1%.", - df, Policy()); - - return 4 * sqrt (2 * (df - 4)) / (df - 6); // Not a function of scale. -} - -template <class RealType, class Policy> -inline RealType kurtosis(const inverse_chi_squared_distribution<RealType, Policy>& dist) -{ - RealType df = dist.degrees_of_freedom(); - static const char* function = "boost::math::kurtosis(const inverse_chi_squared_distribution<%1%>&)"; - if(df <= 8) - return policies::raise_domain_error<RealType>( - function, - "inverse Chi-Squared distribution only has a kurtosis for degrees of freedom > 8, but got degrees of freedom = %1%.", - df, Policy()); - - return kurtosis_excess(dist) + 3; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const inverse_chi_squared_distribution<RealType, Policy>& dist) -{ - RealType df = dist.degrees_of_freedom(); - static const char* function = "boost::math::kurtosis(const inverse_chi_squared_distribution<%1%>&)"; - if(df <= 8) - return policies::raise_domain_error<RealType>( - function, - "inverse Chi-Squared distribution only has a kurtosis excess for degrees of freedom > 8, but got degrees of freedom = %1%.", - df, Policy()); - - return 12 * (5 * df - 22) / ((df - 6 )*(df - 8)); // Not a function of scale. -} - -// -// Parameter estimation comes last: -// - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP
--- a/any/include/boost/math/distributions/inverse_gamma.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,461 +0,0 @@ -// inverse_gamma.hpp - -// Copyright Paul A. Bristow 2010. -// Copyright John Maddock 2010. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_INVERSE_GAMMA_HPP -#define BOOST_STATS_INVERSE_GAMMA_HPP - -// Inverse Gamma Distribution is a two-parameter family -// of continuous probability distributions -// on the positive real line, which is the distribution of -// the reciprocal of a variable distributed according to the gamma distribution. - -// http://en.wikipedia.org/wiki/Inverse-gamma_distribution -// http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html - -// See also gamma distribution at gamma.hpp: -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm -// http://mathworld.wolfram.com/GammaDistribution.html -// http://en.wikipedia.org/wiki/Gamma_distribution - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/gamma.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> - -#include <utility> - -namespace boost{ namespace math -{ -namespace detail -{ - -template <class RealType, class Policy> -inline bool check_inverse_gamma_shape( - const char* function, // inverse_gamma - RealType shape, // shape aka alpha - RealType* result, // to update, perhaps with NaN - const Policy& pol) -{ // Sources say shape argument must be > 0 - // but seems logical to allow shape zero as special case, - // returning pdf and cdf zero (but not < 0). - // (Functions like mean, variance with other limits on shape are checked - // in version including an operator & limit below). - if((shape < 0) || !(boost::math::isfinite)(shape)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but must be >= 0 !", shape, pol); - return false; - } - return true; -} //bool check_inverse_gamma_shape - -template <class RealType, class Policy> -inline bool check_inverse_gamma_x( - const char* function, - RealType const& x, - RealType* result, const Policy& pol) -{ - if((x < 0) || !(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate is %1% but must be >= 0 !", x, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_inverse_gamma( - const char* function, // TODO swap these over, so shape is first. - RealType scale, // scale aka beta - RealType shape, // shape aka alpha - RealType* result, const Policy& pol) -{ - return check_scale(function, scale, result, pol) - && check_inverse_gamma_shape(function, shape, result, pol); -} // bool check_inverse_gamma - -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class inverse_gamma_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - inverse_gamma_distribution(RealType l_shape = 1, RealType l_scale = 1) - : m_shape(l_shape), m_scale(l_scale) - { - RealType result; - detail::check_inverse_gamma( - "boost::math::inverse_gamma_distribution<%1%>::inverse_gamma_distribution", - l_scale, l_shape, &result, Policy()); - } - - RealType shape()const - { - return m_shape; - } - - RealType scale()const - { - return m_scale; - } -private: - // - // Data members: - // - RealType m_shape; // distribution shape - RealType m_scale; // distribution scale -}; - -typedef inverse_gamma_distribution<double> inverse_gamma; -// typedef - but potential clash with name of inverse gamma *function*. -// but there is a typedef for gamma -// typedef boost::math::gamma_distribution<Type, Policy> gamma; - -// Allow random variable x to be zero, treated as a special case (unlike some definitions). - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const inverse_gamma_distribution<RealType, Policy>& /* dist */) -{ // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const inverse_gamma_distribution<RealType, Policy>& /* dist */) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - using boost::math::tools::min_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline RealType pdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::pdf(const inverse_gamma_distribution<%1%>&, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) - { // distribution parameters bad. - return result; - } - if(x == 0) - { // Treat random variate zero as a special case. - return 0; - } - else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy())) - { // x bad. - return result; - } - result = scale / x; - if(result < tools::min_value<RealType>()) - return 0; // random variable is infinite or so close as to make no difference. - result = gamma_p_derivative(shape, result, Policy()) * scale; - if(0 != result) - { - if(x < 0) - { - // x * x may under or overflow, likewise our result, - // so be extra careful about the arithmetic: - RealType lim = tools::max_value<RealType>() * x; - if(lim < result) - return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy()); - result /= x; - if(lim < result) - return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy()); - result /= x; - } - result /= (x * x); - } - // better than naive - // result = (pow(scale, shape) * pow(x, (-shape -1)) * exp(-scale/x) ) / tgamma(shape); - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const inverse_gamma_distribution<%1%>&, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) - { // distribution parameters bad. - return result; - } - if (x == 0) - { // Treat zero as a special case. - return 0; - } - else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy())) - { // x bad - return result; - } - result = boost::math::gamma_q(shape, scale / x, Policy()); - // result = tgamma(shape, scale / x) / tgamma(shape); // naive using tgamma - return result; -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - using boost::math::gamma_q_inv; - - static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - if(p == 1) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - result = gamma_q_inv(shape, p, Policy()); - if((result < 1) && (result * tools::max_value<RealType>() < scale)) - return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy()); - result = scale / result; - return result; -} - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)"; - - RealType shape = c.dist.shape(); - RealType scale = c.dist.scale(); - - RealType result = 0; - if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_inverse_gamma_x(function, c.param, &result, Policy())) - return result; - - if(c.param == 0) - return 1; // Avoid division by zero - - //result = 1. - gamma_q(shape, c.param / scale, Policy()); - result = gamma_p(shape, scale/c.param, Policy()); - return result; -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)"; - - RealType shape = c.dist.shape(); - RealType scale = c.dist.scale(); - RealType q = c.param; - - RealType result = 0; - if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_probability(function, q, &result, Policy())) - return result; - - if(q == 0) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - result = gamma_p_inv(shape, q, Policy()); - if((result < 1) && (result * tools::max_value<RealType>() < scale)) - return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy()); - result = scale / result; - return result; -} - -template <class RealType, class Policy> -inline RealType mean(const inverse_gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::mean(const inverse_gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if((shape <= 1) || !(boost::math::isfinite)(shape)) - { - result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but for a defined mean it must be > 1", shape, Policy()); - return result; - } - result = scale / (shape - 1); - return result; -} // mean - -template <class RealType, class Policy> -inline RealType variance(const inverse_gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::variance(const inverse_gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if((shape <= 2) || !(boost::math::isfinite)(shape)) - { - result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but for a defined variance it must be > 2", shape, Policy()); - return result; - } - result = (scale * scale) / ((shape - 1) * (shape -1) * (shape -2)); - return result; -} - -template <class RealType, class Policy> -inline RealType mode(const inverse_gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::mode(const inverse_gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) - { - return result; - } - // Only defined for shape >= 0, but is checked by check_inverse_gamma. - result = scale / (shape + 1); - return result; -} - -//template <class RealType, class Policy> -//inline RealType median(const gamma_distribution<RealType, Policy>& dist) -//{ // Wikipedia does not define median, - // so rely on default definition quantile(0.5) in derived accessors. -// return result. -//} - -template <class RealType, class Policy> -inline RealType skewness(const inverse_gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::skewness(const inverse_gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - RealType result = 0; - - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if((shape <= 3) || !(boost::math::isfinite)(shape)) - { - result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but for a defined skewness it must be > 3", shape, Policy()); - return result; - } - result = (4 * sqrt(shape - 2) ) / (shape - 3); - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const inverse_gamma_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::kurtosis_excess(const inverse_gamma_distribution<%1%>&)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if((shape <= 4) || !(boost::math::isfinite)(shape)) - { - result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but for a defined kurtosis excess it must be > 4", shape, Policy()); - return result; - } - result = (30 * shape - 66) / ((shape - 3) * (shape - 4)); - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis(const inverse_gamma_distribution<RealType, Policy>& dist) -{ - static const char* function = "boost::math::kurtosis(const inverse_gamma_distribution<%1%>&)"; - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if((shape <= 4) || !(boost::math::isfinite)(shape)) - { - result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but for a defined kurtosis it must be > 4", shape, Policy()); - return result; - } - return kurtosis_excess(dist) + 3; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_INVERSE_GAMMA_HPP
--- a/any/include/boost/math/distributions/inverse_gaussian.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,527 +0,0 @@ -// Copyright John Maddock 2010. -// Copyright Paul A. Bristow 2010. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_INVERSE_GAUSSIAN_HPP -#define BOOST_STATS_INVERSE_GAUSSIAN_HPP - -#ifdef _MSC_VER -#pragma warning(disable: 4512) // assignment operator could not be generated -#endif - -// http://en.wikipedia.org/wiki/Normal-inverse_Gaussian_distribution -// http://mathworld.wolfram.com/InverseGaussianDistribution.html - -// The normal-inverse Gaussian distribution -// also called the Wald distribution (some sources limit this to when mean = 1). - -// It is the continuous probability distribution -// that is defined as the normal variance-mean mixture where the mixing density is the -// inverse Gaussian distribution. The tails of the distribution decrease more slowly -// than the normal distribution. It is therefore suitable to model phenomena -// where numerically large values are more probable than is the case for the normal distribution. - -// The Inverse Gaussian distribution was first studied in relationship to Brownian motion. -// In 1956 M.C.K. Tweedie used the name 'Inverse Gaussian' because there is an inverse -// relationship between the time to cover a unit distance and distance covered in unit time. - -// Examples are returns from financial assets and turbulent wind speeds. -// The normal-inverse Gaussian distributions form -// a subclass of the generalised hyperbolic distributions. - -// See also - -// http://en.wikipedia.org/wiki/Normal_distribution -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm -// Also: -// Weisstein, Eric W. "Normal Distribution." -// From MathWorld--A Wolfram Web Resource. -// http://mathworld.wolfram.com/NormalDistribution.html - -// http://www.jstatsoft.org/v26/i04/paper General class of inverse Gaussian distributions. -// ig package - withdrawn but at http://cran.r-project.org/src/contrib/Archive/ig/ - -// http://www.stat.ucl.ac.be/ISdidactique/Rhelp/library/SuppDists/html/inverse_gaussian.html -// R package for dinverse_gaussian, ... - -// http://www.statsci.org/s/inverse_gaussian.s and http://www.statsci.org/s/inverse_gaussian.html - -//#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/erf.hpp> // for erf/erfc. -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/normal.hpp> -#include <boost/math/distributions/gamma.hpp> // for gamma function -// using boost::math::gamma_p; - -#include <boost/math/tools/tuple.hpp> -//using std::tr1::tuple; -//using std::tr1::make_tuple; -#include <boost/math/tools/roots.hpp> -//using boost::math::tools::newton_raphson_iterate; - -#include <utility> - -namespace boost{ namespace math{ - -template <class RealType = double, class Policy = policies::policy<> > -class inverse_gaussian_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - inverse_gaussian_distribution(RealType l_mean = 1, RealType l_scale = 1) - : m_mean(l_mean), m_scale(l_scale) - { // Default is a 1,1 inverse_gaussian distribution. - static const char* function = "boost::math::inverse_gaussian_distribution<%1%>::inverse_gaussian_distribution"; - - RealType result; - detail::check_scale(function, l_scale, &result, Policy()); - detail::check_location(function, l_mean, &result, Policy()); - detail::check_x_gt0(function, l_mean, &result, Policy()); - } - - RealType mean()const - { // alias for location. - return m_mean; // aka mu - } - - // Synonyms, provided to allow generic use of find_location and find_scale. - RealType location()const - { // location, aka mu. - return m_mean; - } - RealType scale()const - { // scale, aka lambda. - return m_scale; - } - - RealType shape()const - { // shape, aka phi = lambda/mu. - return m_scale / m_mean; - } - -private: - // - // Data members: - // - RealType m_mean; // distribution mean or location, aka mu. - RealType m_scale; // distribution standard deviation or scale, aka lambda. -}; // class normal_distribution - -typedef inverse_gaussian_distribution<double> inverse_gaussian; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const inverse_gaussian_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x, zero to max. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0.), max_value<RealType>()); // - to + max value. -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const inverse_gaussian_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x, zero to max. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0.), max_value<RealType>()); // - to + max value. -} - -template <class RealType, class Policy> -inline RealType pdf(const inverse_gaussian_distribution<RealType, Policy>& dist, const RealType& x) -{ // Probability Density Function - BOOST_MATH_STD_USING // for ADL of std functions - - RealType scale = dist.scale(); - RealType mean = dist.mean(); - RealType result = 0; - static const char* function = "boost::math::pdf(const inverse_gaussian_distribution<%1%>&, %1%)"; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, mean, &result, Policy())) - { - return result; - } - if(false == detail::check_x_gt0(function, mean, &result, Policy())) - { - return result; - } - if(false == detail::check_positive_x(function, x, &result, Policy())) - { - return result; - } - - if (x == 0) - { - return 0; // Convenient, even if not defined mathematically. - } - - result = - sqrt(scale / (constants::two_pi<RealType>() * x * x * x)) - * exp(-scale * (x - mean) * (x - mean) / (2 * x * mean * mean)); - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const inverse_gaussian_distribution<RealType, Policy>& dist, const RealType& x) -{ // Cumulative Density Function. - BOOST_MATH_STD_USING // for ADL of std functions. - - RealType scale = dist.scale(); - RealType mean = dist.mean(); - static const char* function = "boost::math::cdf(const inverse_gaussian_distribution<%1%>&, %1%)"; - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, mean, &result, Policy())) - { - return result; - } - if (false == detail::check_x_gt0(function, mean, &result, Policy())) - { - return result; - } - if(false == detail::check_positive_x(function, x, &result, Policy())) - { - return result; - } - if (x == 0) - { - return 0; // Convenient, even if not defined mathematically. - } - // Problem with this formula for large scale > 1000 or small x, - //result = 0.5 * (erf(sqrt(scale / x) * ((x / mean) - 1) / constants::root_two<RealType>(), Policy()) + 1) - // + exp(2 * scale / mean) / 2 - // * (1 - erf(sqrt(scale / x) * (x / mean + 1) / constants::root_two<RealType>(), Policy())); - // so use normal distribution version: - // Wikipedia CDF equation http://en.wikipedia.org/wiki/Inverse_Gaussian_distribution. - - normal_distribution<RealType> n01; - - RealType n0 = sqrt(scale / x); - n0 *= ((x / mean) -1); - RealType n1 = cdf(n01, n0); - RealType expfactor = exp(2 * scale / mean); - RealType n3 = - sqrt(scale / x); - n3 *= (x / mean) + 1; - RealType n4 = cdf(n01, n3); - result = n1 + expfactor * n4; - return result; -} // cdf - -template <class RealType, class Policy> -struct inverse_gaussian_quantile_functor -{ - - inverse_gaussian_quantile_functor(const boost::math::inverse_gaussian_distribution<RealType, Policy> dist, RealType const& p) - : distribution(dist), prob(p) - { - } - boost::math::tuple<RealType, RealType> operator()(RealType const& x) - { - RealType c = cdf(distribution, x); - RealType fx = c - prob; // Difference cdf - value - to minimize. - RealType dx = pdf(distribution, x); // pdf is 1st derivative. - // return both function evaluation difference f(x) and 1st derivative f'(x). - return boost::math::make_tuple(fx, dx); - } - private: - const boost::math::inverse_gaussian_distribution<RealType, Policy> distribution; - RealType prob; -}; - -template <class RealType, class Policy> -struct inverse_gaussian_quantile_complement_functor -{ - inverse_gaussian_quantile_complement_functor(const boost::math::inverse_gaussian_distribution<RealType, Policy> dist, RealType const& p) - : distribution(dist), prob(p) - { - } - boost::math::tuple<RealType, RealType> operator()(RealType const& x) - { - RealType c = cdf(complement(distribution, x)); - RealType fx = c - prob; // Difference cdf - value - to minimize. - RealType dx = -pdf(distribution, x); // pdf is 1st derivative. - // return both function evaluation difference f(x) and 1st derivative f'(x). - //return std::tr1::make_tuple(fx, dx); if available. - return boost::math::make_tuple(fx, dx); - } - private: - const boost::math::inverse_gaussian_distribution<RealType, Policy> distribution; - RealType prob; -}; - -namespace detail -{ - template <class RealType> - inline RealType guess_ig(RealType p, RealType mu = 1, RealType lambda = 1) - { // guess at random variate value x for inverse gaussian quantile. - BOOST_MATH_STD_USING - using boost::math::policies::policy; - // Error type. - using boost::math::policies::overflow_error; - // Action. - using boost::math::policies::ignore_error; - - typedef policy< - overflow_error<ignore_error> // Ignore overflow (return infinity) - > no_overthrow_policy; - - RealType x; // result is guess at random variate value x. - RealType phi = lambda / mu; - if (phi > 2.) - { // Big phi, so starting to look like normal Gaussian distribution. - // x=(qnorm(p,0,1,true,false) - 0.5 * sqrt(mu/lambda)) / sqrt(lambda/mu); - // Whitmore, G.A. and Yalovsky, M. - // A normalising logarithmic transformation for inverse Gaussian random variables, - // Technometrics 20-2, 207-208 (1978), but using expression from - // V Seshadri, Inverse Gaussian distribution (1998) ISBN 0387 98618 9, page 6. - - normal_distribution<RealType, no_overthrow_policy> n01; - x = mu * exp(quantile(n01, p) / sqrt(phi) - 1/(2 * phi)); - } - else - { // phi < 2 so much less symmetrical with long tail, - // so use gamma distribution as an approximation. - using boost::math::gamma_distribution; - - // Define the distribution, using gamma_nooverflow: - typedef gamma_distribution<RealType, no_overthrow_policy> gamma_nooverflow; - - gamma_nooverflow g(static_cast<RealType>(0.5), static_cast<RealType>(1.)); - - // gamma_nooverflow g(static_cast<RealType>(0.5), static_cast<RealType>(1.)); - // R qgamma(0.2, 0.5, 1) 0.0320923 - RealType qg = quantile(complement(g, p)); - //RealType qg1 = qgamma(1.- p, 0.5, 1.0, true, false); - x = lambda / (qg * 2); - // - if (x > mu/2) // x > mu /2? - { // x too large for the gamma approximation to work well. - //x = qgamma(p, 0.5, 1.0); // qgamma(0.270614, 0.5, 1) = 0.05983807 - RealType q = quantile(g, p); - // x = mu * exp(q * static_cast<RealType>(0.1)); // Said to improve at high p - // x = mu * x; // Improves at high p? - x = mu * exp(q / sqrt(phi) - 1/(2 * phi)); - } - } - return x; - } // guess_ig -} // namespace detail - -template <class RealType, class Policy> -inline RealType quantile(const inverse_gaussian_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions. - // No closed form exists so guess and use Newton Raphson iteration. - - RealType mean = dist.mean(); - RealType scale = dist.scale(); - static const char* function = "boost::math::quantile(const inverse_gaussian_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, mean, &result, Policy())) - return result; - if (false == detail::check_x_gt0(function, mean, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - if (p == 0) - { - return 0; // Convenient, even if not defined mathematically? - } - if (p == 1) - { // overflow - result = policies::raise_overflow_error<RealType>(function, - "probability parameter is 1, but must be < 1!", Policy()); - return result; // std::numeric_limits<RealType>::infinity(); - } - - RealType guess = detail::guess_ig(p, dist.mean(), dist.scale()); - using boost::math::tools::max_value; - - RealType min = 0.; // Minimum possible value is bottom of range of distribution. - RealType max = max_value<RealType>();// Maximum possible value is top of range. - // int digits = std::numeric_limits<RealType>::digits; // Maximum possible binary digits accuracy for type T. - // digits used to control how accurate to try to make the result. - // To allow user to control accuracy versus speed, - int get_digits = policies::digits<RealType, Policy>();// get digits from policy, - boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); // and max iterations. - using boost::math::tools::newton_raphson_iterate; - result = - newton_raphson_iterate(inverse_gaussian_quantile_functor<RealType, Policy>(dist, p), guess, min, max, get_digits, m); - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<inverse_gaussian_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions. - - RealType scale = c.dist.scale(); - RealType mean = c.dist.mean(); - RealType x = c.param; - static const char* function = "boost::math::cdf(const complement(inverse_gaussian_distribution<%1%>&), %1%)"; - // infinite arguments not supported. - //if((boost::math::isinf)(x)) - //{ - // if(x < 0) return 1; // cdf complement -infinity is unity. - // return 0; // cdf complement +infinity is zero - //} - // These produce MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) - //{ // cdf complement +infinity is zero. - // return 0; - //} - //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) - //{ // cdf complement -infinity is unity. - // return 1; - //} - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, mean, &result, Policy())) - return result; - if (false == detail::check_x_gt0(function, mean, &result, Policy())) - return result; - if(false == detail::check_positive_x(function, x, &result, Policy())) - return result; - - normal_distribution<RealType> n01; - RealType n0 = sqrt(scale / x); - n0 *= ((x / mean) -1); - RealType cdf_1 = cdf(complement(n01, n0)); - - RealType expfactor = exp(2 * scale / mean); - RealType n3 = - sqrt(scale / x); - n3 *= (x / mean) + 1; - - //RealType n5 = +sqrt(scale/x) * ((x /mean) + 1); // note now positive sign. - RealType n6 = cdf(complement(n01, +sqrt(scale/x) * ((x /mean) + 1))); - // RealType n4 = cdf(n01, n3); // = - result = cdf_1 - expfactor * n6; - return result; -} // cdf complement - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<inverse_gaussian_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType scale = c.dist.scale(); - RealType mean = c.dist.mean(); - static const char* function = "boost::math::quantile(const complement(inverse_gaussian_distribution<%1%>&), %1%)"; - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, mean, &result, Policy())) - return result; - if (false == detail::check_x_gt0(function, mean, &result, Policy())) - return result; - RealType q = c.param; - if(false == detail::check_probability(function, q, &result, Policy())) - return result; - - RealType guess = detail::guess_ig(q, mean, scale); - // Complement. - using boost::math::tools::max_value; - - RealType min = 0.; // Minimum possible value is bottom of range of distribution. - RealType max = max_value<RealType>();// Maximum possible value is top of range. - // int digits = std::numeric_limits<RealType>::digits; // Maximum possible binary digits accuracy for type T. - // digits used to control how accurate to try to make the result. - int get_digits = policies::digits<RealType, Policy>(); - boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); - using boost::math::tools::newton_raphson_iterate; - result = - newton_raphson_iterate(inverse_gaussian_quantile_complement_functor<RealType, Policy>(c.dist, q), guess, min, max, get_digits, m); - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType mean(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ // aka mu - return dist.mean(); -} - -template <class RealType, class Policy> -inline RealType scale(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ // aka lambda - return dist.scale(); -} - -template <class RealType, class Policy> -inline RealType shape(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ // aka phi - return dist.shape(); -} - -template <class RealType, class Policy> -inline RealType standard_deviation(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING - RealType scale = dist.scale(); - RealType mean = dist.mean(); - RealType result = sqrt(mean * mean * mean / scale); - return result; -} - -template <class RealType, class Policy> -inline RealType mode(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING - RealType scale = dist.scale(); - RealType mean = dist.mean(); - RealType result = mean * (sqrt(1 + (9 * mean * mean)/(4 * scale * scale)) - - 3 * mean / (2 * scale)); - return result; -} - -template <class RealType, class Policy> -inline RealType skewness(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING - RealType scale = dist.scale(); - RealType mean = dist.mean(); - RealType result = 3 * sqrt(mean/scale); - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ - RealType scale = dist.scale(); - RealType mean = dist.mean(); - RealType result = 15 * mean / scale -3; - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const inverse_gaussian_distribution<RealType, Policy>& dist) -{ - RealType scale = dist.scale(); - RealType mean = dist.mean(); - RealType result = 15 * mean / scale; - return result; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_INVERSE_GAUSSIAN_HPP - -
--- a/any/include/boost/math/distributions/laplace.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,350 +0,0 @@ -// Copyright Thijs van den Berg, 2008. -// Copyright John Maddock 2008. -// Copyright Paul A. Bristow 2008, 2014. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -// This module implements the Laplace distribution. -// Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. -// http://mathworld.wolfram.com/LaplaceDistribution.html -// http://en.wikipedia.org/wiki/Laplace_distribution -// -// Abramowitz and Stegun 1972, p 930 -// http://www.math.sfu.ca/~cbm/aands/page_930.htm - -#ifndef BOOST_STATS_LAPLACE_HPP -#define BOOST_STATS_LAPLACE_HPP - -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/constants/constants.hpp> -#include <limits> - -namespace boost{ namespace math{ - -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable:4127) // conditional expression is constant -#endif - -template <class RealType = double, class Policy = policies::policy<> > -class laplace_distribution -{ -public: - // ---------------------------------- - // public Types - // ---------------------------------- - typedef RealType value_type; - typedef Policy policy_type; - - // ---------------------------------- - // Constructor(s) - // ---------------------------------- - laplace_distribution(RealType l_location = 0, RealType l_scale = 1) - : m_location(l_location), m_scale(l_scale) - { - RealType result; - check_parameters("boost::math::laplace_distribution<%1%>::laplace_distribution()", &result); - } - - - // ---------------------------------- - // Public functions - // ---------------------------------- - - RealType location() const - { - return m_location; - } - - RealType scale() const - { - return m_scale; - } - - bool check_parameters(const char* function, RealType* result) const - { - if(false == detail::check_scale(function, m_scale, result, Policy())) return false; - if(false == detail::check_location(function, m_location, result, Policy())) return false; - return true; - } - -private: - RealType m_location; - RealType m_scale; -}; // class laplace_distribution - -// -// Convenient type synonym for double. -typedef laplace_distribution<double> laplace; - -// -// Non-member functions. -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const laplace_distribution<RealType, Policy>&) -{ - if (std::numeric_limits<RealType>::has_infinity) - { // Can use infinity. - return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. - } - else - { // Can only use max_value. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. - } - -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&) -{ - if (std::numeric_limits<RealType>::has_infinity) - { // Can Use infinity. - return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. - } - else - { // Can only use max_value. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. - } -} - -template <class RealType, class Policy> -inline RealType pdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - // Checking function argument - RealType result = 0; - const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))"; - - // Check scale and location. - if (false == dist.check_parameters(function, &result)) return result; - // Special pdf values. - if((boost::math::isinf)(x)) - { - return 0; // pdf + and - infinity is zero. - } - if (false == detail::check_x(function, x, &result, Policy())) return result; - - // General case - RealType scale( dist.scale() ); - RealType location( dist.location() ); - - RealType exponent = x - location; - if (exponent>0) exponent = -exponent; - exponent /= scale; - - result = exp(exponent); - result /= 2 * scale; - - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // For ADL of std functions. - - RealType result = 0; - // Checking function argument. - const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)"; - // Check scale and location. - if (false == dist.check_parameters(function, &result)) return result; - - // Special cdf values: - if((boost::math::isinf)(x)) - { - if(x < 0) return 0; // -infinity. - return 1; // + infinity. - } - if (false == detail::check_x(function, x, &result, Policy())) return result; - - // General cdf values - RealType scale( dist.scale() ); - RealType location( dist.location() ); - - if (x < location) - { - result = exp( (x-location)/scale )/2; - } - else - { - result = 1 - exp( (location-x)/scale )/2; - } - return result; -} // cdf - - -template <class RealType, class Policy> -inline RealType quantile(const laplace_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions. - - // Checking function argument - RealType result = 0; - const char* function = "boost::math::quantile(const laplace_distribution<%1%>&, %1%)"; - if (false == dist.check_parameters(function, &result)) return result; - if(false == detail::check_probability(function, p, &result, Policy())) return result; - - // Extreme values of p: - if(p == 0) - { - result = policies::raise_overflow_error<RealType>(function, - "probability parameter is 0, but must be > 0!", Policy()); - return -result; // -std::numeric_limits<RealType>::infinity(); - } - - if(p == 1) - { - result = policies::raise_overflow_error<RealType>(function, - "probability parameter is 1, but must be < 1!", Policy()); - return result; // std::numeric_limits<RealType>::infinity(); - } - // Calculate Quantile - RealType scale( dist.scale() ); - RealType location( dist.location() ); - - if (p - 0.5 < 0.0) - result = location + scale*log( static_cast<RealType>(p*2) ); - else - result = location - scale*log( static_cast<RealType>(-p*2 + 2) ); - - return result; -} // quantile - - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) -{ - // Calculate complement of cdf. - BOOST_MATH_STD_USING // for ADL of std functions - - RealType scale = c.dist.scale(); - RealType location = c.dist.location(); - RealType x = c.param; - RealType result = 0; - - // Checking function argument. - const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; - - // Check scale and location. - //if(false == detail::check_scale(function, scale, result, Policy())) return false; - //if(false == detail::check_location(function, location, result, Policy())) return false; - if (false == c.dist.check_parameters(function, &result)) return result; - - // Special cdf values. - if((boost::math::isinf)(x)) - { - if(x < 0) return 1; // cdf complement -infinity is unity. - return 0; // cdf complement +infinity is zero. - } - if(false == detail::check_x(function, x, &result, Policy()))return result; - - // Cdf interval value. - if (-x < -location) - { - result = exp( (-x+location)/scale )/2; - } - else - { - result = 1 - exp( (-location+x)/scale )/2; - } - return result; -} // cdf complement - - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions. - - // Calculate quantile. - RealType scale = c.dist.scale(); - RealType location = c.dist.location(); - RealType q = c.param; - RealType result = 0; - - // Checking function argument. - const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; - if (false == c.dist.check_parameters(function, &result)) return result; - - // Extreme values. - if(q == 0) - { - return std::numeric_limits<RealType>::infinity(); - } - if(q == 1) - { - return -std::numeric_limits<RealType>::infinity(); - } - if(false == detail::check_probability(function, q, &result, Policy())) return result; - - if (0.5 - q < 0.0) - result = location + scale*log( static_cast<RealType>(-q*2 + 2) ); - else - result = location - scale*log( static_cast<RealType>(q*2) ); - - - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType mean(const laplace_distribution<RealType, Policy>& dist) -{ - return dist.location(); -} - -template <class RealType, class Policy> -inline RealType standard_deviation(const laplace_distribution<RealType, Policy>& dist) -{ - return constants::root_two<RealType>() * dist.scale(); -} - -template <class RealType, class Policy> -inline RealType mode(const laplace_distribution<RealType, Policy>& dist) -{ - return dist.location(); -} - -template <class RealType, class Policy> -inline RealType median(const laplace_distribution<RealType, Policy>& dist) -{ - return dist.location(); -} - -template <class RealType, class Policy> -inline RealType skewness(const laplace_distribution<RealType, Policy>& /*dist*/) -{ - return 0; -} - -template <class RealType, class Policy> -inline RealType kurtosis(const laplace_distribution<RealType, Policy>& /*dist*/) -{ - return 6; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const laplace_distribution<RealType, Policy>& /*dist*/) -{ - return 3; -} - -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_LAPLACE_HPP - -
--- a/any/include/boost/math/distributions/logistic.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,299 +0,0 @@ -// Copyright 2008 Gautam Sewani -// -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_DISTRIBUTIONS_LOGISTIC -#define BOOST_MATH_DISTRIBUTIONS_LOGISTIC - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/special_functions/log1p.hpp> -#include <boost/math/constants/constants.hpp> -#include <utility> - -namespace boost { namespace math { - - template <class RealType = double, class Policy = policies::policy<> > - class logistic_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - logistic_distribution(RealType l_location=0, RealType l_scale=1) // Constructor. - : m_location(l_location), m_scale(l_scale) - { - static const char* function = "boost::math::logistic_distribution<%1%>::logistic_distribution"; - - RealType result; - detail::check_scale(function, l_scale, &result, Policy()); - detail::check_location(function, l_location, &result, Policy()); - } - // Accessor functions. - RealType scale()const - { - return m_scale; - } - - RealType location()const - { - return m_location; - } - private: - // Data members: - RealType m_location; // distribution location aka mu. - RealType m_scale; // distribution scale aka s. - }; // class logistic_distribution - - - typedef logistic_distribution<double> logistic; - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const logistic_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>( - std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), - std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>()); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const logistic_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity - } - - template <class RealType, class Policy> - inline RealType pdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x) - { - static const char* function = "boost::math::pdf(const logistic_distribution<%1%>&, %1%)"; - RealType scale = dist.scale(); - RealType location = dist.location(); - RealType result = 0; - - if(false == detail::check_scale(function, scale , &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, location, &result, Policy())) - { - return result; - } - - if((boost::math::isinf)(x)) - { - return 0; // pdf + and - infinity is zero. - } - - if(false == detail::check_x(function, x, &result, Policy())) - { - return result; - } - - BOOST_MATH_STD_USING - RealType exp_term = (location - x) / scale; - if(fabs(exp_term) > tools::log_max_value<RealType>()) - return 0; - exp_term = exp(exp_term); - if((exp_term * scale > 1) && (exp_term > tools::max_value<RealType>() / (scale * exp_term))) - return 1 / (scale * exp_term); - return (exp_term) / (scale * (1 + exp_term) * (1 + exp_term)); - } - - template <class RealType, class Policy> - inline RealType cdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x) - { - RealType scale = dist.scale(); - RealType location = dist.location(); - RealType result = 0; // of checks. - static const char* function = "boost::math::cdf(const logistic_distribution<%1%>&, %1%)"; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, location, &result, Policy())) - { - return result; - } - - if((boost::math::isinf)(x)) - { - if(x < 0) return 0; // -infinity - return 1; // + infinity - } - - if(false == detail::check_x(function, x, &result, Policy())) - { - return result; - } - BOOST_MATH_STD_USING - RealType power = (location - x) / scale; - if(power > tools::log_max_value<RealType>()) - return 0; - if(power < -tools::log_max_value<RealType>()) - return 1; - return 1 / (1 + exp(power)); - } - - template <class RealType, class Policy> - inline RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p) - { - BOOST_MATH_STD_USING - RealType location = dist.location(); - RealType scale = dist.scale(); - - static const char* function = "boost::math::quantile(const logistic_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, location, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - - if(p == 0) - { - return -policies::raise_overflow_error<RealType>(function,"probability argument is 0, must be >0 and <1",Policy()); - } - if(p == 1) - { - return policies::raise_overflow_error<RealType>(function,"probability argument is 1, must be >0 and <1",Policy()); - } - //Expressions to try - //return location+scale*log(p/(1-p)); - //return location+scale*log1p((2*p-1)/(1-p)); - - //return location - scale*log( (1-p)/p); - //return location - scale*log1p((1-2*p)/p); - - //return -scale*log(1/p-1) + location; - return location - scale * log((1 - p) / p); - } // RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p) - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c) - { - BOOST_MATH_STD_USING - RealType location = c.dist.location(); - RealType scale = c.dist.scale(); - RealType x = c.param; - static const char* function = "boost::math::cdf(const complement(logistic_distribution<%1%>&), %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, location, &result, Policy())) - { - return result; - } - if((boost::math::isinf)(x)) - { - if(x < 0) return 1; // cdf complement -infinity is unity. - return 0; // cdf complement +infinity is zero. - } - if(false == detail::check_x(function, x, &result, Policy())) - { - return result; - } - RealType power = (x - location) / scale; - if(power > tools::log_max_value<RealType>()) - return 0; - if(power < -tools::log_max_value<RealType>()) - return 1; - return 1 / (1 + exp(power)); - } - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c) - { - BOOST_MATH_STD_USING - RealType scale = c.dist.scale(); - RealType location = c.dist.location(); - static const char* function = "boost::math::quantile(const complement(logistic_distribution<%1%>&), %1%)"; - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, location, &result, Policy())) - return result; - RealType q = c.param; - if(false == detail::check_probability(function, q, &result, Policy())) - return result; - using boost::math::tools::max_value; - - if(q == 1) - { - return -policies::raise_overflow_error<RealType>(function,"probability argument is 1, but must be >0 and <1",Policy()); - } - if(q == 0) - { - return policies::raise_overflow_error<RealType>(function,"probability argument is 0, but must be >0 and <1",Policy()); - } - //Expressions to try - //return location+scale*log((1-q)/q); - return location + scale * log((1 - q) / q); - - //return location-scale*log(q/(1-q)); - //return location-scale*log1p((2*q-1)/(1-q)); - - //return location+scale*log(1/q-1); - //return location+scale*log1p(1/q-2); - } - - template <class RealType, class Policy> - inline RealType mean(const logistic_distribution<RealType, Policy>& dist) - { - return dist.location(); - } // RealType mean(const logistic_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType variance(const logistic_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING - RealType scale = dist.scale(); - return boost::math::constants::pi<RealType>()*boost::math::constants::pi<RealType>()*scale*scale/3; - } // RealType variance(const logistic_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType mode(const logistic_distribution<RealType, Policy>& dist) - { - return dist.location(); - } - - template <class RealType, class Policy> - inline RealType median(const logistic_distribution<RealType, Policy>& dist) - { - return dist.location(); - } - template <class RealType, class Policy> - inline RealType skewness(const logistic_distribution<RealType, Policy>& /*dist*/) - { - return 0; - } // RealType skewness(const logistic_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& /*dist*/) - { - return static_cast<RealType>(6)/5; - } // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis(const logistic_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist) + 3; - } // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist) - }} - - -// Must come at the end: -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_DISTRIBUTIONS_LOGISTIC
--- a/any/include/boost/math/distributions/lognormal.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,341 +0,0 @@ -// Copyright John Maddock 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_LOGNORMAL_HPP -#define BOOST_STATS_LOGNORMAL_HPP - -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm -// http://mathworld.wolfram.com/LogNormalDistribution.html -// http://en.wikipedia.org/wiki/Lognormal_distribution - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/distributions/normal.hpp> -#include <boost/math/special_functions/expm1.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> - -#include <utility> - -namespace boost{ namespace math -{ -namespace detail -{ - - template <class RealType, class Policy> - inline bool check_lognormal_x( - const char* function, - RealType const& x, - RealType* result, const Policy& pol) - { - if((x < 0) || !(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate is %1% but must be >= 0 !", x, pol); - return false; - } - return true; - } - -} // namespace detail - - -template <class RealType = double, class Policy = policies::policy<> > -class lognormal_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - lognormal_distribution(RealType l_location = 0, RealType l_scale = 1) - : m_location(l_location), m_scale(l_scale) - { - RealType result; - detail::check_scale("boost::math::lognormal_distribution<%1%>::lognormal_distribution", l_scale, &result, Policy()); - detail::check_location("boost::math::lognormal_distribution<%1%>::lognormal_distribution", l_location, &result, Policy()); - } - - RealType location()const - { - return m_location; - } - - RealType scale()const - { - return m_scale; - } -private: - // - // Data members: - // - RealType m_location; // distribution location. - RealType m_scale; // distribution scale. -}; - -typedef lognormal_distribution<double> lognormal; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const lognormal_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x is >0 to +infinity. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const lognormal_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -RealType pdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType mu = dist.location(); - RealType sigma = dist.scale(); - - static const char* function = "boost::math::pdf(const lognormal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(0 == detail::check_scale(function, sigma, &result, Policy())) - return result; - if(0 == detail::check_location(function, mu, &result, Policy())) - return result; - if(0 == detail::check_lognormal_x(function, x, &result, Policy())) - return result; - - if(x == 0) - return 0; - - RealType exponent = log(x) - mu; - exponent *= -exponent; - exponent /= 2 * sigma * sigma; - - result = exp(exponent); - result /= sigma * sqrt(2 * constants::pi<RealType>()) * x; - - return result; -} - -template <class RealType, class Policy> -inline RealType cdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(0 == detail::check_scale(function, dist.scale(), &result, Policy())) - return result; - if(0 == detail::check_location(function, dist.location(), &result, Policy())) - return result; - if(0 == detail::check_lognormal_x(function, x, &result, Policy())) - return result; - - if(x == 0) - return 0; - - normal_distribution<RealType, Policy> norm(dist.location(), dist.scale()); - return cdf(norm, log(x)); -} - -template <class RealType, class Policy> -inline RealType quantile(const lognormal_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(0 == detail::check_scale(function, dist.scale(), &result, Policy())) - return result; - if(0 == detail::check_location(function, dist.location(), &result, Policy())) - return result; - if(0 == detail::check_probability(function, p, &result, Policy())) - return result; - - if(p == 0) - return 0; - if(p == 1) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - normal_distribution<RealType, Policy> norm(dist.location(), dist.scale()); - return exp(quantile(norm, p)); -} - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(0 == detail::check_scale(function, c.dist.scale(), &result, Policy())) - return result; - if(0 == detail::check_location(function, c.dist.location(), &result, Policy())) - return result; - if(0 == detail::check_lognormal_x(function, c.param, &result, Policy())) - return result; - - if(c.param == 0) - return 1; - - normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale()); - return cdf(complement(norm, log(c.param))); -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(0 == detail::check_scale(function, c.dist.scale(), &result, Policy())) - return result; - if(0 == detail::check_location(function, c.dist.location(), &result, Policy())) - return result; - if(0 == detail::check_probability(function, c.param, &result, Policy())) - return result; - - if(c.param == 1) - return 0; - if(c.param == 0) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale()); - return exp(quantile(complement(norm, c.param))); -} - -template <class RealType, class Policy> -inline RealType mean(const lognormal_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType mu = dist.location(); - RealType sigma = dist.scale(); - - RealType result = 0; - if(0 == detail::check_scale("boost::math::mean(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) - return result; - if(0 == detail::check_location("boost::math::mean(const lognormal_distribution<%1%>&)", mu, &result, Policy())) - return result; - - return exp(mu + sigma * sigma / 2); -} - -template <class RealType, class Policy> -inline RealType variance(const lognormal_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType mu = dist.location(); - RealType sigma = dist.scale(); - - RealType result = 0; - if(0 == detail::check_scale("boost::math::variance(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) - return result; - if(0 == detail::check_location("boost::math::variance(const lognormal_distribution<%1%>&)", mu, &result, Policy())) - return result; - - return boost::math::expm1(sigma * sigma, Policy()) * exp(2 * mu + sigma * sigma); -} - -template <class RealType, class Policy> -inline RealType mode(const lognormal_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType mu = dist.location(); - RealType sigma = dist.scale(); - - RealType result = 0; - if(0 == detail::check_scale("boost::math::mode(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) - return result; - if(0 == detail::check_location("boost::math::mode(const lognormal_distribution<%1%>&)", mu, &result, Policy())) - return result; - - return exp(mu - sigma * sigma); -} - -template <class RealType, class Policy> -inline RealType median(const lognormal_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - RealType mu = dist.location(); - return exp(mu); // e^mu -} - -template <class RealType, class Policy> -inline RealType skewness(const lognormal_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - //RealType mu = dist.location(); - RealType sigma = dist.scale(); - - RealType ss = sigma * sigma; - RealType ess = exp(ss); - - RealType result = 0; - if(0 == detail::check_scale("boost::math::skewness(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) - return result; - if(0 == detail::check_location("boost::math::skewness(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) - return result; - - return (ess + 2) * sqrt(boost::math::expm1(ss, Policy())); -} - -template <class RealType, class Policy> -inline RealType kurtosis(const lognormal_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - //RealType mu = dist.location(); - RealType sigma = dist.scale(); - RealType ss = sigma * sigma; - - RealType result = 0; - if(0 == detail::check_scale("boost::math::kurtosis(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) - return result; - if(0 == detail::check_location("boost::math::kurtosis(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) - return result; - - return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 3; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const lognormal_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - // RealType mu = dist.location(); - RealType sigma = dist.scale(); - RealType ss = sigma * sigma; - - RealType result = 0; - if(0 == detail::check_scale("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) - return result; - if(0 == detail::check_location("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) - return result; - - return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 6; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_STUDENTS_T_HPP - -
--- a/any/include/boost/math/distributions/negative_binomial.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,607 +0,0 @@ -// boost\math\special_functions\negative_binomial.hpp - -// Copyright Paul A. Bristow 2007. -// Copyright John Maddock 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -// http://en.wikipedia.org/wiki/negative_binomial_distribution -// http://mathworld.wolfram.com/NegativeBinomialDistribution.html -// http://documents.wolfram.com/teachersedition/Teacher/Statistics/DiscreteDistributions.html - -// The negative binomial distribution NegativeBinomialDistribution[n, p] -// is the distribution of the number (k) of failures that occur in a sequence of trials before -// r successes have occurred, where the probability of success in each trial is p. - -// In a sequence of Bernoulli trials or events -// (independent, yes or no, succeed or fail) with success_fraction probability p, -// negative_binomial is the probability that k or fewer failures -// preceed the r th trial's success. -// random variable k is the number of failures (NOT the probability). - -// Negative_binomial distribution is a discrete probability distribution. -// But note that the negative binomial distribution -// (like others including the binomial, Poisson & Bernoulli) -// is strictly defined as a discrete function: only integral values of k are envisaged. -// However because of the method of calculation using a continuous gamma function, -// it is convenient to treat it as if a continous function, -// and permit non-integral values of k. - -// However, by default the policy is to use discrete_quantile_policy. - -// To enforce the strict mathematical model, users should use conversion -// on k outside this function to ensure that k is integral. - -// MATHCAD cumulative negative binomial pnbinom(k, n, p) - -// Implementation note: much greater speed, and perhaps greater accuracy, -// might be achieved for extreme values by using a normal approximation. -// This is NOT been tested or implemented. - -#ifndef BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP -#define BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x) == Ix(a, b). -#include <boost/math/distributions/complement.hpp> // complement. -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks domain_error & logic_error. -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. -#include <boost/math/distributions/detail/inv_discrete_quantile.hpp> - -#include <boost/type_traits/is_floating_point.hpp> -#include <boost/type_traits/is_integral.hpp> -#include <boost/type_traits/is_same.hpp> -#include <boost/mpl/if.hpp> - -#include <limits> // using std::numeric_limits; -#include <utility> - -#if defined (BOOST_MSVC) -# pragma warning(push) -// This believed not now necessary, so commented out. -//# pragma warning(disable: 4702) // unreachable code. -// in domain_error_imp in error_handling. -#endif - -namespace boost -{ - namespace math - { - namespace negative_binomial_detail - { - // Common error checking routines for negative binomial distribution functions: - template <class RealType, class Policy> - inline bool check_successes(const char* function, const RealType& r, RealType* result, const Policy& pol) - { - if( !(boost::math::isfinite)(r) || (r <= 0) ) - { - *result = policies::raise_domain_error<RealType>( - function, - "Number of successes argument is %1%, but must be > 0 !", r, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_success_fraction(const char* function, const RealType& p, RealType* result, const Policy& pol) - { - if( !(boost::math::isfinite)(p) || (p < 0) || (p > 1) ) - { - *result = policies::raise_domain_error<RealType>( - function, - "Success fraction argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& r, const RealType& p, RealType* result, const Policy& pol) - { - return check_success_fraction(function, p, result, pol) - && check_successes(function, r, result, pol); - } - template <class RealType, class Policy> - inline bool check_dist_and_k(const char* function, const RealType& r, const RealType& p, RealType k, RealType* result, const Policy& pol) - { - if(check_dist(function, r, p, result, pol) == false) - { - return false; - } - if( !(boost::math::isfinite)(k) || (k < 0) ) - { // Check k failures. - *result = policies::raise_domain_error<RealType>( - function, - "Number of failures argument is %1%, but must be >= 0 !", k, pol); - return false; - } - return true; - } // Check_dist_and_k - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, const RealType& r, RealType p, RealType prob, RealType* result, const Policy& pol) - { - if((check_dist(function, r, p, result, pol) && detail::check_probability(function, prob, result, pol)) == false) - { - return false; - } - return true; - } // check_dist_and_prob - } // namespace negative_binomial_detail - - template <class RealType = double, class Policy = policies::policy<> > - class negative_binomial_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - negative_binomial_distribution(RealType r, RealType p) : m_r(r), m_p(p) - { // Constructor. - RealType result; - negative_binomial_detail::check_dist( - "negative_binomial_distribution<%1%>::negative_binomial_distribution", - m_r, // Check successes r > 0. - m_p, // Check success_fraction 0 <= p <= 1. - &result, Policy()); - } // negative_binomial_distribution constructor. - - // Private data getter class member functions. - RealType success_fraction() const - { // Probability of success as fraction in range 0 to 1. - return m_p; - } - RealType successes() const - { // Total number of successes r. - return m_r; - } - - static RealType find_lower_bound_on_p( - RealType trials, - RealType successes, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_lower_bound_on_p"; - RealType result = 0; // of error checks. - RealType failures = trials - successes; - if(false == detail::check_probability(function, alpha, &result, Policy()) - && negative_binomial_detail::check_dist_and_k( - function, successes, RealType(0), failures, &result, Policy())) - { - return result; - } - // Use complement ibeta_inv function for lower bound. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibeta_inv(successes, failures + 1, alpha, static_cast<RealType*>(0), Policy()); - } // find_lower_bound_on_p - - static RealType find_upper_bound_on_p( - RealType trials, - RealType successes, - RealType alpha) // alpha 0.05 equivalent to 95% for one-sided test. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_upper_bound_on_p"; - RealType result = 0; // of error checks. - RealType failures = trials - successes; - if(false == negative_binomial_detail::check_dist_and_k( - function, successes, RealType(0), failures, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { - return result; - } - if(failures == 0) - return 1; - // Use complement ibetac_inv function for upper bound. - // Note adjusted failures value: *not* failures+1 as usual. - // This is adapted from the corresponding binomial formula - // here: http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm - // This is a Clopper-Pearson interval, and may be overly conservative, - // see also "A Simple Improved Inferential Method for Some - // Discrete Distributions" Yong CAI and K. KRISHNAMOORTHY - // http://www.ucs.louisiana.edu/~kxk4695/Discrete_new.pdf - // - return ibetac_inv(successes, failures, alpha, static_cast<RealType*>(0), Policy()); - } // find_upper_bound_on_p - - // Estimate number of trials : - // "How many trials do I need to be P% sure of seeing k or fewer failures?" - - static RealType find_minimum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_minimum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, RealType(1), p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { return result; } - - result = ibeta_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_failures - - static RealType find_maximum_number_of_trials( - RealType k, // number of failures (k >= 0). - RealType p, // success fraction 0 <= p <= 1. - RealType alpha) // risk level threshold 0 <= alpha <= 1. - { - static const char* function = "boost::math::negative_binomial<%1%>::find_maximum_number_of_trials"; - // Error checks: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, RealType(1), p, k, &result, Policy()) - && detail::check_probability(function, alpha, &result, Policy())) - { return result; } - - result = ibetac_inva(k + 1, p, alpha, Policy()); // returns n - k - return result + k; - } // RealType find_number_of_trials complemented - - private: - RealType m_r; // successes. - RealType m_p; // success_fraction - }; // template <class RealType, class Policy> class negative_binomial_distribution - - typedef negative_binomial_distribution<double> negative_binomial; // Reserved name of type double. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const negative_binomial_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const negative_binomial_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // max_integer? - } - - template <class RealType, class Policy> - inline RealType mean(const negative_binomial_distribution<RealType, Policy>& dist) - { // Mean of Negative Binomial distribution = r(1-p)/p. - return dist.successes() * (1 - dist.success_fraction() ) / dist.success_fraction(); - } // mean - - //template <class RealType, class Policy> - //inline RealType median(const negative_binomial_distribution<RealType, Policy>& dist) - //{ // Median of negative_binomial_distribution is not defined. - // return policies::raise_domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN()); - //} // median - // Now implemented via quantile(half) in derived accessors. - - template <class RealType, class Policy> - inline RealType mode(const negative_binomial_distribution<RealType, Policy>& dist) - { // Mode of Negative Binomial distribution = floor[(r-1) * (1 - p)/p] - BOOST_MATH_STD_USING // ADL of std functions. - return floor((dist.successes() -1) * (1 - dist.success_fraction()) / dist.success_fraction()); - } // mode - - template <class RealType, class Policy> - inline RealType skewness(const negative_binomial_distribution<RealType, Policy>& dist) - { // skewness of Negative Binomial distribution = 2-p / (sqrt(r(1-p)) - BOOST_MATH_STD_USING // ADL of std functions. - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - - return (2 - p) / - sqrt(r * (1 - p)); - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis(const negative_binomial_distribution<RealType, Policy>& dist) - { // kurtosis of Negative Binomial distribution - // http://en.wikipedia.org/wiki/Negative_binomial is kurtosis_excess so add 3 - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - return 3 + (6 / r) + ((p * p) / (r * (1 - p))); - } // kurtosis - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const negative_binomial_distribution<RealType, Policy>& dist) - { // kurtosis excess of Negative Binomial distribution - // http://mathworld.wolfram.com/Kurtosis.html table of kurtosis_excess - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - return (6 - p * (6-p)) / (r * (1-p)); - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType variance(const negative_binomial_distribution<RealType, Policy>& dist) - { // Variance of Binomial distribution = r (1-p) / p^2. - return dist.successes() * (1 - dist.success_fraction()) - / (dist.success_fraction() * dist.success_fraction()); - } // variance - - // RealType standard_deviation(const negative_binomial_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - // RealType hazard(const negative_binomial_distribution<RealType, Policy>& dist) - // hazard of Negative Binomial distribution provided by derived accessors. - // RealType chf(const negative_binomial_distribution<RealType, Policy>& dist) - // chf of Negative Binomial distribution provided by derived accessors. - - template <class RealType, class Policy> - inline RealType pdf(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& k) - { // Probability Density/Mass Function. - BOOST_FPU_EXCEPTION_GUARD - - static const char* function = "boost::math::pdf(const negative_binomial_distribution<%1%>&, %1%)"; - - RealType r = dist.successes(); - RealType p = dist.success_fraction(); - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, - r, - dist.success_fraction(), - k, - &result, Policy())) - { - return result; - } - - result = (p/(r + k)) * ibeta_derivative(r, static_cast<RealType>(k+1), p, Policy()); - // Equivalent to: - // return exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p, r) * pow((1-p), k); - return result; - } // negative_binomial_pdf - - template <class RealType, class Policy> - inline RealType cdf(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& k) - { // Cumulative Distribution Function of Negative Binomial. - static const char* function = "boost::math::cdf(const negative_binomial_distribution<%1%>&, %1%)"; - using boost::math::ibeta; // Regularized incomplete beta function. - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - // Error check: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, - r, - dist.success_fraction(), - k, - &result, Policy())) - { - return result; - } - - RealType probability = ibeta(r, static_cast<RealType>(k+1), p, Policy()); - // Ip(r, k+1) = ibeta(r, k+1, p) - return probability; - } // cdf Cumulative Distribution Function Negative Binomial. - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<negative_binomial_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function Negative Binomial. - - static const char* function = "boost::math::cdf(const negative_binomial_distribution<%1%>&, %1%)"; - using boost::math::ibetac; // Regularized incomplete beta function complement. - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - RealType const& k = c.param; - negative_binomial_distribution<RealType, Policy> const& dist = c.dist; - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - // Error check: - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_k( - function, - r, - p, - k, - &result, Policy())) - { - return result; - } - // Calculate cdf negative binomial using the incomplete beta function. - // Use of ibeta here prevents cancellation errors in calculating - // 1-p if p is very small, perhaps smaller than machine epsilon. - // Ip(k+1, r) = ibetac(r, k+1, p) - // constrain_probability here? - RealType probability = ibetac(r, static_cast<RealType>(k+1), p, Policy()); - // Numerical errors might cause probability to be slightly outside the range < 0 or > 1. - // This might cause trouble downstream, so warn, possibly throw exception, but constrain to the limits. - return probability; - } // cdf Cumulative Distribution Function Negative Binomial. - - template <class RealType, class Policy> - inline RealType quantile(const negative_binomial_distribution<RealType, Policy>& dist, const RealType& P) - { // Quantile, percentile/100 or Percent Point Negative Binomial function. - // Return the number of expected failures k for a given probability p. - - // Inverse cumulative Distribution Function or Quantile (percentile / 100) of negative_binomial Probability. - // MAthCAD pnbinom return smallest k such that negative_binomial(k, n, p) >= probability. - // k argument may be integral, signed, or unsigned, or floating point. - // BUT Cephes/CodeCogs says: finds argument p (0 to 1) such that cdf(k, n, p) = y - static const char* function = "boost::math::quantile(const negative_binomial_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING // ADL of std functions. - - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - // Check dist and P. - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_prob - (function, r, p, P, &result, Policy())) - { - return result; - } - - // Special cases. - if (P == 1) - { // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument is 1, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - if (P == 0) - { // No failures are expected if P = 0. - return 0; // Total trials will be just dist.successes. - } - if (P <= pow(dist.success_fraction(), dist.successes())) - { // p <= pdf(dist, 0) == cdf(dist, 0) - return 0; - } - if(p == 0) - { // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Success fraction is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - /* - // Calculate quantile of negative_binomial using the inverse incomplete beta function. - using boost::math::ibeta_invb; - return ibeta_invb(r, p, P, Policy()) - 1; // - */ - RealType guess = 0; - RealType factor = 5; - if(r * r * r * P * p > 0.005) - guess = detail::inverse_negative_binomial_cornish_fisher(r, p, RealType(1-p), P, RealType(1-P), Policy()); - - if(guess < 10) - { - // - // Cornish-Fisher Negative binomial approximation not accurate in this area: - // - guess = (std::min)(RealType(r * 2), RealType(10)); - } - else - factor = (1-P < sqrt(tools::epsilon<RealType>())) ? 2 : (guess < 20 ? 1.2f : 1.1f); - BOOST_MATH_INSTRUMENT_CODE("guess = " << guess); - // - // Max iterations permitted: - // - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - typedef typename Policy::discrete_quantile_type discrete_type; - return detail::inverse_discrete_quantile( - dist, - P, - false, - guess, - factor, - RealType(1), - discrete_type(), - max_iter); - } // RealType quantile(const negative_binomial_distribution dist, p) - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<negative_binomial_distribution<RealType, Policy>, RealType>& c) - { // Quantile or Percent Point Binomial function. - // Return the number of expected failures k for a given - // complement of the probability Q = 1 - P. - static const char* function = "boost::math::quantile(const negative_binomial_distribution<%1%>&, %1%)"; - BOOST_MATH_STD_USING - - // Error checks: - RealType Q = c.param; - const negative_binomial_distribution<RealType, Policy>& dist = c.dist; - RealType p = dist.success_fraction(); - RealType r = dist.successes(); - RealType result = 0; - if(false == negative_binomial_detail::check_dist_and_prob( - function, - r, - p, - Q, - &result, Policy())) - { - return result; - } - - // Special cases: - // - if(Q == 1) - { // There may actually be no answer to this question, - // since the probability of zero failures may be non-zero, - return 0; // but zero is the best we can do: - } - if(Q == 0) - { // Probability 1 - Q == 1 so infinite failures to achieve certainty. - // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Probability argument complement is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - if (-Q <= boost::math::powm1(dist.success_fraction(), dist.successes(), Policy())) - { // q <= cdf(complement(dist, 0)) == pdf(dist, 0) - return 0; // - } - if(p == 0) - { // Success fraction is 0 so infinite failures to achieve certainty. - // Would need +infinity failures for total confidence. - result = policies::raise_overflow_error<RealType>( - function, - "Success fraction is 0, which implies infinite failures !", Policy()); - return result; - // usually means return +std::numeric_limits<RealType>::infinity(); - // unless #define BOOST_MATH_THROW_ON_OVERFLOW_ERROR - } - //return ibetac_invb(r, p, Q, Policy()) -1; - RealType guess = 0; - RealType factor = 5; - if(r * r * r * (1-Q) * p > 0.005) - guess = detail::inverse_negative_binomial_cornish_fisher(r, p, RealType(1-p), RealType(1-Q), Q, Policy()); - - if(guess < 10) - { - // - // Cornish-Fisher Negative binomial approximation not accurate in this area: - // - guess = (std::min)(RealType(r * 2), RealType(10)); - } - else - factor = (Q < sqrt(tools::epsilon<RealType>())) ? 2 : (guess < 20 ? 1.2f : 1.1f); - BOOST_MATH_INSTRUMENT_CODE("guess = " << guess); - // - // Max iterations permitted: - // - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - typedef typename Policy::discrete_quantile_type discrete_type; - return detail::inverse_discrete_quantile( - dist, - Q, - true, - guess, - factor, - RealType(1), - discrete_type(), - max_iter); - } // quantile complement - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#if defined (BOOST_MSVC) -# pragma warning(pop) -#endif - -#endif // BOOST_MATH_SPECIAL_NEGATIVE_BINOMIAL_HPP
--- a/any/include/boost/math/distributions/non_central_beta.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,929 +0,0 @@ -// boost\math\distributions\non_central_beta.hpp - -// Copyright John Maddock 2008. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP -#define BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for incomplete gamma. gamma_q -#include <boost/math/distributions/complement.hpp> // complements -#include <boost/math/distributions/beta.hpp> // central distribution -#include <boost/math/distributions/detail/generic_mode.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. -#include <boost/math/tools/series.hpp> - -namespace boost -{ - namespace math - { - - template <class RealType, class Policy> - class non_central_beta_distribution; - - namespace detail{ - - template <class T, class Policy> - T non_central_beta_p(T a, T b, T lam, T x, T y, const Policy& pol, T init_val = 0) - { - BOOST_MATH_STD_USING - using namespace boost::math; - // - // Variables come first: - // - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T l2 = lam / 2; - // - // k is the starting point for iteration, and is the - // maximum of the poisson weighting term, - // note that unlike other similar code, we do not set - // k to zero, when l2 is small, as forward iteration - // is unstable: - // - int k = itrunc(l2); - if(k == 0) - k = 1; - // Starting Poisson weight: - T pois = gamma_p_derivative(T(k+1), l2, pol); - if(pois == 0) - return init_val; - // recurance term: - T xterm; - // Starting beta term: - T beta = x < y - ? detail::ibeta_imp(T(a + k), b, x, pol, false, true, &xterm) - : detail::ibeta_imp(b, T(a + k), y, pol, true, true, &xterm); - - xterm *= y / (a + b + k - 1); - T poisf(pois), betaf(beta), xtermf(xterm); - T sum = init_val; - - if((beta == 0) && (xterm == 0)) - return init_val; - - // - // Backwards recursion first, this is the stable - // direction for recursion: - // - T last_term = 0; - boost::uintmax_t count = k; - for(int i = k; i >= 0; --i) - { - T term = beta * pois; - sum += term; - if(((fabs(term/sum) < errtol) && (last_term >= term)) || (term == 0)) - { - count = k - i; - break; - } - pois *= i / l2; - beta += xterm; - xterm *= (a + i - 1) / (x * (a + b + i - 2)); - last_term = term; - } - for(int i = k + 1; ; ++i) - { - poisf *= l2 / i; - xtermf *= (x * (a + b + i - 2)) / (a + i - 1); - betaf -= xtermf; - - T term = poisf * betaf; - sum += term; - if((fabs(term/sum) < errtol) || (term == 0)) - { - break; - } - if(static_cast<boost::uintmax_t>(count + i - k) > max_iter) - { - return policies::raise_evaluation_error( - "cdf(non_central_beta_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - } - return sum; - } - - template <class T, class Policy> - T non_central_beta_q(T a, T b, T lam, T x, T y, const Policy& pol, T init_val = 0) - { - BOOST_MATH_STD_USING - using namespace boost::math; - // - // Variables come first: - // - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T l2 = lam / 2; - // - // k is the starting point for iteration, and is the - // maximum of the poisson weighting term: - // - int k = itrunc(l2); - T pois; - if(k <= 30) - { - // - // Might as well start at 0 since we'll likely have this number of terms anyway: - // - if(a + b > 1) - k = 0; - else if(k == 0) - k = 1; - } - if(k == 0) - { - // Starting Poisson weight: - pois = exp(-l2); - } - else - { - // Starting Poisson weight: - pois = gamma_p_derivative(T(k+1), l2, pol); - } - if(pois == 0) - return init_val; - // recurance term: - T xterm; - // Starting beta term: - T beta = x < y - ? detail::ibeta_imp(T(a + k), b, x, pol, true, true, &xterm) - : detail::ibeta_imp(b, T(a + k), y, pol, false, true, &xterm); - - xterm *= y / (a + b + k - 1); - T poisf(pois), betaf(beta), xtermf(xterm); - T sum = init_val; - if((beta == 0) && (xterm == 0)) - return init_val; - // - // Forwards recursion first, this is the stable - // direction for recursion, and the location - // of the bulk of the sum: - // - T last_term = 0; - boost::uintmax_t count = 0; - for(int i = k + 1; ; ++i) - { - poisf *= l2 / i; - xtermf *= (x * (a + b + i - 2)) / (a + i - 1); - betaf += xtermf; - - T term = poisf * betaf; - sum += term; - if((fabs(term/sum) < errtol) && (last_term >= term)) - { - count = i - k; - break; - } - if(static_cast<boost::uintmax_t>(i - k) > max_iter) - { - return policies::raise_evaluation_error( - "cdf(non_central_beta_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - last_term = term; - } - for(int i = k; i >= 0; --i) - { - T term = beta * pois; - sum += term; - if(fabs(term/sum) < errtol) - { - break; - } - if(static_cast<boost::uintmax_t>(count + k - i) > max_iter) - { - return policies::raise_evaluation_error( - "cdf(non_central_beta_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - pois *= i / l2; - beta -= xterm; - xterm *= (a + i - 1) / (x * (a + b + i - 2)); - } - return sum; - } - - template <class RealType, class Policy> - inline RealType non_central_beta_cdf(RealType x, RealType y, RealType a, RealType b, RealType l, bool invert, const Policy&) - { - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - BOOST_MATH_STD_USING - - if(x == 0) - return invert ? 1.0f : 0.0f; - if(y == 0) - return invert ? 0.0f : 1.0f; - value_type result; - value_type c = a + b + l / 2; - value_type cross = 1 - (b / c) * (1 + l / (2 * c * c)); - if(l == 0) - result = cdf(boost::math::beta_distribution<RealType, Policy>(a, b), x); - else if(x > cross) - { - // Complement is the smaller of the two: - result = detail::non_central_beta_q( - static_cast<value_type>(a), - static_cast<value_type>(b), - static_cast<value_type>(l), - static_cast<value_type>(x), - static_cast<value_type>(y), - forwarding_policy(), - static_cast<value_type>(invert ? 0 : -1)); - invert = !invert; - } - else - { - result = detail::non_central_beta_p( - static_cast<value_type>(a), - static_cast<value_type>(b), - static_cast<value_type>(l), - static_cast<value_type>(x), - static_cast<value_type>(y), - forwarding_policy(), - static_cast<value_type>(invert ? -1 : 0)); - } - if(invert) - result = -result; - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - "boost::math::non_central_beta_cdf<%1%>(%1%, %1%, %1%)"); - } - - template <class T, class Policy> - struct nc_beta_quantile_functor - { - nc_beta_quantile_functor(const non_central_beta_distribution<T,Policy>& d, T t, bool c) - : dist(d), target(t), comp(c) {} - - T operator()(const T& x) - { - return comp ? - T(target - cdf(complement(dist, x))) - : T(cdf(dist, x) - target); - } - - private: - non_central_beta_distribution<T,Policy> dist; - T target; - bool comp; - }; - - // - // This is more or less a copy of bracket_and_solve_root, but - // modified to search only the interval [0,1] using similar - // heuristics. - // - template <class F, class T, class Tol, class Policy> - std::pair<T, T> bracket_and_solve_root_01(F f, const T& guess, T factor, bool rising, Tol tol, boost::uintmax_t& max_iter, const Policy& pol) - { - BOOST_MATH_STD_USING - static const char* function = "boost::math::tools::bracket_and_solve_root_01<%1%>"; - // - // Set up inital brackets: - // - T a = guess; - T b = a; - T fa = f(a); - T fb = fa; - // - // Set up invocation count: - // - boost::uintmax_t count = max_iter - 1; - - if((fa < 0) == (guess < 0 ? !rising : rising)) - { - // - // Zero is to the right of b, so walk upwards - // until we find it: - // - while((boost::math::sign)(fb) == (boost::math::sign)(fa)) - { - if(count == 0) - { - b = policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", b, pol); - return std::make_pair(a, b); - } - // - // Heuristic: every 20 iterations we double the growth factor in case the - // initial guess was *really* bad ! - // - if((max_iter - count) % 20 == 0) - factor *= 2; - // - // Now go ahead and move are guess by "factor", - // we do this by reducing 1-guess by factor: - // - a = b; - fa = fb; - b = 1 - ((1 - b) / factor); - fb = f(b); - --count; - BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count); - } - } - else - { - // - // Zero is to the left of a, so walk downwards - // until we find it: - // - while((boost::math::sign)(fb) == (boost::math::sign)(fa)) - { - if(fabs(a) < tools::min_value<T>()) - { - // Escape route just in case the answer is zero! - max_iter -= count; - max_iter += 1; - return a > 0 ? std::make_pair(T(0), T(a)) : std::make_pair(T(a), T(0)); - } - if(count == 0) - { - a = policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", a, pol); - return std::make_pair(a, b); - } - // - // Heuristic: every 20 iterations we double the growth factor in case the - // initial guess was *really* bad ! - // - if((max_iter - count) % 20 == 0) - factor *= 2; - // - // Now go ahead and move are guess by "factor": - // - b = a; - fb = fa; - a /= factor; - fa = f(a); - --count; - BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count); - } - } - max_iter -= count; - max_iter += 1; - std::pair<T, T> r = toms748_solve( - f, - (a < 0 ? b : a), - (a < 0 ? a : b), - (a < 0 ? fb : fa), - (a < 0 ? fa : fb), - tol, - count, - pol); - max_iter += count; - BOOST_MATH_INSTRUMENT_CODE("max_iter = " << max_iter << " count = " << count); - return r; - } - - template <class RealType, class Policy> - RealType nc_beta_quantile(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& p, bool comp) - { - static const char* function = "quantile(non_central_beta_distribution<%1%>, %1%)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - value_type a = dist.alpha(); - value_type b = dist.beta(); - value_type l = dist.non_centrality(); - value_type r; - if(!beta_detail::check_alpha( - function, - a, &r, Policy()) - || - !beta_detail::check_beta( - function, - b, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !detail::check_probability( - function, - static_cast<value_type>(p), - &r, - Policy())) - return (RealType)r; - // - // Special cases first: - // - if(p == 0) - return comp - ? 1.0f - : 0.0f; - if(p == 1) - return !comp - ? 1.0f - : 0.0f; - - value_type c = a + b + l / 2; - value_type mean = 1 - (b / c) * (1 + l / (2 * c * c)); - /* - // - // Calculate a normal approximation to the quantile, - // uses mean and variance approximations from: - // Algorithm AS 310: - // Computing the Non-Central Beta Distribution Function - // R. Chattamvelli; R. Shanmugam - // Applied Statistics, Vol. 46, No. 1. (1997), pp. 146-156. - // - // Unfortunately, when this is wrong it tends to be *very* - // wrong, so it's disabled for now, even though it often - // gets the initial guess quite close. Probably we could - // do much better by factoring in the skewness if only - // we could calculate it.... - // - value_type delta = l / 2; - value_type delta2 = delta * delta; - value_type delta3 = delta * delta2; - value_type delta4 = delta2 * delta2; - value_type G = c * (c + 1) + delta; - value_type alpha = a + b; - value_type alpha2 = alpha * alpha; - value_type eta = (2 * alpha + 1) * (2 * alpha + 1) + 1; - value_type H = 3 * alpha2 + 5 * alpha + 2; - value_type F = alpha2 * (alpha + 1) + H * delta - + (2 * alpha + 4) * delta2 + delta3; - value_type P = (3 * alpha + 1) * (9 * alpha + 17) - + 2 * alpha * (3 * alpha + 2) * (3 * alpha + 4) + 15; - value_type Q = 54 * alpha2 + 162 * alpha + 130; - value_type R = 6 * (6 * alpha + 11); - value_type D = delta - * (H * H + 2 * P * delta + Q * delta2 + R * delta3 + 9 * delta4); - value_type variance = (b / G) - * (1 + delta * (l * l + 3 * l + eta) / (G * G)) - - (b * b / F) * (1 + D / (F * F)); - value_type sd = sqrt(variance); - - value_type guess = comp - ? quantile(complement(normal_distribution<RealType, Policy>(static_cast<RealType>(mean), static_cast<RealType>(sd)), p)) - : quantile(normal_distribution<RealType, Policy>(static_cast<RealType>(mean), static_cast<RealType>(sd)), p); - - if(guess >= 1) - guess = mean; - if(guess <= tools::min_value<value_type>()) - guess = mean; - */ - value_type guess = mean; - detail::nc_beta_quantile_functor<value_type, Policy> - f(non_central_beta_distribution<value_type, Policy>(a, b, l), p, comp); - tools::eps_tolerance<value_type> tol(policies::digits<RealType, Policy>()); - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - - std::pair<value_type, value_type> ir - = bracket_and_solve_root_01( - f, guess, value_type(2.5), true, tol, - max_iter, Policy()); - value_type result = ir.first + (ir.second - ir.first) / 2; - - if(max_iter >= policies::get_max_root_iterations<Policy>()) - { - return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:" - " either there is no answer to quantile of the non central beta distribution" - " or the answer is infinite. Current best guess is %1%", - policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function), Policy()); - } - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - - template <class T, class Policy> - T non_central_beta_pdf(T a, T b, T lam, T x, T y, const Policy& pol) - { - BOOST_MATH_STD_USING - // - // Special cases: - // - if((x == 0) || (y == 0)) - return 0; - // - // Variables come first: - // - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T l2 = lam / 2; - // - // k is the starting point for iteration, and is the - // maximum of the poisson weighting term: - // - int k = itrunc(l2); - // Starting Poisson weight: - T pois = gamma_p_derivative(T(k+1), l2, pol); - // Starting beta term: - T beta = x < y ? - ibeta_derivative(a + k, b, x, pol) - : ibeta_derivative(b, a + k, y, pol); - T sum = 0; - T poisf(pois); - T betaf(beta); - - // - // Stable backwards recursion first: - // - boost::uintmax_t count = k; - for(int i = k; i >= 0; --i) - { - T term = beta * pois; - sum += term; - if((fabs(term/sum) < errtol) || (term == 0)) - { - count = k - i; - break; - } - pois *= i / l2; - beta *= (a + i - 1) / (x * (a + i + b - 1)); - } - for(int i = k + 1; ; ++i) - { - poisf *= l2 / i; - betaf *= x * (a + b + i - 1) / (a + i - 1); - - T term = poisf * betaf; - sum += term; - if((fabs(term/sum) < errtol) || (term == 0)) - { - break; - } - if(static_cast<boost::uintmax_t>(count + i - k) > max_iter) - { - return policies::raise_evaluation_error( - "pdf(non_central_beta_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - } - return sum; - } - - template <class RealType, class Policy> - RealType nc_beta_pdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x) - { - BOOST_MATH_STD_USING - static const char* function = "pdf(non_central_beta_distribution<%1%>, %1%)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - value_type a = dist.alpha(); - value_type b = dist.beta(); - value_type l = dist.non_centrality(); - value_type r; - if(!beta_detail::check_alpha( - function, - a, &r, Policy()) - || - !beta_detail::check_beta( - function, - b, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !beta_detail::check_x( - function, - static_cast<value_type>(x), - &r, - Policy())) - return (RealType)r; - - if(l == 0) - return pdf(boost::math::beta_distribution<RealType, Policy>(dist.alpha(), dist.beta()), x); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - non_central_beta_pdf(a, b, l, static_cast<value_type>(x), value_type(1 - static_cast<value_type>(x)), forwarding_policy()), - "function"); - } - - template <class T> - struct hypergeometric_2F2_sum - { - typedef T result_type; - hypergeometric_2F2_sum(T a1_, T a2_, T b1_, T b2_, T z_) : a1(a1_), a2(a2_), b1(b1_), b2(b2_), z(z_), term(1), k(0) {} - T operator()() - { - T result = term; - term *= a1 * a2 / (b1 * b2); - a1 += 1; - a2 += 1; - b1 += 1; - b2 += 1; - k += 1; - term /= k; - term *= z; - return result; - } - T a1, a2, b1, b2, z, term, k; - }; - - template <class T, class Policy> - T hypergeometric_2F2(T a1, T a2, T b1, T b2, T z, const Policy& pol) - { - typedef typename policies::evaluation<T, Policy>::type value_type; - - const char* function = "boost::math::detail::hypergeometric_2F2<%1%>(%1%,%1%,%1%,%1%,%1%)"; - - hypergeometric_2F2_sum<value_type> s(a1, a2, b1, b2, z); - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); -#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582)) - value_type zero = 0; - value_type result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<value_type, Policy>(), max_iter, zero); -#else - value_type result = boost::math::tools::sum_series(s, boost::math::policies::get_epsilon<value_type, Policy>(), max_iter); -#endif - policies::check_series_iterations<T>(function, max_iter, pol); - return policies::checked_narrowing_cast<T, Policy>(result, function); - } - - } // namespace detail - - template <class RealType = double, class Policy = policies::policy<> > - class non_central_beta_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - non_central_beta_distribution(RealType a_, RealType b_, RealType lambda) : a(a_), b(b_), ncp(lambda) - { - const char* function = "boost::math::non_central_beta_distribution<%1%>::non_central_beta_distribution(%1%,%1%)"; - RealType r; - beta_detail::check_alpha( - function, - a, &r, Policy()); - beta_detail::check_beta( - function, - b, &r, Policy()); - detail::check_non_centrality( - function, - lambda, - &r, - Policy()); - } // non_central_beta_distribution constructor. - - RealType alpha() const - { // Private data getter function. - return a; - } - RealType beta() const - { // Private data getter function. - return b; - } - RealType non_centrality() const - { // Private data getter function. - return ncp; - } - private: - // Data member, initialized by constructor. - RealType a; // alpha. - RealType b; // beta. - RealType ncp; // non-centrality parameter - }; // template <class RealType, class Policy> class non_central_beta_distribution - - typedef non_central_beta_distribution<double> non_central_beta; // Reserved name of type double. - - // Non-member functions to give properties of the distribution. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const non_central_beta_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1)); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const non_central_beta_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), static_cast<RealType>(1)); - } - - template <class RealType, class Policy> - inline RealType mode(const non_central_beta_distribution<RealType, Policy>& dist) - { // mode. - static const char* function = "mode(non_central_beta_distribution<%1%> const&)"; - - RealType a = dist.alpha(); - RealType b = dist.beta(); - RealType l = dist.non_centrality(); - RealType r; - if(!beta_detail::check_alpha( - function, - a, &r, Policy()) - || - !beta_detail::check_beta( - function, - b, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return (RealType)r; - RealType c = a + b + l / 2; - RealType mean = 1 - (b / c) * (1 + l / (2 * c * c)); - return detail::generic_find_mode_01( - dist, - mean, - function); - } - - // - // We don't have the necessary information to implement - // these at present. These are just disabled for now, - // prototypes retained so we can fill in the blanks - // later: - // - template <class RealType, class Policy> - inline RealType mean(const non_central_beta_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING - RealType a = dist.alpha(); - RealType b = dist.beta(); - RealType d = dist.non_centrality(); - RealType apb = a + b; - return exp(-d / 2) * a * detail::hypergeometric_2F2<RealType, Policy>(1 + a, apb, a, 1 + apb, d / 2, Policy()) / apb; - } // mean - - template <class RealType, class Policy> - inline RealType variance(const non_central_beta_distribution<RealType, Policy>& dist) - { - // - // Relative error of this function may be arbitarily large... absolute - // error will be small however... that's the best we can do for now. - // - BOOST_MATH_STD_USING - RealType a = dist.alpha(); - RealType b = dist.beta(); - RealType d = dist.non_centrality(); - RealType apb = a + b; - RealType result = detail::hypergeometric_2F2(RealType(1 + a), apb, a, RealType(1 + apb), RealType(d / 2), Policy()); - result *= result * -exp(-d) * a * a / (apb * apb); - result += exp(-d / 2) * a * (1 + a) * detail::hypergeometric_2F2(RealType(2 + a), apb, a, RealType(2 + apb), RealType(d / 2), Policy()) / (apb * (1 + apb)); - return result; - } - - // RealType standard_deviation(const non_central_beta_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - template <class RealType, class Policy> - inline RealType skewness(const non_central_beta_distribution<RealType, Policy>& /*dist*/) - { // skewness = sqrt(l). - const char* function = "boost::math::non_central_beta_distribution<%1%>::skewness()"; - typedef typename Policy::assert_undefined_type assert_type; - BOOST_STATIC_ASSERT(assert_type::value == 0); - - return policies::raise_evaluation_error<RealType>( - function, - "This function is not yet implemented, the only sensible result is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity? - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const non_central_beta_distribution<RealType, Policy>& /*dist*/) - { - const char* function = "boost::math::non_central_beta_distribution<%1%>::kurtosis_excess()"; - typedef typename Policy::assert_undefined_type assert_type; - BOOST_STATIC_ASSERT(assert_type::value == 0); - - return policies::raise_evaluation_error<RealType>( - function, - "This function is not yet implemented, the only sensible result is %1%.", - std::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity? - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const non_central_beta_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist) + 3; - } - - template <class RealType, class Policy> - inline RealType pdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x) - { // Probability Density/Mass Function. - return detail::nc_beta_pdf(dist, x); - } // pdf - - template <class RealType, class Policy> - RealType cdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x) - { - const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)"; - RealType a = dist.alpha(); - RealType b = dist.beta(); - RealType l = dist.non_centrality(); - RealType r; - if(!beta_detail::check_alpha( - function, - a, &r, Policy()) - || - !beta_detail::check_beta( - function, - b, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !beta_detail::check_x( - function, - x, - &r, - Policy())) - return (RealType)r; - - if(l == 0) - return cdf(beta_distribution<RealType, Policy>(a, b), x); - - return detail::non_central_beta_cdf(x, RealType(1 - x), a, b, l, false, Policy()); - } // cdf - - template <class RealType, class Policy> - RealType cdf(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function - const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)"; - non_central_beta_distribution<RealType, Policy> const& dist = c.dist; - RealType a = dist.alpha(); - RealType b = dist.beta(); - RealType l = dist.non_centrality(); - RealType x = c.param; - RealType r; - if(!beta_detail::check_alpha( - function, - a, &r, Policy()) - || - !beta_detail::check_beta( - function, - b, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !beta_detail::check_x( - function, - x, - &r, - Policy())) - return (RealType)r; - - if(l == 0) - return cdf(complement(beta_distribution<RealType, Policy>(a, b), x)); - - return detail::non_central_beta_cdf(x, RealType(1 - x), a, b, l, true, Policy()); - } // ccdf - - template <class RealType, class Policy> - inline RealType quantile(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile (or Percent Point) function. - return detail::nc_beta_quantile(dist, p, false); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c) - { // Quantile (or Percent Point) function. - return detail::nc_beta_quantile(c.dist, c.param, true); - } // quantile complement. - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP -
--- a/any/include/boost/math/distributions/non_central_chi_squared.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,999 +0,0 @@ -// boost\math\distributions\non_central_chi_squared.hpp - -// Copyright John Maddock 2008. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_CHI_SQUARE_HPP -#define BOOST_MATH_SPECIAL_NON_CENTRAL_CHI_SQUARE_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/gamma.hpp> // for incomplete gamma. gamma_q -#include <boost/math/special_functions/bessel.hpp> // for cyl_bessel_i -#include <boost/math/special_functions/round.hpp> // for iround -#include <boost/math/distributions/complement.hpp> // complements -#include <boost/math/distributions/chi_squared.hpp> // central distribution -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/tools/roots.hpp> // for root finding. -#include <boost/math/distributions/detail/generic_mode.hpp> -#include <boost/math/distributions/detail/generic_quantile.hpp> - -namespace boost -{ - namespace math - { - - template <class RealType, class Policy> - class non_central_chi_squared_distribution; - - namespace detail{ - - template <class T, class Policy> - T non_central_chi_square_q(T x, T f, T theta, const Policy& pol, T init_sum = 0) - { - // - // Computes the complement of the Non-Central Chi-Square - // Distribution CDF by summing a weighted sum of complements - // of the central-distributions. The weighting factor is - // a Poisson Distribution. - // - // This is an application of the technique described in: - // - // Computing discrete mixtures of continuous - // distributions: noncentral chisquare, noncentral t - // and the distribution of the square of the sample - // multiple correlation coeficient. - // D. Benton, K. Krishnamoorthy. - // Computational Statistics & Data Analysis 43 (2003) 249 - 267 - // - BOOST_MATH_STD_USING - - // Special case: - if(x == 0) - return 1; - - // - // Initialize the variables we'll be using: - // - T lambda = theta / 2; - T del = f / 2; - T y = x / 2; - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T sum = init_sum; - // - // k is the starting location for iteration, we'll - // move both forwards and backwards from this point. - // k is chosen as the peek of the Poisson weights, which - // will occur *before* the largest term. - // - int k = iround(lambda, pol); - // Forwards and backwards Poisson weights: - T poisf = boost::math::gamma_p_derivative(static_cast<T>(1 + k), lambda, pol); - T poisb = poisf * k / lambda; - // Initial forwards central chi squared term: - T gamf = boost::math::gamma_q(del + k, y, pol); - // Forwards and backwards recursion terms on the central chi squared: - T xtermf = boost::math::gamma_p_derivative(del + 1 + k, y, pol); - T xtermb = xtermf * (del + k) / y; - // Initial backwards central chi squared term: - T gamb = gamf - xtermb; - - // - // Forwards iteration first, this is the - // stable direction for the gamma function - // recurrences: - // - int i; - for(i = k; static_cast<boost::uintmax_t>(i-k) < max_iter; ++i) - { - T term = poisf * gamf; - sum += term; - poisf *= lambda / (i + 1); - gamf += xtermf; - xtermf *= y / (del + i + 1); - if(((sum == 0) || (fabs(term / sum) < errtol)) && (term >= poisf * gamf)) - break; - } - //Error check: - if(static_cast<boost::uintmax_t>(i-k) >= max_iter) - return policies::raise_evaluation_error( - "cdf(non_central_chi_squared_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - // - // Now backwards iteration: the gamma - // function recurrences are unstable in this - // direction, we rely on the terms deminishing in size - // faster than we introduce cancellation errors. - // For this reason it's very important that we start - // *before* the largest term so that backwards iteration - // is strictly converging. - // - for(i = k - 1; i >= 0; --i) - { - T term = poisb * gamb; - sum += term; - poisb *= i / lambda; - xtermb *= (del + i) / y; - gamb -= xtermb; - if((sum == 0) || (fabs(term / sum) < errtol)) - break; - } - - return sum; - } - - template <class T, class Policy> - T non_central_chi_square_p_ding(T x, T f, T theta, const Policy& pol, T init_sum = 0) - { - // - // This is an implementation of: - // - // Algorithm AS 275: - // Computing the Non-Central #2 Distribution Function - // Cherng G. Ding - // Applied Statistics, Vol. 41, No. 2. (1992), pp. 478-482. - // - // This uses a stable forward iteration to sum the - // CDF, unfortunately this can not be used for large - // values of the non-centrality parameter because: - // * The first term may underfow to zero. - // * We may need an extra-ordinary number of terms - // before we reach the first *significant* term. - // - BOOST_MATH_STD_USING - // Special case: - if(x == 0) - return 0; - T tk = boost::math::gamma_p_derivative(f/2 + 1, x/2, pol); - T lambda = theta / 2; - T vk = exp(-lambda); - T uk = vk; - T sum = init_sum + tk * vk; - if(sum == 0) - return sum; - - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - - int i; - T lterm(0), term(0); - for(i = 1; static_cast<boost::uintmax_t>(i) < max_iter; ++i) - { - tk = tk * x / (f + 2 * i); - uk = uk * lambda / i; - vk = vk + uk; - lterm = term; - term = vk * tk; - sum += term; - if((fabs(term / sum) < errtol) && (term <= lterm)) - break; - } - //Error check: - if(static_cast<boost::uintmax_t>(i) >= max_iter) - return policies::raise_evaluation_error( - "cdf(non_central_chi_squared_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - return sum; - } - - - template <class T, class Policy> - T non_central_chi_square_p(T y, T n, T lambda, const Policy& pol, T init_sum) - { - // - // This is taken more or less directly from: - // - // Computing discrete mixtures of continuous - // distributions: noncentral chisquare, noncentral t - // and the distribution of the square of the sample - // multiple correlation coeficient. - // D. Benton, K. Krishnamoorthy. - // Computational Statistics & Data Analysis 43 (2003) 249 - 267 - // - // We're summing a Poisson weighting term multiplied by - // a central chi squared distribution. - // - BOOST_MATH_STD_USING - // Special case: - if(y == 0) - return 0; - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T errorf(0), errorb(0); - - T x = y / 2; - T del = lambda / 2; - // - // Starting location for the iteration, we'll iterate - // both forwards and backwards from this point. The - // location chosen is the maximum of the Poisson weight - // function, which ocurrs *after* the largest term in the - // sum. - // - int k = iround(del, pol); - T a = n / 2 + k; - // Central chi squared term for forward iteration: - T gamkf = boost::math::gamma_p(a, x, pol); - - if(lambda == 0) - return gamkf; - // Central chi squared term for backward iteration: - T gamkb = gamkf; - // Forwards Poisson weight: - T poiskf = gamma_p_derivative(static_cast<T>(k+1), del, pol); - // Backwards Poisson weight: - T poiskb = poiskf; - // Forwards gamma function recursion term: - T xtermf = boost::math::gamma_p_derivative(a, x, pol); - // Backwards gamma function recursion term: - T xtermb = xtermf * x / a; - T sum = init_sum + poiskf * gamkf; - if(sum == 0) - return sum; - int i = 1; - // - // Backwards recursion first, this is the stable - // direction for gamma function recurrences: - // - while(i <= k) - { - xtermb *= (a - i + 1) / x; - gamkb += xtermb; - poiskb = poiskb * (k - i + 1) / del; - errorf = errorb; - errorb = gamkb * poiskb; - sum += errorb; - if((fabs(errorb / sum) < errtol) && (errorb <= errorf)) - break; - ++i; - } - i = 1; - // - // Now forwards recursion, the gamma function - // recurrence relation is unstable in this direction, - // so we rely on the magnitude of successive terms - // decreasing faster than we introduce cancellation error. - // For this reason it's vital that k is chosen to be *after* - // the largest term, so that successive forward iterations - // are strictly (and rapidly) converging. - // - do - { - xtermf = xtermf * x / (a + i - 1); - gamkf = gamkf - xtermf; - poiskf = poiskf * del / (k + i); - errorf = poiskf * gamkf; - sum += errorf; - ++i; - }while((fabs(errorf / sum) > errtol) && (static_cast<boost::uintmax_t>(i) < max_iter)); - - //Error check: - if(static_cast<boost::uintmax_t>(i) >= max_iter) - return policies::raise_evaluation_error( - "cdf(non_central_chi_squared_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - - return sum; - } - - template <class T, class Policy> - T non_central_chi_square_pdf(T x, T n, T lambda, const Policy& pol) - { - // - // As above but for the PDF: - // - BOOST_MATH_STD_USING - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T x2 = x / 2; - T n2 = n / 2; - T l2 = lambda / 2; - T sum = 0; - int k = itrunc(l2); - T pois = gamma_p_derivative(static_cast<T>(k + 1), l2, pol) * gamma_p_derivative(static_cast<T>(n2 + k), x2); - if(pois == 0) - return 0; - T poisb = pois; - for(int i = k; ; ++i) - { - sum += pois; - if(pois / sum < errtol) - break; - if(static_cast<boost::uintmax_t>(i - k) >= max_iter) - return policies::raise_evaluation_error( - "pdf(non_central_chi_squared_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - pois *= l2 * x2 / ((i + 1) * (n2 + i)); - } - for(int i = k - 1; i >= 0; --i) - { - poisb *= (i + 1) * (n2 + i) / (l2 * x2); - sum += poisb; - if(poisb / sum < errtol) - break; - } - return sum / 2; - } - - template <class RealType, class Policy> - inline RealType non_central_chi_squared_cdf(RealType x, RealType k, RealType l, bool invert, const Policy&) - { - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - BOOST_MATH_STD_USING - value_type result; - if(l == 0) - return invert == false ? cdf(boost::math::chi_squared_distribution<RealType, Policy>(k), x) : cdf(complement(boost::math::chi_squared_distribution<RealType, Policy>(k), x)); - else if(x > k + l) - { - // Complement is the smaller of the two: - result = detail::non_central_chi_square_q( - static_cast<value_type>(x), - static_cast<value_type>(k), - static_cast<value_type>(l), - forwarding_policy(), - static_cast<value_type>(invert ? 0 : -1)); - invert = !invert; - } - else if(l < 200) - { - // For small values of the non-centrality parameter - // we can use Ding's method: - result = detail::non_central_chi_square_p_ding( - static_cast<value_type>(x), - static_cast<value_type>(k), - static_cast<value_type>(l), - forwarding_policy(), - static_cast<value_type>(invert ? -1 : 0)); - } - else - { - // For largers values of the non-centrality - // parameter Ding's method will consume an - // extra-ordinary number of terms, and worse - // may return zero when the result is in fact - // finite, use Krishnamoorthy's method instead: - result = detail::non_central_chi_square_p( - static_cast<value_type>(x), - static_cast<value_type>(k), - static_cast<value_type>(l), - forwarding_policy(), - static_cast<value_type>(invert ? -1 : 0)); - } - if(invert) - result = -result; - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - "boost::math::non_central_chi_squared_cdf<%1%>(%1%, %1%, %1%)"); - } - - template <class T, class Policy> - struct nccs_quantile_functor - { - nccs_quantile_functor(const non_central_chi_squared_distribution<T,Policy>& d, T t, bool c) - : dist(d), target(t), comp(c) {} - - T operator()(const T& x) - { - return comp ? - target - cdf(complement(dist, x)) - : cdf(dist, x) - target; - } - - private: - non_central_chi_squared_distribution<T,Policy> dist; - T target; - bool comp; - }; - - template <class RealType, class Policy> - RealType nccs_quantile(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& p, bool comp) - { - BOOST_MATH_STD_USING - static const char* function = "quantile(non_central_chi_squared_distribution<%1%>, %1%)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - value_type k = dist.degrees_of_freedom(); - value_type l = dist.non_centrality(); - value_type r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !detail::check_probability( - function, - static_cast<value_type>(p), - &r, - Policy())) - return (RealType)r; - // - // Special cases get short-circuited first: - // - if(p == 0) - return comp ? policies::raise_overflow_error<RealType>(function, 0, Policy()) : 0; - if(p == 1) - return comp ? 0 : policies::raise_overflow_error<RealType>(function, 0, Policy()); - // - // This is Pearson's approximation to the quantile, see - // Pearson, E. S. (1959) "Note on an approximation to the distribution of - // noncentral chi squared", Biometrika 46: 364. - // See also: - // "A comparison of approximations to percentiles of the noncentral chi2-distribution", - // Hardeo Sahai and Mario Miguel Ojeda, Revista de Matematica: Teoria y Aplicaciones 2003 10(1-2) : 57-76. - // Note that the latter reference refers to an approximation of the CDF, when they really mean the quantile. - // - value_type b = -(l * l) / (k + 3 * l); - value_type c = (k + 3 * l) / (k + 2 * l); - value_type ff = (k + 2 * l) / (c * c); - value_type guess; - if(comp) - { - guess = b + c * quantile(complement(chi_squared_distribution<value_type, forwarding_policy>(ff), p)); - } - else - { - guess = b + c * quantile(chi_squared_distribution<value_type, forwarding_policy>(ff), p); - } - // - // Sometimes guess goes very small or negative, in that case we have - // to do something else for the initial guess, this approximation - // was provided in a private communication from Thomas Luu, PhD candidate, - // University College London. It's an asymptotic expansion for the - // quantile which usually gets us within an order of magnitude of the - // correct answer. - // Fast and accurate parallel computation of quantile functions for random number generation, - // Thomas LuuDoctorial Thesis 2016 - // http://discovery.ucl.ac.uk/1482128/ - // - if(guess < 0.005) - { - value_type pp = comp ? 1 - p : p; - //guess = pow(pow(value_type(2), (k / 2 - 1)) * exp(l / 2) * pp * k, 2 / k); - guess = pow(pow(value_type(2), (k / 2 - 1)) * exp(l / 2) * pp * k * boost::math::tgamma(k / 2, forwarding_policy()), (2 / k)); - if(guess == 0) - guess = tools::min_value<value_type>(); - } - value_type result = detail::generic_quantile( - non_central_chi_squared_distribution<value_type, forwarding_policy>(k, l), - p, - guess, - comp, - function); - - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - - template <class RealType, class Policy> - RealType nccs_pdf(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) - { - BOOST_MATH_STD_USING - static const char* function = "pdf(non_central_chi_squared_distribution<%1%>, %1%)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - value_type k = dist.degrees_of_freedom(); - value_type l = dist.non_centrality(); - value_type r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !detail::check_positive_x( - function, - (value_type)x, - &r, - Policy())) - return (RealType)r; - - if(l == 0) - return pdf(boost::math::chi_squared_distribution<RealType, forwarding_policy>(dist.degrees_of_freedom()), x); - - // Special case: - if(x == 0) - return 0; - if(l > 50) - { - r = non_central_chi_square_pdf(static_cast<value_type>(x), k, l, forwarding_policy()); - } - else - { - r = log(x / l) * (k / 4 - 0.5f) - (x + l) / 2; - if(fabs(r) >= tools::log_max_value<RealType>() / 4) - { - r = non_central_chi_square_pdf(static_cast<value_type>(x), k, l, forwarding_policy()); - } - else - { - r = exp(r); - r = 0.5f * r - * boost::math::cyl_bessel_i(k/2 - 1, sqrt(l * x), forwarding_policy()); - } - } - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - r, - function); - } - - template <class RealType, class Policy> - struct degrees_of_freedom_finder - { - degrees_of_freedom_finder( - RealType lam_, RealType x_, RealType p_, bool c) - : lam(lam_), x(x_), p(p_), comp(c) {} - - RealType operator()(const RealType& v) - { - non_central_chi_squared_distribution<RealType, Policy> d(v, lam); - return comp ? - RealType(p - cdf(complement(d, x))) - : RealType(cdf(d, x) - p); - } - private: - RealType lam; - RealType x; - RealType p; - bool comp; - }; - - template <class RealType, class Policy> - inline RealType find_degrees_of_freedom( - RealType lam, RealType x, RealType p, RealType q, const Policy& pol) - { - const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom"; - if((p == 0) || (q == 0)) - { - // - // Can't a thing if one of p and q is zero: - // - return policies::raise_evaluation_error<RealType>(function, - "Can't find degrees of freedom when the probability is 0 or 1, only possible answer is %1%", - RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy()); - } - degrees_of_freedom_finder<RealType, Policy> f(lam, x, p < q ? p : q, p < q ? false : true); - tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>()); - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - // - // Pick an initial guess that we know will give us a probability - // right around 0.5. - // - RealType guess = x - lam; - if(guess < 1) - guess = 1; - std::pair<RealType, RealType> ir = tools::bracket_and_solve_root( - f, guess, RealType(2), false, tol, max_iter, pol); - RealType result = ir.first + (ir.second - ir.first) / 2; - if(max_iter >= policies::get_max_root_iterations<Policy>()) - { - return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:" - " or there is no answer to problem. Current best guess is %1%", result, Policy()); - } - return result; - } - - template <class RealType, class Policy> - struct non_centrality_finder - { - non_centrality_finder( - RealType v_, RealType x_, RealType p_, bool c) - : v(v_), x(x_), p(p_), comp(c) {} - - RealType operator()(const RealType& lam) - { - non_central_chi_squared_distribution<RealType, Policy> d(v, lam); - return comp ? - RealType(p - cdf(complement(d, x))) - : RealType(cdf(d, x) - p); - } - private: - RealType v; - RealType x; - RealType p; - bool comp; - }; - - template <class RealType, class Policy> - inline RealType find_non_centrality( - RealType v, RealType x, RealType p, RealType q, const Policy& pol) - { - const char* function = "non_central_chi_squared<%1%>::find_non_centrality"; - if((p == 0) || (q == 0)) - { - // - // Can't do a thing if one of p and q is zero: - // - return policies::raise_evaluation_error<RealType>(function, - "Can't find non centrality parameter when the probability is 0 or 1, only possible answer is %1%", - RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy()); - } - non_centrality_finder<RealType, Policy> f(v, x, p < q ? p : q, p < q ? false : true); - tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>()); - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - // - // Pick an initial guess that we know will give us a probability - // right around 0.5. - // - RealType guess = x - v; - if(guess < 1) - guess = 1; - std::pair<RealType, RealType> ir = tools::bracket_and_solve_root( - f, guess, RealType(2), false, tol, max_iter, pol); - RealType result = ir.first + (ir.second - ir.first) / 2; - if(max_iter >= policies::get_max_root_iterations<Policy>()) - { - return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:" - " or there is no answer to problem. Current best guess is %1%", result, Policy()); - } - return result; - } - - } - - template <class RealType = double, class Policy = policies::policy<> > - class non_central_chi_squared_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - non_central_chi_squared_distribution(RealType df_, RealType lambda) : df(df_), ncp(lambda) - { - const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::non_central_chi_squared_distribution(%1%,%1%)"; - RealType r; - detail::check_df( - function, - df, &r, Policy()); - detail::check_non_centrality( - function, - ncp, - &r, - Policy()); - } // non_central_chi_squared_distribution constructor. - - RealType degrees_of_freedom() const - { // Private data getter function. - return df; - } - RealType non_centrality() const - { // Private data getter function. - return ncp; - } - static RealType find_degrees_of_freedom(RealType lam, RealType x, RealType p) - { - const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom"; - typedef typename policies::evaluation<RealType, Policy>::type eval_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - eval_type result = detail::find_degrees_of_freedom( - static_cast<eval_type>(lam), - static_cast<eval_type>(x), - static_cast<eval_type>(p), - static_cast<eval_type>(1-p), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - template <class A, class B, class C> - static RealType find_degrees_of_freedom(const complemented3_type<A,B,C>& c) - { - const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom"; - typedef typename policies::evaluation<RealType, Policy>::type eval_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - eval_type result = detail::find_degrees_of_freedom( - static_cast<eval_type>(c.dist), - static_cast<eval_type>(c.param1), - static_cast<eval_type>(1-c.param2), - static_cast<eval_type>(c.param2), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - static RealType find_non_centrality(RealType v, RealType x, RealType p) - { - const char* function = "non_central_chi_squared<%1%>::find_non_centrality"; - typedef typename policies::evaluation<RealType, Policy>::type eval_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - eval_type result = detail::find_non_centrality( - static_cast<eval_type>(v), - static_cast<eval_type>(x), - static_cast<eval_type>(p), - static_cast<eval_type>(1-p), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - template <class A, class B, class C> - static RealType find_non_centrality(const complemented3_type<A,B,C>& c) - { - const char* function = "non_central_chi_squared<%1%>::find_non_centrality"; - typedef typename policies::evaluation<RealType, Policy>::type eval_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - eval_type result = detail::find_non_centrality( - static_cast<eval_type>(c.dist), - static_cast<eval_type>(c.param1), - static_cast<eval_type>(1-c.param2), - static_cast<eval_type>(c.param2), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - private: - // Data member, initialized by constructor. - RealType df; // degrees of freedom. - RealType ncp; // non-centrality parameter - }; // template <class RealType, class Policy> class non_central_chi_squared_distribution - - typedef non_central_chi_squared_distribution<double> non_central_chi_squared; // Reserved name of type double. - - // Non-member functions to give properties of the distribution. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const non_central_chi_squared_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // Max integer? - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const non_central_chi_squared_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); - } - - template <class RealType, class Policy> - inline RealType mean(const non_central_chi_squared_distribution<RealType, Policy>& dist) - { // Mean of poisson distribution = lambda. - const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::mean()"; - RealType k = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - return k + l; - } // mean - - template <class RealType, class Policy> - inline RealType mode(const non_central_chi_squared_distribution<RealType, Policy>& dist) - { // mode. - static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)"; - - RealType k = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return (RealType)r; - return detail::generic_find_mode(dist, 1 + k, function); - } - - template <class RealType, class Policy> - inline RealType variance(const non_central_chi_squared_distribution<RealType, Policy>& dist) - { // variance. - const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::variance()"; - RealType k = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - return 2 * (2 * l + k); - } - - // RealType standard_deviation(const non_central_chi_squared_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - - template <class RealType, class Policy> - inline RealType skewness(const non_central_chi_squared_distribution<RealType, Policy>& dist) - { // skewness = sqrt(l). - const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::skewness()"; - RealType k = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - BOOST_MATH_STD_USING - return pow(2 / (k + 2 * l), RealType(3)/2) * (k + 3 * l); - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const non_central_chi_squared_distribution<RealType, Policy>& dist) - { - const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::kurtosis_excess()"; - RealType k = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - return 12 * (k + 4 * l) / ((k + 2 * l) * (k + 2 * l)); - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const non_central_chi_squared_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist) + 3; - } - - template <class RealType, class Policy> - inline RealType pdf(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) - { // Probability Density/Mass Function. - return detail::nccs_pdf(dist, x); - } // pdf - - template <class RealType, class Policy> - RealType cdf(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) - { - const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::cdf(%1%)"; - RealType k = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !detail::check_positive_x( - function, - x, - &r, - Policy())) - return r; - - return detail::non_central_chi_squared_cdf(x, k, l, false, Policy()); - } // cdf - - template <class RealType, class Policy> - RealType cdf(const complemented2_type<non_central_chi_squared_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function - const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::cdf(%1%)"; - non_central_chi_squared_distribution<RealType, Policy> const& dist = c.dist; - RealType x = c.param; - RealType k = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - k, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy()) - || - !detail::check_positive_x( - function, - x, - &r, - Policy())) - return r; - - return detail::non_central_chi_squared_cdf(x, k, l, true, Policy()); - } // ccdf - - template <class RealType, class Policy> - inline RealType quantile(const non_central_chi_squared_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile (or Percent Point) function. - return detail::nccs_quantile(dist, p, false); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<non_central_chi_squared_distribution<RealType, Policy>, RealType>& c) - { // Quantile (or Percent Point) function. - return detail::nccs_quantile(c.dist, c.param, true); - } // quantile complement. - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_CHI_SQUARE_HPP - - -
--- a/any/include/boost/math/distributions/non_central_f.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,410 +0,0 @@ -// boost\math\distributions\non_central_f.hpp - -// Copyright John Maddock 2008. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP -#define BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP - -#include <boost/math/distributions/non_central_beta.hpp> -#include <boost/math/distributions/detail/generic_mode.hpp> -#include <boost/math/special_functions/pow.hpp> - -namespace boost -{ - namespace math - { - template <class RealType = double, class Policy = policies::policy<> > - class non_central_f_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - non_central_f_distribution(RealType v1_, RealType v2_, RealType lambda) : v1(v1_), v2(v2_), ncp(lambda) - { - const char* function = "boost::math::non_central_f_distribution<%1%>::non_central_f_distribution(%1%,%1%)"; - RealType r; - detail::check_df( - function, - v1, &r, Policy()); - detail::check_df( - function, - v2, &r, Policy()); - detail::check_non_centrality( - function, - lambda, - &r, - Policy()); - } // non_central_f_distribution constructor. - - RealType degrees_of_freedom1()const - { - return v1; - } - RealType degrees_of_freedom2()const - { - return v2; - } - RealType non_centrality() const - { // Private data getter function. - return ncp; - } - private: - // Data member, initialized by constructor. - RealType v1; // alpha. - RealType v2; // beta. - RealType ncp; // non-centrality parameter - }; // template <class RealType, class Policy> class non_central_f_distribution - - typedef non_central_f_distribution<double> non_central_f; // Reserved name of type double. - - // Non-member functions to give properties of the distribution. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const non_central_f_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const non_central_f_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); - } - - template <class RealType, class Policy> - inline RealType mean(const non_central_f_distribution<RealType, Policy>& dist) - { - const char* function = "mean(non_central_f_distribution<%1%> const&)"; - RealType v1 = dist.degrees_of_freedom1(); - RealType v2 = dist.degrees_of_freedom2(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - v1, &r, Policy()) - || - !detail::check_df( - function, - v2, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - if(v2 <= 2) - return policies::raise_domain_error( - function, - "Second degrees of freedom parameter was %1%, but must be > 2 !", - v2, Policy()); - return v2 * (v1 + l) / (v1 * (v2 - 2)); - } // mean - - template <class RealType, class Policy> - inline RealType mode(const non_central_f_distribution<RealType, Policy>& dist) - { // mode. - static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)"; - - RealType n = dist.degrees_of_freedom1(); - RealType m = dist.degrees_of_freedom2(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - n, &r, Policy()) - || - !detail::check_df( - function, - m, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - RealType guess = m > 2 ? RealType(m * (n + l) / (n * (m - 2))) : RealType(1); - return detail::generic_find_mode( - dist, - guess, - function); - } - - template <class RealType, class Policy> - inline RealType variance(const non_central_f_distribution<RealType, Policy>& dist) - { // variance. - const char* function = "variance(non_central_f_distribution<%1%> const&)"; - RealType n = dist.degrees_of_freedom1(); - RealType m = dist.degrees_of_freedom2(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - n, &r, Policy()) - || - !detail::check_df( - function, - m, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - if(m <= 4) - return policies::raise_domain_error( - function, - "Second degrees of freedom parameter was %1%, but must be > 4 !", - m, Policy()); - RealType result = 2 * m * m * ((n + l) * (n + l) - + (m - 2) * (n + 2 * l)); - result /= (m - 4) * (m - 2) * (m - 2) * n * n; - return result; - } - - // RealType standard_deviation(const non_central_f_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - - template <class RealType, class Policy> - inline RealType skewness(const non_central_f_distribution<RealType, Policy>& dist) - { // skewness = sqrt(l). - const char* function = "skewness(non_central_f_distribution<%1%> const&)"; - BOOST_MATH_STD_USING - RealType n = dist.degrees_of_freedom1(); - RealType m = dist.degrees_of_freedom2(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - n, &r, Policy()) - || - !detail::check_df( - function, - m, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - if(m <= 6) - return policies::raise_domain_error( - function, - "Second degrees of freedom parameter was %1%, but must be > 6 !", - m, Policy()); - RealType result = 2 * constants::root_two<RealType>(); - result *= sqrt(m - 4); - result *= (n * (m + n - 2) *(m + 2 * n - 2) - + 3 * (m + n - 2) * (m + 2 * n - 2) * l - + 6 * (m + n - 2) * l * l + 2 * l * l * l); - result /= (m - 6) * pow(n * (m + n - 2) + 2 * (m + n - 2) * l + l * l, RealType(1.5f)); - return result; - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const non_central_f_distribution<RealType, Policy>& dist) - { - const char* function = "kurtosis_excess(non_central_f_distribution<%1%> const&)"; - BOOST_MATH_STD_USING - RealType n = dist.degrees_of_freedom1(); - RealType m = dist.degrees_of_freedom2(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df( - function, - n, &r, Policy()) - || - !detail::check_df( - function, - m, &r, Policy()) - || - !detail::check_non_centrality( - function, - l, - &r, - Policy())) - return r; - if(m <= 8) - return policies::raise_domain_error( - function, - "Second degrees of freedom parameter was %1%, but must be > 8 !", - m, Policy()); - RealType l2 = l * l; - RealType l3 = l2 * l; - RealType l4 = l2 * l2; - RealType result = (3 * (m - 4) * (n * (m + n - 2) - * (4 * (m - 2) * (m - 2) - + (m - 2) * (m + 10) * n - + (10 + m) * n * n) - + 4 * (m + n - 2) * (4 * (m - 2) * (m - 2) - + (m - 2) * (10 + m) * n - + (10 + m) * n * n) * l + 2 * (10 + m) - * (m + n - 2) * (2 * m + 3 * n - 4) * l2 - + 4 * (10 + m) * (-2 + m + n) * l3 - + (10 + m) * l4)) - / - ((-8 + m) * (-6 + m) * boost::math::pow<2>(n * (-2 + m + n) - + 2 * (-2 + m + n) * l + l2)); - return result; - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const non_central_f_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist) + 3; - } - - template <class RealType, class Policy> - inline RealType pdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x) - { // Probability Density/Mass Function. - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - value_type alpha = dist.degrees_of_freedom1() / 2; - value_type beta = dist.degrees_of_freedom2() / 2; - value_type y = x * alpha / beta; - value_type r = pdf(boost::math::non_central_beta_distribution<value_type, forwarding_policy>(alpha, beta, dist.non_centrality()), y / (1 + y)); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - r * (dist.degrees_of_freedom1() / dist.degrees_of_freedom2()) / ((1 + y) * (1 + y)), - "pdf(non_central_f_distribution<%1%>, %1%)"); - } // pdf - - template <class RealType, class Policy> - RealType cdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x) - { - const char* function = "cdf(const non_central_f_distribution<%1%>&, %1%)"; - RealType r; - if(!detail::check_df( - function, - dist.degrees_of_freedom1(), &r, Policy()) - || - !detail::check_df( - function, - dist.degrees_of_freedom2(), &r, Policy()) - || - !detail::check_non_centrality( - function, - dist.non_centrality(), - &r, - Policy())) - return r; - - if((x < 0) || !(boost::math::isfinite)(x)) - { - return policies::raise_domain_error<RealType>( - function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy()); - } - - RealType alpha = dist.degrees_of_freedom1() / 2; - RealType beta = dist.degrees_of_freedom2() / 2; - RealType y = x * alpha / beta; - RealType c = y / (1 + y); - RealType cp = 1 / (1 + y); - // - // To ensure accuracy, we pass both x and 1-x to the - // non-central beta cdf routine, this ensures accuracy - // even when we compute x to be ~ 1: - // - r = detail::non_central_beta_cdf(c, cp, alpha, beta, - dist.non_centrality(), false, Policy()); - return r; - } // cdf - - template <class RealType, class Policy> - RealType cdf(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function - const char* function = "cdf(complement(const non_central_f_distribution<%1%>&, %1%))"; - RealType r; - if(!detail::check_df( - function, - c.dist.degrees_of_freedom1(), &r, Policy()) - || - !detail::check_df( - function, - c.dist.degrees_of_freedom2(), &r, Policy()) - || - !detail::check_non_centrality( - function, - c.dist.non_centrality(), - &r, - Policy())) - return r; - - if((c.param < 0) || !(boost::math::isfinite)(c.param)) - { - return policies::raise_domain_error<RealType>( - function, "Random Variable parameter was %1%, but must be > 0 !", c.param, Policy()); - } - - RealType alpha = c.dist.degrees_of_freedom1() / 2; - RealType beta = c.dist.degrees_of_freedom2() / 2; - RealType y = c.param * alpha / beta; - RealType x = y / (1 + y); - RealType cx = 1 / (1 + y); - // - // To ensure accuracy, we pass both x and 1-x to the - // non-central beta cdf routine, this ensures accuracy - // even when we compute x to be ~ 1: - // - r = detail::non_central_beta_cdf(x, cx, alpha, beta, - c.dist.non_centrality(), true, Policy()); - return r; - } // ccdf - - template <class RealType, class Policy> - inline RealType quantile(const non_central_f_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile (or Percent Point) function. - RealType alpha = dist.degrees_of_freedom1() / 2; - RealType beta = dist.degrees_of_freedom2() / 2; - RealType x = quantile(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, dist.non_centrality()), p); - if(x == 1) - return policies::raise_overflow_error<RealType>( - "quantile(const non_central_f_distribution<%1%>&, %1%)", - "Result of non central F quantile is too large to represent.", - Policy()); - return (x / (1 - x)) * (dist.degrees_of_freedom2() / dist.degrees_of_freedom1()); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c) - { // Quantile (or Percent Point) function. - RealType alpha = c.dist.degrees_of_freedom1() / 2; - RealType beta = c.dist.degrees_of_freedom2() / 2; - RealType x = quantile(complement(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, c.dist.non_centrality()), c.param)); - if(x == 1) - return policies::raise_overflow_error<RealType>( - "quantile(complement(const non_central_f_distribution<%1%>&, %1%))", - "Result of non central F quantile is too large to represent.", - Policy()); - return (x / (1 - x)) * (c.dist.degrees_of_freedom2() / c.dist.degrees_of_freedom1()); - } // quantile complement. - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP - - -
--- a/any/include/boost/math/distributions/non_central_t.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,1202 +0,0 @@ -// boost\math\distributions\non_central_t.hpp - -// Copyright John Maddock 2008. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_T_HPP -#define BOOST_MATH_SPECIAL_NON_CENTRAL_T_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/distributions/non_central_beta.hpp> // for nc beta -#include <boost/math/distributions/normal.hpp> // for normal CDF and quantile -#include <boost/math/distributions/students_t.hpp> -#include <boost/math/distributions/detail/generic_quantile.hpp> // quantile - -namespace boost -{ - namespace math - { - - template <class RealType, class Policy> - class non_central_t_distribution; - - namespace detail{ - - template <class T, class Policy> - T non_central_t2_p(T v, T delta, T x, T y, const Policy& pol, T init_val) - { - BOOST_MATH_STD_USING - // - // Variables come first: - // - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = policies::get_epsilon<T, Policy>(); - T d2 = delta * delta / 2; - // - // k is the starting point for iteration, and is the - // maximum of the poisson weighting term, we don't - // ever allow k == 0 as this can lead to catastrophic - // cancellation errors later (test case is v = 1621286869049072.3 - // delta = 0.16212868690490723, x = 0.86987415482475994). - // - int k = itrunc(d2); - T pois; - if(k == 0) k = 1; - // Starting Poisson weight: - pois = gamma_p_derivative(T(k+1), d2, pol) - * tgamma_delta_ratio(T(k + 1), T(0.5f)) - * delta / constants::root_two<T>(); - if(pois == 0) - return init_val; - T xterm, beta; - // Recurrance & starting beta terms: - beta = x < y - ? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, false, true, &xterm) - : detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, true, true, &xterm); - xterm *= y / (v / 2 + k); - T poisf(pois), betaf(beta), xtermf(xterm); - T sum = init_val; - if((xterm == 0) && (beta == 0)) - return init_val; - - // - // Backwards recursion first, this is the stable - // direction for recursion: - // - boost::uintmax_t count = 0; - T last_term = 0; - for(int i = k; i >= 0; --i) - { - T term = beta * pois; - sum += term; - // Don't terminate on first term in case we "fixed" k above: - if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol) - break; - last_term = term; - pois *= (i + 0.5f) / d2; - beta += xterm; - xterm *= (i) / (x * (v / 2 + i - 1)); - ++count; - } - last_term = 0; - for(int i = k + 1; ; ++i) - { - poisf *= d2 / (i + 0.5f); - xtermf *= (x * (v / 2 + i - 1)) / (i); - betaf -= xtermf; - T term = poisf * betaf; - sum += term; - if((fabs(last_term) >= fabs(term)) && (fabs(term/sum) < errtol)) - break; - last_term = term; - ++count; - if(count > max_iter) - { - return policies::raise_evaluation_error( - "cdf(non_central_t_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - } - return sum; - } - - template <class T, class Policy> - T non_central_t2_q(T v, T delta, T x, T y, const Policy& pol, T init_val) - { - BOOST_MATH_STD_USING - // - // Variables come first: - // - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T d2 = delta * delta / 2; - // - // k is the starting point for iteration, and is the - // maximum of the poisson weighting term, we don't allow - // k == 0 as this can cause catastrophic cancellation errors - // (test case is v = 561908036470413.25, delta = 0.056190803647041321, - // x = 1.6155232703966216): - // - int k = itrunc(d2); - if(k == 0) k = 1; - // Starting Poisson weight: - T pois; - if((k < (int)(max_factorial<T>::value)) && (d2 < tools::log_max_value<T>()) && (log(d2) * k < tools::log_max_value<T>())) - { - // - // For small k we can optimise this calculation by using - // a simpler reduced formula: - // - pois = exp(-d2); - pois *= pow(d2, static_cast<T>(k)); - pois /= boost::math::tgamma(T(k + 1 + 0.5), pol); - pois *= delta / constants::root_two<T>(); - } - else - { - pois = gamma_p_derivative(T(k+1), d2, pol) - * tgamma_delta_ratio(T(k + 1), T(0.5f)) - * delta / constants::root_two<T>(); - } - if(pois == 0) - return init_val; - // Recurance term: - T xterm; - T beta; - // Starting beta term: - if(k != 0) - { - beta = x < y - ? detail::ibeta_imp(T(k + 1), T(v / 2), x, pol, true, true, &xterm) - : detail::ibeta_imp(T(v / 2), T(k + 1), y, pol, false, true, &xterm); - - xterm *= y / (v / 2 + k); - } - else - { - beta = pow(y, v / 2); - xterm = beta; - } - T poisf(pois), betaf(beta), xtermf(xterm); - T sum = init_val; - if((xterm == 0) && (beta == 0)) - return init_val; - - // - // Fused forward and backwards recursion: - // - boost::uintmax_t count = 0; - T last_term = 0; - for(int i = k + 1, j = k; ; ++i, --j) - { - poisf *= d2 / (i + 0.5f); - xtermf *= (x * (v / 2 + i - 1)) / (i); - betaf += xtermf; - T term = poisf * betaf; - - if(j >= 0) - { - term += beta * pois; - pois *= (j + 0.5f) / d2; - beta -= xterm; - xterm *= (j) / (x * (v / 2 + j - 1)); - } - - sum += term; - // Don't terminate on first term in case we "fixed" the value of k above: - if((fabs(last_term) > fabs(term)) && fabs(term/sum) < errtol) - break; - last_term = term; - if(count > max_iter) - { - return policies::raise_evaluation_error( - "cdf(non_central_t_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - ++count; - } - return sum; - } - - template <class T, class Policy> - T non_central_t_cdf(T v, T delta, T t, bool invert, const Policy& pol) - { - BOOST_MATH_STD_USING - if ((boost::math::isinf)(v)) - { // Infinite degrees of freedom, so use normal distribution located at delta. - normal_distribution<T, Policy> n(delta, 1); - return cdf(n, t); - } - // - // Otherwise, for t < 0 we have to use the reflection formula: - if(t < 0) - { - t = -t; - delta = -delta; - invert = !invert; - } - if(fabs(delta / (4 * v)) < policies::get_epsilon<T, Policy>()) - { - // Approximate with a Student's T centred on delta, - // the crossover point is based on eq 2.6 from - // "A Comparison of Approximations To Percentiles of the - // Noncentral t-Distribution". H. Sahai and M. M. Ojeda, - // Revista Investigacion Operacional Vol 21, No 2, 2000. - // Original sources referenced in the above are: - // "Some Approximations to the Percentage Points of the Noncentral - // t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31. - // "Continuous Univariate Distributions". N.L. Johnson, S. Kotz and - // N. Balkrishnan. 1995. John Wiley and Sons New York. - T result = cdf(students_t_distribution<T, Policy>(v), t - delta); - return invert ? 1 - result : result; - } - // - // x and y are the corresponding random - // variables for the noncentral beta distribution, - // with y = 1 - x: - // - T x = t * t / (v + t * t); - T y = v / (v + t * t); - T d2 = delta * delta; - T a = 0.5f; - T b = v / 2; - T c = a + b + d2 / 2; - // - // Crossover point for calculating p or q is the same - // as for the noncentral beta: - // - T cross = 1 - (b / c) * (1 + d2 / (2 * c * c)); - T result; - if(x < cross) - { - // - // Calculate p: - // - if(x != 0) - { - result = non_central_beta_p(a, b, d2, x, y, pol); - result = non_central_t2_p(v, delta, x, y, pol, result); - result /= 2; - } - else - result = 0; - result += cdf(boost::math::normal_distribution<T, Policy>(), -delta); - } - else - { - // - // Calculate q: - // - invert = !invert; - if(x != 0) - { - result = non_central_beta_q(a, b, d2, x, y, pol); - result = non_central_t2_q(v, delta, x, y, pol, result); - result /= 2; - } - else // x == 0 - result = cdf(complement(boost::math::normal_distribution<T, Policy>(), -delta)); - } - if(invert) - result = 1 - result; - return result; - } - - template <class T, class Policy> - T non_central_t_quantile(const char* function, T v, T delta, T p, T q, const Policy&) - { - BOOST_MATH_STD_USING - // static const char* function = "quantile(non_central_t_distribution<%1%>, %1%)"; - // now passed as function - typedef typename policies::evaluation<T, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - T r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - delta, - &r, - Policy()) - || - !detail::check_probability( - function, - p, - &r, - Policy())) - return r; - - - value_type guess = 0; - if ( ((boost::math::isinf)(v)) || (v > 1 / boost::math::tools::epsilon<T>()) ) - { // Infinite or very large degrees of freedom, so use normal distribution located at delta. - normal_distribution<T, Policy> n(delta, 1); - if (p < q) - { - return quantile(n, p); - } - else - { - return quantile(complement(n, q)); - } - } - else if(v > 3) - { // Use normal distribution to calculate guess. - value_type mean = (v > 1 / policies::get_epsilon<T, Policy>()) ? delta : delta * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, T(0.5f)); - value_type var = (v > 1 / policies::get_epsilon<T, Policy>()) ? value_type(1) : (((delta * delta + 1) * v) / (v - 2) - mean * mean); - if(p < q) - guess = quantile(normal_distribution<value_type, forwarding_policy>(mean, var), p); - else - guess = quantile(complement(normal_distribution<value_type, forwarding_policy>(mean, var), q)); - } - // - // We *must* get the sign of the initial guess correct, - // or our root-finder will fail, so double check it now: - // - value_type pzero = non_central_t_cdf( - static_cast<value_type>(v), - static_cast<value_type>(delta), - static_cast<value_type>(0), - !(p < q), - forwarding_policy()); - int s; - if(p < q) - s = boost::math::sign(p - pzero); - else - s = boost::math::sign(pzero - q); - if(s != boost::math::sign(guess)) - { - guess = static_cast<T>(s); - } - - value_type result = detail::generic_quantile( - non_central_t_distribution<value_type, forwarding_policy>(v, delta), - (p < q ? p : q), - guess, - (p >= q), - function); - return policies::checked_narrowing_cast<T, forwarding_policy>( - result, - function); - } - - template <class T, class Policy> - T non_central_t2_pdf(T n, T delta, T x, T y, const Policy& pol, T init_val) - { - BOOST_MATH_STD_USING - // - // Variables come first: - // - boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>(); - T errtol = boost::math::policies::get_epsilon<T, Policy>(); - T d2 = delta * delta / 2; - // - // k is the starting point for iteration, and is the - // maximum of the poisson weighting term: - // - int k = itrunc(d2); - T pois, xterm; - if(k == 0) - k = 1; - // Starting Poisson weight: - pois = gamma_p_derivative(T(k+1), d2, pol) - * tgamma_delta_ratio(T(k + 1), T(0.5f)) - * delta / constants::root_two<T>(); - // Starting beta term: - xterm = x < y - ? ibeta_derivative(T(k + 1), n / 2, x, pol) - : ibeta_derivative(n / 2, T(k + 1), y, pol); - T poisf(pois), xtermf(xterm); - T sum = init_val; - if((pois == 0) || (xterm == 0)) - return init_val; - - // - // Backwards recursion first, this is the stable - // direction for recursion: - // - boost::uintmax_t count = 0; - for(int i = k; i >= 0; --i) - { - T term = xterm * pois; - sum += term; - if(((fabs(term/sum) < errtol) && (i != k)) || (term == 0)) - break; - pois *= (i + 0.5f) / d2; - xterm *= (i) / (x * (n / 2 + i)); - ++count; - if(count > max_iter) - { - return policies::raise_evaluation_error( - "pdf(non_central_t_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - } - for(int i = k + 1; ; ++i) - { - poisf *= d2 / (i + 0.5f); - xtermf *= (x * (n / 2 + i)) / (i); - T term = poisf * xtermf; - sum += term; - if((fabs(term/sum) < errtol) || (term == 0)) - break; - ++count; - if(count > max_iter) - { - return policies::raise_evaluation_error( - "pdf(non_central_t_distribution<%1%>, %1%)", - "Series did not converge, closest value was %1%", sum, pol); - } - } - return sum; - } - - template <class T, class Policy> - T non_central_t_pdf(T n, T delta, T t, const Policy& pol) - { - BOOST_MATH_STD_USING - if ((boost::math::isinf)(n)) - { // Infinite degrees of freedom, so use normal distribution located at delta. - normal_distribution<T, Policy> norm(delta, 1); - return pdf(norm, t); - } - // - // Otherwise, for t < 0 we have to use the reflection formula: - if(t < 0) - { - t = -t; - delta = -delta; - } - if(t == 0) - { - // - // Handle this as a special case, using the formula - // from Weisstein, Eric W. - // "Noncentral Student's t-Distribution." - // From MathWorld--A Wolfram Web Resource. - // http://mathworld.wolfram.com/NoncentralStudentst-Distribution.html - // - // The formula is simplified thanks to the relation - // 1F1(a,b,0) = 1. - // - return tgamma_delta_ratio(n / 2 + 0.5f, T(0.5f)) - * sqrt(n / constants::pi<T>()) - * exp(-delta * delta / 2) / 2; - } - if(fabs(delta / (4 * n)) < policies::get_epsilon<T, Policy>()) - { - // Approximate with a Student's T centred on delta, - // the crossover point is based on eq 2.6 from - // "A Comparison of Approximations To Percentiles of the - // Noncentral t-Distribution". H. Sahai and M. M. Ojeda, - // Revista Investigacion Operacional Vol 21, No 2, 2000. - // Original sources referenced in the above are: - // "Some Approximations to the Percentage Points of the Noncentral - // t-Distribution". C. van Eeden. International Statistical Review, 29, 4-31. - // "Continuous Univariate Distributions". N.L. Johnson, S. Kotz and - // N. Balkrishnan. 1995. John Wiley and Sons New York. - return pdf(students_t_distribution<T, Policy>(n), t - delta); - } - // - // x and y are the corresponding random - // variables for the noncentral beta distribution, - // with y = 1 - x: - // - T x = t * t / (n + t * t); - T y = n / (n + t * t); - T a = 0.5f; - T b = n / 2; - T d2 = delta * delta; - // - // Calculate pdf: - // - T dt = n * t / (n * n + 2 * n * t * t + t * t * t * t); - T result = non_central_beta_pdf(a, b, d2, x, y, pol); - T tol = tools::epsilon<T>() * result * 500; - result = non_central_t2_pdf(n, delta, x, y, pol, result); - if(result <= tol) - result = 0; - result *= dt; - return result; - } - - template <class T, class Policy> - T mean(T v, T delta, const Policy& pol) - { - if ((boost::math::isinf)(v)) - { - return delta; - } - BOOST_MATH_STD_USING - if (v > 1 / boost::math::tools::epsilon<T>() ) - { - //normal_distribution<T, Policy> n(delta, 1); - //return boost::math::mean(n); - return delta; - } - else - { - return delta * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, T(0.5f), pol); - } - // Other moments use mean so using normal distribution is propagated. - } - - template <class T, class Policy> - T variance(T v, T delta, const Policy& pol) - { - if ((boost::math::isinf)(v)) - { - return 1; - } - if (delta == 0) - { // == Student's t - return v / (v - 2); - } - T result = ((delta * delta + 1) * v) / (v - 2); - T m = mean(v, delta, pol); - result -= m * m; - return result; - } - - template <class T, class Policy> - T skewness(T v, T delta, const Policy& pol) - { - BOOST_MATH_STD_USING - if ((boost::math::isinf)(v)) - { - return 0; - } - if(delta == 0) - { // == Student's t - return 0; - } - T mean = boost::math::detail::mean(v, delta, pol); - T l2 = delta * delta; - T var = ((l2 + 1) * v) / (v - 2) - mean * mean; - T result = -2 * var; - result += v * (l2 + 2 * v - 3) / ((v - 3) * (v - 2)); - result *= mean; - result /= pow(var, T(1.5f)); - return result; - } - - template <class T, class Policy> - T kurtosis_excess(T v, T delta, const Policy& pol) - { - BOOST_MATH_STD_USING - if ((boost::math::isinf)(v)) - { - return 3; - } - if (delta == 0) - { // == Student's t - return 3; - } - T mean = boost::math::detail::mean(v, delta, pol); - T l2 = delta * delta; - T var = ((l2 + 1) * v) / (v - 2) - mean * mean; - T result = -3 * var; - result += v * (l2 * (v + 1) + 3 * (3 * v - 5)) / ((v - 3) * (v - 2)); - result *= -mean * mean; - result += v * v * (l2 * l2 + 6 * l2 + 3) / ((v - 4) * (v - 2)); - result /= var * var; - return result; - } - -#if 0 - // - // This code is disabled, since there can be multiple answers to the - // question, and it's not clear how to find the "right" one. - // - template <class RealType, class Policy> - struct t_degrees_of_freedom_finder - { - t_degrees_of_freedom_finder( - RealType delta_, RealType x_, RealType p_, bool c) - : delta(delta_), x(x_), p(p_), comp(c) {} - - RealType operator()(const RealType& v) - { - non_central_t_distribution<RealType, Policy> d(v, delta); - return comp ? - p - cdf(complement(d, x)) - : cdf(d, x) - p; - } - private: - RealType delta; - RealType x; - RealType p; - bool comp; - }; - - template <class RealType, class Policy> - inline RealType find_t_degrees_of_freedom( - RealType delta, RealType x, RealType p, RealType q, const Policy& pol) - { - const char* function = "non_central_t<%1%>::find_degrees_of_freedom"; - if((p == 0) || (q == 0)) - { - // - // Can't a thing if one of p and q is zero: - // - return policies::raise_evaluation_error<RealType>(function, - "Can't find degrees of freedom when the probability is 0 or 1, only possible answer is %1%", - RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy()); - } - t_degrees_of_freedom_finder<RealType, Policy> f(delta, x, p < q ? p : q, p < q ? false : true); - tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>()); - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - // - // Pick an initial guess: - // - RealType guess = 200; - std::pair<RealType, RealType> ir = tools::bracket_and_solve_root( - f, guess, RealType(2), false, tol, max_iter, pol); - RealType result = ir.first + (ir.second - ir.first) / 2; - if(max_iter >= policies::get_max_root_iterations<Policy>()) - { - return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:" - " or there is no answer to problem. Current best guess is %1%", result, Policy()); - } - return result; - } - - template <class RealType, class Policy> - struct t_non_centrality_finder - { - t_non_centrality_finder( - RealType v_, RealType x_, RealType p_, bool c) - : v(v_), x(x_), p(p_), comp(c) {} - - RealType operator()(const RealType& delta) - { - non_central_t_distribution<RealType, Policy> d(v, delta); - return comp ? - p - cdf(complement(d, x)) - : cdf(d, x) - p; - } - private: - RealType v; - RealType x; - RealType p; - bool comp; - }; - - template <class RealType, class Policy> - inline RealType find_t_non_centrality( - RealType v, RealType x, RealType p, RealType q, const Policy& pol) - { - const char* function = "non_central_t<%1%>::find_t_non_centrality"; - if((p == 0) || (q == 0)) - { - // - // Can't do a thing if one of p and q is zero: - // - return policies::raise_evaluation_error<RealType>(function, - "Can't find non-centrality parameter when the probability is 0 or 1, only possible answer is %1%", - RealType(std::numeric_limits<RealType>::quiet_NaN()), Policy()); - } - t_non_centrality_finder<RealType, Policy> f(v, x, p < q ? p : q, p < q ? false : true); - tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>()); - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - // - // Pick an initial guess that we know is the right side of - // zero: - // - RealType guess; - if(f(0) < 0) - guess = 1; - else - guess = -1; - std::pair<RealType, RealType> ir = tools::bracket_and_solve_root( - f, guess, RealType(2), false, tol, max_iter, pol); - RealType result = ir.first + (ir.second - ir.first) / 2; - if(max_iter >= policies::get_max_root_iterations<Policy>()) - { - return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:" - " or there is no answer to problem. Current best guess is %1%", result, Policy()); - } - return result; - } -#endif - } // namespace detail ====================================================================== - - template <class RealType = double, class Policy = policies::policy<> > - class non_central_t_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - non_central_t_distribution(RealType v_, RealType lambda) : v(v_), ncp(lambda) - { - const char* function = "boost::math::non_central_t_distribution<%1%>::non_central_t_distribution(%1%,%1%)"; - RealType r; - detail::check_df_gt0_to_inf( - function, - v, &r, Policy()); - detail::check_finite( - function, - lambda, - &r, - Policy()); - } // non_central_t_distribution constructor. - - RealType degrees_of_freedom() const - { // Private data getter function. - return v; - } - RealType non_centrality() const - { // Private data getter function. - return ncp; - } -#if 0 - // - // This code is disabled, since there can be multiple answers to the - // question, and it's not clear how to find the "right" one. - // - static RealType find_degrees_of_freedom(RealType delta, RealType x, RealType p) - { - const char* function = "non_central_t<%1%>::find_degrees_of_freedom"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - value_type result = detail::find_t_degrees_of_freedom( - static_cast<value_type>(delta), - static_cast<value_type>(x), - static_cast<value_type>(p), - static_cast<value_type>(1-p), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - template <class A, class B, class C> - static RealType find_degrees_of_freedom(const complemented3_type<A,B,C>& c) - { - const char* function = "non_central_t<%1%>::find_degrees_of_freedom"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - value_type result = detail::find_t_degrees_of_freedom( - static_cast<value_type>(c.dist), - static_cast<value_type>(c.param1), - static_cast<value_type>(1-c.param2), - static_cast<value_type>(c.param2), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - static RealType find_non_centrality(RealType v, RealType x, RealType p) - { - const char* function = "non_central_t<%1%>::find_t_non_centrality"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - value_type result = detail::find_t_non_centrality( - static_cast<value_type>(v), - static_cast<value_type>(x), - static_cast<value_type>(p), - static_cast<value_type>(1-p), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } - template <class A, class B, class C> - static RealType find_non_centrality(const complemented3_type<A,B,C>& c) - { - const char* function = "non_central_t<%1%>::find_t_non_centrality"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - value_type result = detail::find_t_non_centrality( - static_cast<value_type>(c.dist), - static_cast<value_type>(c.param1), - static_cast<value_type>(1-c.param2), - static_cast<value_type>(c.param2), - forwarding_policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - result, - function); - } -#endif - private: - // Data member, initialized by constructor. - RealType v; // degrees of freedom - RealType ncp; // non-centrality parameter - }; // template <class RealType, class Policy> class non_central_t_distribution - - typedef non_central_t_distribution<double> non_central_t; // Reserved name of type double. - - // Non-member functions to give properties of the distribution. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const non_central_t_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const non_central_t_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); - } - - template <class RealType, class Policy> - inline RealType mode(const non_central_t_distribution<RealType, Policy>& dist) - { // mode. - static const char* function = "mode(non_central_t_distribution<%1%> const&)"; - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy())) - return (RealType)r; - - BOOST_MATH_STD_USING - - RealType m = v < 3 ? 0 : detail::mean(v, l, Policy()); - RealType var = v < 4 ? 1 : detail::variance(v, l, Policy()); - - return detail::generic_find_mode( - dist, - m, - function, - sqrt(var)); - } - - template <class RealType, class Policy> - inline RealType mean(const non_central_t_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING - const char* function = "mean(const non_central_t_distribution<%1%>&)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy())) - return (RealType)r; - if(v <= 1) - return policies::raise_domain_error<RealType>( - function, - "The non-central t distribution has no defined mean for degrees of freedom <= 1: got v=%1%.", v, Policy()); - // return l * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, RealType(0.5f)); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - detail::mean(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function); - - } // mean - - template <class RealType, class Policy> - inline RealType variance(const non_central_t_distribution<RealType, Policy>& dist) - { // variance. - const char* function = "variance(const non_central_t_distribution<%1%>&)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - BOOST_MATH_STD_USING - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy())) - return (RealType)r; - if(v <= 2) - return policies::raise_domain_error<RealType>( - function, - "The non-central t distribution has no defined variance for degrees of freedom <= 2: got v=%1%.", v, Policy()); - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - detail::variance(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function); - } - - // RealType standard_deviation(const non_central_t_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - - template <class RealType, class Policy> - inline RealType skewness(const non_central_t_distribution<RealType, Policy>& dist) - { // skewness = sqrt(l). - const char* function = "skewness(const non_central_t_distribution<%1%>&)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy())) - return (RealType)r; - if(v <= 3) - return policies::raise_domain_error<RealType>( - function, - "The non-central t distribution has no defined skewness for degrees of freedom <= 3: got v=%1%.", v, Policy());; - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - detail::skewness(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function); - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const non_central_t_distribution<RealType, Policy>& dist) - { - const char* function = "kurtosis_excess(const non_central_t_distribution<%1%>&)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy())) - return (RealType)r; - if(v <= 4) - return policies::raise_domain_error<RealType>( - function, - "The non-central t distribution has no defined kurtosis for degrees of freedom <= 4: got v=%1%.", v, Policy());; - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - detail::kurtosis_excess(static_cast<value_type>(v), static_cast<value_type>(l), forwarding_policy()), function); - } // kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const non_central_t_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist) + 3; - } - - template <class RealType, class Policy> - inline RealType pdf(const non_central_t_distribution<RealType, Policy>& dist, const RealType& t) - { // Probability Density/Mass Function. - const char* function = "pdf(non_central_t_distribution<%1%>, %1%)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy()) - || - !detail::check_x( - function, - t, - &r, - Policy())) - return (RealType)r; - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - detail::non_central_t_pdf(static_cast<value_type>(v), - static_cast<value_type>(l), - static_cast<value_type>(t), - Policy()), - function); - } // pdf - - template <class RealType, class Policy> - RealType cdf(const non_central_t_distribution<RealType, Policy>& dist, const RealType& x) - { - const char* function = "boost::math::cdf(non_central_t_distribution<%1%>&, %1%)"; -// was const char* function = "boost::math::non_central_t_distribution<%1%>::cdf(%1%)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy()) - || - !detail::check_x( - function, - x, - &r, - Policy())) - return (RealType)r; - if ((boost::math::isinf)(v)) - { // Infinite degrees of freedom, so use normal distribution located at delta. - normal_distribution<RealType, Policy> n(l, 1); - cdf(n, x); - //return cdf(normal_distribution<RealType, Policy>(l, 1), x); - } - - if(l == 0) - { // NO non-centrality, so use Student's t instead. - return cdf(students_t_distribution<RealType, Policy>(v), x); - } - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - detail::non_central_t_cdf( - static_cast<value_type>(v), - static_cast<value_type>(l), - static_cast<value_type>(x), - false, Policy()), - function); - } // cdf - - template <class RealType, class Policy> - RealType cdf(const complemented2_type<non_central_t_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function - // was const char* function = "boost::math::non_central_t_distribution<%1%>::cdf(%1%)"; - const char* function = "boost::math::cdf(const complement(non_central_t_distribution<%1%>&), %1%)"; - typedef typename policies::evaluation<RealType, Policy>::type value_type; - typedef typename policies::normalise< - Policy, - policies::promote_float<false>, - policies::promote_double<false>, - policies::discrete_quantile<>, - policies::assert_undefined<> >::type forwarding_policy; - - non_central_t_distribution<RealType, Policy> const& dist = c.dist; - RealType x = c.param; - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); // aka delta - RealType r; - if(!detail::check_df_gt0_to_inf( - function, - v, &r, Policy()) - || - !detail::check_finite( - function, - l, - &r, - Policy()) - || - !detail::check_x( - function, - x, - &r, - Policy())) - return (RealType)r; - - if ((boost::math::isinf)(v)) - { // Infinite degrees of freedom, so use normal distribution located at delta. - normal_distribution<RealType, Policy> n(l, 1); - return cdf(complement(n, x)); - } - if(l == 0) - { // zero non-centrality so use Student's t distribution. - return cdf(complement(students_t_distribution<RealType, Policy>(v), x)); - } - return policies::checked_narrowing_cast<RealType, forwarding_policy>( - detail::non_central_t_cdf( - static_cast<value_type>(v), - static_cast<value_type>(l), - static_cast<value_type>(x), - true, Policy()), - function); - } // ccdf - - template <class RealType, class Policy> - inline RealType quantile(const non_central_t_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile (or Percent Point) function. - static const char* function = "quantile(const non_central_t_distribution<%1%>, %1%)"; - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - return detail::non_central_t_quantile(function, v, l, p, RealType(1-p), Policy()); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<non_central_t_distribution<RealType, Policy>, RealType>& c) - { // Quantile (or Percent Point) function. - static const char* function = "quantile(const complement(non_central_t_distribution<%1%>, %1%))"; - non_central_t_distribution<RealType, Policy> const& dist = c.dist; - RealType q = c.param; - RealType v = dist.degrees_of_freedom(); - RealType l = dist.non_centrality(); - return detail::non_central_t_quantile(function, v, l, RealType(1-q), q, Policy()); - } // quantile complement. - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_T_HPP -
--- a/any/include/boost/math/distributions/normal.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,329 +0,0 @@ -// Copyright John Maddock 2006, 2007. -// Copyright Paul A. Bristow 2006, 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_NORMAL_HPP -#define BOOST_STATS_NORMAL_HPP - -// http://en.wikipedia.org/wiki/Normal_distribution -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm -// Also: -// Weisstein, Eric W. "Normal Distribution." -// From MathWorld--A Wolfram Web Resource. -// http://mathworld.wolfram.com/NormalDistribution.html - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/erf.hpp> // for erf/erfc. -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> - -#include <utility> - -namespace boost{ namespace math{ - -template <class RealType = double, class Policy = policies::policy<> > -class normal_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - normal_distribution(RealType l_mean = 0, RealType sd = 1) - : m_mean(l_mean), m_sd(sd) - { // Default is a 'standard' normal distribution N01. - static const char* function = "boost::math::normal_distribution<%1%>::normal_distribution"; - - RealType result; - detail::check_scale(function, sd, &result, Policy()); - detail::check_location(function, l_mean, &result, Policy()); - } - - RealType mean()const - { // alias for location. - return m_mean; - } - - RealType standard_deviation()const - { // alias for scale. - return m_sd; - } - - // Synonyms, provided to allow generic use of find_location and find_scale. - RealType location()const - { // location. - return m_mean; - } - RealType scale()const - { // scale. - return m_sd; - } - -private: - // - // Data members: - // - RealType m_mean; // distribution mean or location. - RealType m_sd; // distribution standard deviation or scale. -}; // class normal_distribution - -typedef normal_distribution<double> normal; - -#ifdef BOOST_MSVC -#pragma warning(push) -#pragma warning(disable:4127) -#endif - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const normal_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - if (std::numeric_limits<RealType>::has_infinity) - { - return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. - } - else - { // Can only use max_value. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. - } -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const normal_distribution<RealType, Policy>& /*dist*/) -{ // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero. - if (std::numeric_limits<RealType>::has_infinity) - { - return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. - } - else - { // Can only use max_value. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. - } -} - -#ifdef BOOST_MSVC -#pragma warning(pop) -#endif - -template <class RealType, class Policy> -inline RealType pdf(const normal_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType sd = dist.standard_deviation(); - RealType mean = dist.mean(); - - static const char* function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, sd, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, mean, &result, Policy())) - { - return result; - } - if((boost::math::isinf)(x)) - { - return 0; // pdf + and - infinity is zero. - } - // Below produces MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity()) - //{ // pdf + and - infinity is zero. - // return 0; - //} - if(false == detail::check_x(function, x, &result, Policy())) - { - return result; - } - - RealType exponent = x - mean; - exponent *= -exponent; - exponent /= 2 * sd * sd; - - result = exp(exponent); - result /= sd * sqrt(2 * constants::pi<RealType>()); - - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const normal_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType sd = dist.standard_deviation(); - RealType mean = dist.mean(); - static const char* function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)"; - RealType result = 0; - if(false == detail::check_scale(function, sd, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, mean, &result, Policy())) - { - return result; - } - if((boost::math::isinf)(x)) - { - if(x < 0) return 0; // -infinity - return 1; // + infinity - } - // These produce MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) - //{ // cdf +infinity is unity. - // return 1; - //} - //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) - //{ // cdf -infinity is zero. - // return 0; - //} - if(false == detail::check_x(function, x, &result, Policy())) - { - return result; - } - RealType diff = (x - mean) / (sd * constants::root_two<RealType>()); - result = boost::math::erfc(-diff, Policy()) / 2; - return result; -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const normal_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType sd = dist.standard_deviation(); - RealType mean = dist.mean(); - static const char* function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, sd, &result, Policy())) - return result; - if(false == detail::check_location(function, mean, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - - result= boost::math::erfc_inv(2 * p, Policy()); - result = -result; - result *= sd * constants::root_two<RealType>(); - result += mean; - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType sd = c.dist.standard_deviation(); - RealType mean = c.dist.mean(); - RealType x = c.param; - static const char* function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, sd, &result, Policy())) - return result; - if(false == detail::check_location(function, mean, &result, Policy())) - return result; - if((boost::math::isinf)(x)) - { - if(x < 0) return 1; // cdf complement -infinity is unity. - return 0; // cdf complement +infinity is zero - } - // These produce MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) - //{ // cdf complement +infinity is zero. - // return 0; - //} - //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) - //{ // cdf complement -infinity is unity. - // return 1; - //} - if(false == detail::check_x(function, x, &result, Policy())) - return result; - - RealType diff = (x - mean) / (sd * constants::root_two<RealType>()); - result = boost::math::erfc(diff, Policy()) / 2; - return result; -} // cdf complement - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType sd = c.dist.standard_deviation(); - RealType mean = c.dist.mean(); - static const char* function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)"; - RealType result = 0; - if(false == detail::check_scale(function, sd, &result, Policy())) - return result; - if(false == detail::check_location(function, mean, &result, Policy())) - return result; - RealType q = c.param; - if(false == detail::check_probability(function, q, &result, Policy())) - return result; - result = boost::math::erfc_inv(2 * q, Policy()); - result *= sd * constants::root_two<RealType>(); - result += mean; - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType mean(const normal_distribution<RealType, Policy>& dist) -{ - return dist.mean(); -} - -template <class RealType, class Policy> -inline RealType standard_deviation(const normal_distribution<RealType, Policy>& dist) -{ - return dist.standard_deviation(); -} - -template <class RealType, class Policy> -inline RealType mode(const normal_distribution<RealType, Policy>& dist) -{ - return dist.mean(); -} - -template <class RealType, class Policy> -inline RealType median(const normal_distribution<RealType, Policy>& dist) -{ - return dist.mean(); -} - -template <class RealType, class Policy> -inline RealType skewness(const normal_distribution<RealType, Policy>& /*dist*/) -{ - return 0; -} - -template <class RealType, class Policy> -inline RealType kurtosis(const normal_distribution<RealType, Policy>& /*dist*/) -{ - return 3; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const normal_distribution<RealType, Policy>& /*dist*/) -{ - return 0; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_NORMAL_HPP - -
--- a/any/include/boost/math/distributions/pareto.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,444 +0,0 @@ -// Copyright John Maddock 2007. -// Copyright Paul A. Bristow 2007, 2009 -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_PARETO_HPP -#define BOOST_STATS_PARETO_HPP - -// http://en.wikipedia.org/wiki/Pareto_distribution -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm -// Also: -// Weisstein, Eric W. "Pareto Distribution." -// From MathWorld--A Wolfram Web Resource. -// http://mathworld.wolfram.com/ParetoDistribution.html -// Handbook of Statistical Distributions with Applications, K Krishnamoorthy, ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. -// Caution KK's a and b are the reverse of Mathworld! - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/special_functions/powm1.hpp> - -#include <utility> // for BOOST_CURRENT_VALUE? - -namespace boost -{ - namespace math - { - namespace detail - { // Parameter checking. - template <class RealType, class Policy> - inline bool check_pareto_scale( - const char* function, - RealType scale, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(scale)) - { // any > 0 finite value is OK. - if (scale > 0) - { - return true; - } - else - { - *result = policies::raise_domain_error<RealType>( - function, - "Scale parameter is %1%, but must be > 0!", scale, pol); - return false; - } - } - else - { // Not finite. - *result = policies::raise_domain_error<RealType>( - function, - "Scale parameter is %1%, but must be finite!", scale, pol); - return false; - } - } // bool check_pareto_scale - - template <class RealType, class Policy> - inline bool check_pareto_shape( - const char* function, - RealType shape, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(shape)) - { // Any finite value > 0 is OK. - if (shape > 0) - { - return true; - } - else - { - *result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but must be > 0!", shape, pol); - return false; - } - } - else - { // Not finite. - *result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but must be finite!", shape, pol); - return false; - } - } // bool check_pareto_shape( - - template <class RealType, class Policy> - inline bool check_pareto_x( - const char* function, - RealType const& x, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(x)) - { // - if (x > 0) - { - return true; - } - else - { - *result = policies::raise_domain_error<RealType>( - function, - "x parameter is %1%, but must be > 0 !", x, pol); - return false; - } - } - else - { // Not finite.. - *result = policies::raise_domain_error<RealType>( - function, - "x parameter is %1%, but must be finite!", x, pol); - return false; - } - } // bool check_pareto_x - - template <class RealType, class Policy> - inline bool check_pareto( // distribution parameters. - const char* function, - RealType scale, - RealType shape, - RealType* result, const Policy& pol) - { - return check_pareto_scale(function, scale, result, pol) - && check_pareto_shape(function, shape, result, pol); - } // bool check_pareto( - - } // namespace detail - - template <class RealType = double, class Policy = policies::policy<> > - class pareto_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - pareto_distribution(RealType l_scale = 1, RealType l_shape = 1) - : m_scale(l_scale), m_shape(l_shape) - { // Constructor. - RealType result = 0; - detail::check_pareto("boost::math::pareto_distribution<%1%>::pareto_distribution", l_scale, l_shape, &result, Policy()); - } - - RealType scale()const - { // AKA Xm and Wolfram b and beta - return m_scale; - } - - RealType shape()const - { // AKA k and Wolfram a and alpha - return m_shape; - } - private: - // Data members: - RealType m_scale; // distribution scale (xm) or beta - RealType m_shape; // distribution shape (k) or alpha - }; - - typedef pareto_distribution<double> pareto; // Convenience to allow pareto(2., 3.); - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const pareto_distribution<RealType, Policy>& /*dist*/) - { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // scale zero to + infinity. - } // range - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const pareto_distribution<RealType, Policy>& dist) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(dist.scale(), max_value<RealType>() ); // scale to + infinity. - } // support - - template <class RealType, class Policy> - inline RealType pdf(const pareto_distribution<RealType, Policy>& dist, const RealType& x) - { - BOOST_MATH_STD_USING // for ADL of std function pow. - static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)"; - RealType scale = dist.scale(); - RealType shape = dist.shape(); - RealType result = 0; - if(false == (detail::check_pareto_x(function, x, &result, Policy()) - && detail::check_pareto(function, scale, shape, &result, Policy()))) - return result; - if (x < scale) - { // regardless of shape, pdf is zero (or should be disallow x < scale and throw an exception?). - return 0; - } - result = shape * pow(scale, shape) / pow(x, shape+1); - return result; - } // pdf - - template <class RealType, class Policy> - inline RealType cdf(const pareto_distribution<RealType, Policy>& dist, const RealType& x) - { - BOOST_MATH_STD_USING // for ADL of std function pow. - static const char* function = "boost::math::cdf(const pareto_distribution<%1%>&, %1%)"; - RealType scale = dist.scale(); - RealType shape = dist.shape(); - RealType result = 0; - - if(false == (detail::check_pareto_x(function, x, &result, Policy()) - && detail::check_pareto(function, scale, shape, &result, Policy()))) - return result; - - if (x <= scale) - { // regardless of shape, cdf is zero. - return 0; - } - - // result = RealType(1) - pow((scale / x), shape); - result = -boost::math::powm1(scale/x, shape, Policy()); // should be more accurate. - return result; - } // cdf - - template <class RealType, class Policy> - inline RealType quantile(const pareto_distribution<RealType, Policy>& dist, const RealType& p) - { - BOOST_MATH_STD_USING // for ADL of std function pow. - static const char* function = "boost::math::quantile(const pareto_distribution<%1%>&, %1%)"; - RealType result = 0; - RealType scale = dist.scale(); - RealType shape = dist.shape(); - if(false == (detail::check_probability(function, p, &result, Policy()) - && detail::check_pareto(function, scale, shape, &result, Policy()))) - { - return result; - } - if (p == 0) - { - return scale; // x must be scale (or less). - } - if (p == 1) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); // x = + infinity. - } - result = scale / - (pow((1 - p), 1 / shape)); - // K. Krishnamoorthy, ISBN 1-58488-635-8 eq 23.1.3 - return result; - } // quantile - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<pareto_distribution<RealType, Policy>, RealType>& c) - { - BOOST_MATH_STD_USING // for ADL of std function pow. - static const char* function = "boost::math::cdf(const pareto_distribution<%1%>&, %1%)"; - RealType result = 0; - RealType x = c.param; - RealType scale = c.dist.scale(); - RealType shape = c.dist.shape(); - if(false == (detail::check_pareto_x(function, x, &result, Policy()) - && detail::check_pareto(function, scale, shape, &result, Policy()))) - return result; - - if (x <= scale) - { // regardless of shape, cdf is zero, and complement is unity. - return 1; - } - result = pow((scale/x), shape); - - return result; - } // cdf complement - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<pareto_distribution<RealType, Policy>, RealType>& c) - { - BOOST_MATH_STD_USING // for ADL of std function pow. - static const char* function = "boost::math::quantile(const pareto_distribution<%1%>&, %1%)"; - RealType result = 0; - RealType q = c.param; - RealType scale = c.dist.scale(); - RealType shape = c.dist.shape(); - if(false == (detail::check_probability(function, q, &result, Policy()) - && detail::check_pareto(function, scale, shape, &result, Policy()))) - { - return result; - } - if (q == 1) - { - return scale; // x must be scale (or less). - } - if (q == 0) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); // x = + infinity. - } - result = scale / (pow(q, 1 / shape)); - // K. Krishnamoorthy, ISBN 1-58488-635-8 eq 23.1.3 - return result; - } // quantile complement - - template <class RealType, class Policy> - inline RealType mean(const pareto_distribution<RealType, Policy>& dist) - { - RealType result = 0; - static const char* function = "boost::math::mean(const pareto_distribution<%1%>&, %1%)"; - if(false == detail::check_pareto(function, dist.scale(), dist.shape(), &result, Policy())) - { - return result; - } - if (dist.shape() > RealType(1)) - { - return dist.shape() * dist.scale() / (dist.shape() - 1); - } - else - { - using boost::math::tools::max_value; - return max_value<RealType>(); // +infinity. - } - } // mean - - template <class RealType, class Policy> - inline RealType mode(const pareto_distribution<RealType, Policy>& dist) - { - return dist.scale(); - } // mode - - template <class RealType, class Policy> - inline RealType median(const pareto_distribution<RealType, Policy>& dist) - { - RealType result = 0; - static const char* function = "boost::math::median(const pareto_distribution<%1%>&, %1%)"; - if(false == detail::check_pareto(function, dist.scale(), dist.shape(), &result, Policy())) - { - return result; - } - BOOST_MATH_STD_USING - return dist.scale() * pow(RealType(2), (1/dist.shape())); - } // median - - template <class RealType, class Policy> - inline RealType variance(const pareto_distribution<RealType, Policy>& dist) - { - RealType result = 0; - RealType scale = dist.scale(); - RealType shape = dist.shape(); - static const char* function = "boost::math::variance(const pareto_distribution<%1%>&, %1%)"; - if(false == detail::check_pareto(function, scale, shape, &result, Policy())) - { - return result; - } - if (shape > 2) - { - result = (scale * scale * shape) / - ((shape - 1) * (shape - 1) * (shape - 2)); - } - else - { - result = policies::raise_domain_error<RealType>( - function, - "variance is undefined for shape <= 2, but got %1%.", dist.shape(), Policy()); - } - return result; - } // variance - - template <class RealType, class Policy> - inline RealType skewness(const pareto_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING - RealType result = 0; - RealType shape = dist.shape(); - static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)"; - if(false == detail::check_pareto(function, dist.scale(), shape, &result, Policy())) - { - return result; - } - if (shape > 3) - { - result = sqrt((shape - 2) / shape) * - 2 * (shape + 1) / - (shape - 3); - } - else - { - result = policies::raise_domain_error<RealType>( - function, - "skewness is undefined for shape <= 3, but got %1%.", dist.shape(), Policy()); - } - return result; - } // skewness - - template <class RealType, class Policy> - inline RealType kurtosis(const pareto_distribution<RealType, Policy>& dist) - { - RealType result = 0; - RealType shape = dist.shape(); - static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)"; - if(false == detail::check_pareto(function, dist.scale(), shape, &result, Policy())) - { - return result; - } - if (shape > 4) - { - result = 3 * ((shape - 2) * (3 * shape * shape + shape + 2)) / - (shape * (shape - 3) * (shape - 4)); - } - else - { - result = policies::raise_domain_error<RealType>( - function, - "kurtosis_excess is undefined for shape <= 4, but got %1%.", shape, Policy()); - } - return result; - } // kurtosis - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const pareto_distribution<RealType, Policy>& dist) - { - RealType result = 0; - RealType shape = dist.shape(); - static const char* function = "boost::math::pdf(const pareto_distribution<%1%>&, %1%)"; - if(false == detail::check_pareto(function, dist.scale(), shape, &result, Policy())) - { - return result; - } - if (shape > 4) - { - result = 6 * ((shape * shape * shape) + (shape * shape) - 6 * shape - 2) / - (shape * (shape - 3) * (shape - 4)); - } - else - { - result = policies::raise_domain_error<RealType>( - function, - "kurtosis_excess is undefined for shape <= 4, but got %1%.", dist.shape(), Policy()); - } - return result; - } // kurtosis_excess - - } // namespace math - } // namespace boost - - // This include must be at the end, *after* the accessors - // for this distribution have been defined, in order to - // keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_PARETO_HPP - -
--- a/any/include/boost/math/distributions/poisson.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,527 +0,0 @@ -// boost\math\distributions\poisson.hpp - -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2007. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. -// (See accompanying file LICENSE_1_0.txt -// or copy at http://www.boost.org/LICENSE_1_0.txt) - -// Poisson distribution is a discrete probability distribution. -// It expresses the probability of a number (k) of -// events, occurrences, failures or arrivals occurring in a fixed time, -// assuming these events occur with a known average or mean rate (lambda) -// and are independent of the time since the last event. -// The distribution was discovered by Simeon-Denis Poisson (1781-1840). - -// Parameter lambda is the mean number of events in the given time interval. -// The random variate k is the number of events, occurrences or arrivals. -// k argument may be integral, signed, or unsigned, or floating point. -// If necessary, it has already been promoted from an integral type. - -// Note that the Poisson distribution -// (like others including the binomial, negative binomial & Bernoulli) -// is strictly defined as a discrete function: -// only integral values of k are envisaged. -// However because the method of calculation uses a continuous gamma function, -// it is convenient to treat it as if a continous function, -// and permit non-integral values of k. -// To enforce the strict mathematical model, users should use floor or ceil functions -// on k outside this function to ensure that k is integral. - -// See http://en.wikipedia.org/wiki/Poisson_distribution -// http://documents.wolfram.com/v5/Add-onsLinks/StandardPackages/Statistics/DiscreteDistributions.html - -#ifndef BOOST_MATH_SPECIAL_POISSON_HPP -#define BOOST_MATH_SPECIAL_POISSON_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/gamma.hpp> // for incomplete gamma. gamma_q -#include <boost/math/special_functions/trunc.hpp> // for incomplete gamma. gamma_q -#include <boost/math/distributions/complement.hpp> // complements -#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks -#include <boost/math/special_functions/fpclassify.hpp> // isnan. -#include <boost/math/special_functions/factorials.hpp> // factorials. -#include <boost/math/tools/roots.hpp> // for root finding. -#include <boost/math/distributions/detail/inv_discrete_quantile.hpp> - -#include <utility> - -namespace boost -{ - namespace math - { - namespace poisson_detail - { - // Common error checking routines for Poisson distribution functions. - // These are convoluted, & apparently redundant, to try to ensure that - // checks are always performed, even if exceptions are not enabled. - - template <class RealType, class Policy> - inline bool check_mean(const char* function, const RealType& mean, RealType* result, const Policy& pol) - { - if(!(boost::math::isfinite)(mean) || (mean < 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Mean argument is %1%, but must be >= 0 !", mean, pol); - return false; - } - return true; - } // bool check_mean - - template <class RealType, class Policy> - inline bool check_mean_NZ(const char* function, const RealType& mean, RealType* result, const Policy& pol) - { // mean == 0 is considered an error. - if( !(boost::math::isfinite)(mean) || (mean <= 0)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Mean argument is %1%, but must be > 0 !", mean, pol); - return false; - } - return true; - } // bool check_mean_NZ - - template <class RealType, class Policy> - inline bool check_dist(const char* function, const RealType& mean, RealType* result, const Policy& pol) - { // Only one check, so this is redundant really but should be optimized away. - return check_mean_NZ(function, mean, result, pol); - } // bool check_dist - - template <class RealType, class Policy> - inline bool check_k(const char* function, const RealType& k, RealType* result, const Policy& pol) - { - if((k < 0) || !(boost::math::isfinite)(k)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Number of events k argument is %1%, but must be >= 0 !", k, pol); - return false; - } - return true; - } // bool check_k - - template <class RealType, class Policy> - inline bool check_dist_and_k(const char* function, RealType mean, RealType k, RealType* result, const Policy& pol) - { - if((check_dist(function, mean, result, pol) == false) || - (check_k(function, k, result, pol) == false)) - { - return false; - } - return true; - } // bool check_dist_and_k - - template <class RealType, class Policy> - inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol) - { // Check 0 <= p <= 1 - if(!(boost::math::isfinite)(p) || (p < 0) || (p > 1)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol); - return false; - } - return true; - } // bool check_prob - - template <class RealType, class Policy> - inline bool check_dist_and_prob(const char* function, RealType mean, RealType p, RealType* result, const Policy& pol) - { - if((check_dist(function, mean, result, pol) == false) || - (check_prob(function, p, result, pol) == false)) - { - return false; - } - return true; - } // bool check_dist_and_prob - - } // namespace poisson_detail - - template <class RealType = double, class Policy = policies::policy<> > - class poisson_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - poisson_distribution(RealType l_mean = 1) : m_l(l_mean) // mean (lambda). - { // Expected mean number of events that occur during the given interval. - RealType r; - poisson_detail::check_dist( - "boost::math::poisson_distribution<%1%>::poisson_distribution", - m_l, - &r, Policy()); - } // poisson_distribution constructor. - - RealType mean() const - { // Private data getter function. - return m_l; - } - private: - // Data member, initialized by constructor. - RealType m_l; // mean number of occurrences. - }; // template <class RealType, class Policy> class poisson_distribution - - typedef poisson_distribution<double> poisson; // Reserved name of type double. - - // Non-member functions to give properties of the distribution. - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const poisson_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable k. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // Max integer? - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const poisson_distribution<RealType, Policy>& /* dist */) - { // Range of supported values for random variable k. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); - } - - template <class RealType, class Policy> - inline RealType mean(const poisson_distribution<RealType, Policy>& dist) - { // Mean of poisson distribution = lambda. - return dist.mean(); - } // mean - - template <class RealType, class Policy> - inline RealType mode(const poisson_distribution<RealType, Policy>& dist) - { // mode. - BOOST_MATH_STD_USING // ADL of std functions. - return floor(dist.mean()); - } - - //template <class RealType, class Policy> - //inline RealType median(const poisson_distribution<RealType, Policy>& dist) - //{ // median = approximately lambda + 1/3 - 0.2/lambda - // RealType l = dist.mean(); - // return dist.mean() + static_cast<RealType>(0.3333333333333333333333333333333333333333333333) - // - static_cast<RealType>(0.2) / l; - //} // BUT this formula appears to be out-by-one compared to quantile(half) - // Query posted on Wikipedia. - // Now implemented via quantile(half) in derived accessors. - - template <class RealType, class Policy> - inline RealType variance(const poisson_distribution<RealType, Policy>& dist) - { // variance. - return dist.mean(); - } - - // RealType standard_deviation(const poisson_distribution<RealType, Policy>& dist) - // standard_deviation provided by derived accessors. - - template <class RealType, class Policy> - inline RealType skewness(const poisson_distribution<RealType, Policy>& dist) - { // skewness = sqrt(l). - BOOST_MATH_STD_USING // ADL of std functions. - return 1 / sqrt(dist.mean()); - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const poisson_distribution<RealType, Policy>& dist) - { // skewness = sqrt(l). - return 1 / dist.mean(); // kurtosis_excess 1/mean from Wiki & MathWorld eq 31. - // http://mathworld.wolfram.com/Kurtosis.html explains that the kurtosis excess - // is more convenient because the kurtosis excess of a normal distribution is zero - // whereas the true kurtosis is 3. - } // RealType kurtosis_excess - - template <class RealType, class Policy> - inline RealType kurtosis(const poisson_distribution<RealType, Policy>& dist) - { // kurtosis is 4th moment about the mean = u4 / sd ^ 4 - // http://en.wikipedia.org/wiki/Curtosis - // kurtosis can range from -2 (flat top) to +infinity (sharp peak & heavy tails). - // http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm - return 3 + 1 / dist.mean(); // NIST. - // http://mathworld.wolfram.com/Kurtosis.html explains that the kurtosis excess - // is more convenient because the kurtosis excess of a normal distribution is zero - // whereas the true kurtosis is 3. - } // RealType kurtosis - - template <class RealType, class Policy> - RealType pdf(const poisson_distribution<RealType, Policy>& dist, const RealType& k) - { // Probability Density/Mass Function. - // Probability that there are EXACTLY k occurrences (or arrivals). - BOOST_FPU_EXCEPTION_GUARD - - BOOST_MATH_STD_USING // for ADL of std functions. - - RealType mean = dist.mean(); - // Error check: - RealType result = 0; - if(false == poisson_detail::check_dist_and_k( - "boost::math::pdf(const poisson_distribution<%1%>&, %1%)", - mean, - k, - &result, Policy())) - { - return result; - } - - // Special case of mean zero, regardless of the number of events k. - if (mean == 0) - { // Probability for any k is zero. - return 0; - } - if (k == 0) - { // mean ^ k = 1, and k! = 1, so can simplify. - return exp(-mean); - } - return boost::math::gamma_p_derivative(k+1, mean, Policy()); - } // pdf - - template <class RealType, class Policy> - RealType cdf(const poisson_distribution<RealType, Policy>& dist, const RealType& k) - { // Cumulative Distribution Function Poisson. - // The random variate k is the number of occurrences(or arrivals) - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - // Returns the sum of the terms 0 through k of the Poisson Probability Density or Mass (pdf). - - // But note that the Poisson distribution - // (like others including the binomial, negative binomial & Bernoulli) - // is strictly defined as a discrete function: only integral values of k are envisaged. - // However because of the method of calculation using a continuous gamma function, - // it is convenient to treat it as if it is a continous function - // and permit non-integral values of k. - // To enforce the strict mathematical model, users should use floor or ceil functions - // outside this function to ensure that k is integral. - - // The terms are not summed directly (at least for larger k) - // instead the incomplete gamma integral is employed, - - BOOST_MATH_STD_USING // for ADL of std function exp. - - RealType mean = dist.mean(); - // Error checks: - RealType result = 0; - if(false == poisson_detail::check_dist_and_k( - "boost::math::cdf(const poisson_distribution<%1%>&, %1%)", - mean, - k, - &result, Policy())) - { - return result; - } - // Special cases: - if (mean == 0) - { // Probability for any k is zero. - return 0; - } - if (k == 0) - { // return pdf(dist, static_cast<RealType>(0)); - // but mean (and k) have already been checked, - // so this avoids unnecessary repeated checks. - return exp(-mean); - } - // For small integral k could use a finite sum - - // it's cheaper than the gamma function. - // BUT this is now done efficiently by gamma_q function. - // Calculate poisson cdf using the gamma_q function. - return gamma_q(k+1, mean, Policy()); - } // binomial cdf - - template <class RealType, class Policy> - RealType cdf(const complemented2_type<poisson_distribution<RealType, Policy>, RealType>& c) - { // Complemented Cumulative Distribution Function Poisson - // The random variate k is the number of events, occurrences or arrivals. - // k argument may be integral, signed, or unsigned, or floating point. - // If necessary, it has already been promoted from an integral type. - // But note that the Poisson distribution - // (like others including the binomial, negative binomial & Bernoulli) - // is strictly defined as a discrete function: only integral values of k are envisaged. - // However because of the method of calculation using a continuous gamma function, - // it is convenient to treat it as is it is a continous function - // and permit non-integral values of k. - // To enforce the strict mathematical model, users should use floor or ceil functions - // outside this function to ensure that k is integral. - - // Returns the sum of the terms k+1 through inf of the Poisson Probability Density/Mass (pdf). - // The terms are not summed directly (at least for larger k) - // instead the incomplete gamma integral is employed, - - RealType const& k = c.param; - poisson_distribution<RealType, Policy> const& dist = c.dist; - - RealType mean = dist.mean(); - - // Error checks: - RealType result = 0; - if(false == poisson_detail::check_dist_and_k( - "boost::math::cdf(const poisson_distribution<%1%>&, %1%)", - mean, - k, - &result, Policy())) - { - return result; - } - // Special case of mean, regardless of the number of events k. - if (mean == 0) - { // Probability for any k is unity, complement of zero. - return 1; - } - if (k == 0) - { // Avoid repeated checks on k and mean in gamma_p. - return -boost::math::expm1(-mean, Policy()); - } - // Unlike un-complemented cdf (sum from 0 to k), - // can't use finite sum from k+1 to infinity for small integral k, - // anyway it is now done efficiently by gamma_p. - return gamma_p(k + 1, mean, Policy()); // Calculate Poisson cdf using the gamma_p function. - // CCDF = gamma_p(k+1, lambda) - } // poisson ccdf - - template <class RealType, class Policy> - inline RealType quantile(const poisson_distribution<RealType, Policy>& dist, const RealType& p) - { // Quantile (or Percent Point) Poisson function. - // Return the number of expected events k for a given probability p. - static const char* function = "boost::math::quantile(const poisson_distribution<%1%>&, %1%)"; - RealType result = 0; // of Argument checks: - if(false == poisson_detail::check_prob( - function, - p, - &result, Policy())) - { - return result; - } - // Special case: - if (dist.mean() == 0) - { // if mean = 0 then p = 0, so k can be anything? - if (false == poisson_detail::check_mean_NZ( - function, - dist.mean(), - &result, Policy())) - { - return result; - } - } - if(p == 0) - { - return 0; // Exact result regardless of discrete-quantile Policy - } - if(p == 1) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - typedef typename Policy::discrete_quantile_type discrete_type; - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - RealType guess, factor = 8; - RealType z = dist.mean(); - if(z < 1) - guess = z; - else - guess = boost::math::detail::inverse_poisson_cornish_fisher(z, p, RealType(1-p), Policy()); - if(z > 5) - { - if(z > 1000) - factor = 1.01f; - else if(z > 50) - factor = 1.1f; - else if(guess > 10) - factor = 1.25f; - else - factor = 2; - if(guess < 1.1) - factor = 8; - } - - return detail::inverse_discrete_quantile( - dist, - p, - false, - guess, - factor, - RealType(1), - discrete_type(), - max_iter); - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<poisson_distribution<RealType, Policy>, RealType>& c) - { // Quantile (or Percent Point) of Poisson function. - // Return the number of expected events k for a given - // complement of the probability q. - // - // Error checks: - static const char* function = "boost::math::quantile(complement(const poisson_distribution<%1%>&, %1%))"; - RealType q = c.param; - const poisson_distribution<RealType, Policy>& dist = c.dist; - RealType result = 0; // of argument checks. - if(false == poisson_detail::check_prob( - function, - q, - &result, Policy())) - { - return result; - } - // Special case: - if (dist.mean() == 0) - { // if mean = 0 then p = 0, so k can be anything? - if (false == poisson_detail::check_mean_NZ( - function, - dist.mean(), - &result, Policy())) - { - return result; - } - } - if(q == 0) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - if(q == 1) - { - return 0; // Exact result regardless of discrete-quantile Policy - } - typedef typename Policy::discrete_quantile_type discrete_type; - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - RealType guess, factor = 8; - RealType z = dist.mean(); - if(z < 1) - guess = z; - else - guess = boost::math::detail::inverse_poisson_cornish_fisher(z, RealType(1-q), q, Policy()); - if(z > 5) - { - if(z > 1000) - factor = 1.01f; - else if(z > 50) - factor = 1.1f; - else if(guess > 10) - factor = 1.25f; - else - factor = 2; - if(guess < 1.1) - factor = 8; - } - - return detail::inverse_discrete_quantile( - dist, - q, - true, - guess, - factor, - RealType(1), - discrete_type(), - max_iter); - } // quantile complement. - - } // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> -#include <boost/math/distributions/detail/inv_discrete_quantile.hpp> - -#endif // BOOST_MATH_SPECIAL_POISSON_HPP - - -
--- a/any/include/boost/math/distributions/rayleigh.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,301 +0,0 @@ -// Copyright Paul A. Bristow 2007. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_rayleigh_HPP -#define BOOST_STATS_rayleigh_HPP - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/constants/constants.hpp> -#include <boost/math/special_functions/log1p.hpp> -#include <boost/math/special_functions/expm1.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/config/no_tr1/cmath.hpp> - -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable: 4702) // unreachable code (return after domain_error throw). -#endif - -#include <utility> - -namespace boost{ namespace math{ - -namespace detail -{ // Error checks: - template <class RealType, class Policy> - inline bool verify_sigma(const char* function, RealType sigma, RealType* presult, const Policy& pol) - { - if((sigma <= 0) || (!(boost::math::isfinite)(sigma))) - { - *presult = policies::raise_domain_error<RealType>( - function, - "The scale parameter \"sigma\" must be > 0 and finite, but was: %1%.", sigma, pol); - return false; - } - return true; - } // bool verify_sigma - - template <class RealType, class Policy> - inline bool verify_rayleigh_x(const char* function, RealType x, RealType* presult, const Policy& pol) - { - if((x < 0) || (boost::math::isnan)(x)) - { - *presult = policies::raise_domain_error<RealType>( - function, - "The random variable must be >= 0, but was: %1%.", x, pol); - return false; - } - return true; - } // bool verify_rayleigh_x -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class rayleigh_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - rayleigh_distribution(RealType l_sigma = 1) - : m_sigma(l_sigma) - { - RealType err; - detail::verify_sigma("boost::math::rayleigh_distribution<%1%>::rayleigh_distribution", l_sigma, &err, Policy()); - } // rayleigh_distribution - - RealType sigma()const - { // Accessor. - return m_sigma; - } - -private: - RealType m_sigma; -}; // class rayleigh_distribution - -typedef rayleigh_distribution<double> rayleigh; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const rayleigh_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>()); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const rayleigh_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline RealType pdf(const rayleigh_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std function exp. - - RealType sigma = dist.sigma(); - RealType result = 0; - static const char* function = "boost::math::pdf(const rayleigh_distribution<%1%>&, %1%)"; - if(false == detail::verify_sigma(function, sigma, &result, Policy())) - { - return result; - } - if(false == detail::verify_rayleigh_x(function, x, &result, Policy())) - { - return result; - } - if((boost::math::isinf)(x)) - { - return 0; - } - RealType sigmasqr = sigma * sigma; - result = x * (exp(-(x * x) / ( 2 * sigmasqr))) / sigmasqr; - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const rayleigh_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType result = 0; - RealType sigma = dist.sigma(); - static const char* function = "boost::math::cdf(const rayleigh_distribution<%1%>&, %1%)"; - if(false == detail::verify_sigma(function, sigma, &result, Policy())) - { - return result; - } - if(false == detail::verify_rayleigh_x(function, x, &result, Policy())) - { - return result; - } - result = -boost::math::expm1(-x * x / ( 2 * sigma * sigma), Policy()); - return result; -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const rayleigh_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType result = 0; - RealType sigma = dist.sigma(); - static const char* function = "boost::math::quantile(const rayleigh_distribution<%1%>&, %1%)"; - if(false == detail::verify_sigma(function, sigma, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - - if(p == 0) - { - return 0; - } - if(p == 1) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - result = sqrt(-2 * sigma * sigma * boost::math::log1p(-p, Policy())); - return result; -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<rayleigh_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - RealType result = 0; - RealType sigma = c.dist.sigma(); - static const char* function = "boost::math::cdf(const rayleigh_distribution<%1%>&, %1%)"; - if(false == detail::verify_sigma(function, sigma, &result, Policy())) - { - return result; - } - RealType x = c.param; - if(false == detail::verify_rayleigh_x(function, x, &result, Policy())) - { - return result; - } - RealType ea = x * x / (2 * sigma * sigma); - // Fix for VC11/12 x64 bug in exp(float): - if (ea >= tools::max_value<RealType>()) - return 0; - result = exp(-ea); - return result; -} // cdf complement - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<rayleigh_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions, log & sqrt. - - RealType result = 0; - RealType sigma = c.dist.sigma(); - static const char* function = "boost::math::quantile(const rayleigh_distribution<%1%>&, %1%)"; - if(false == detail::verify_sigma(function, sigma, &result, Policy())) - { - return result; - } - RealType q = c.param; - if(false == detail::check_probability(function, q, &result, Policy())) - { - return result; - } - if(q == 1) - { - return 0; - } - if(q == 0) - { - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - result = sqrt(-2 * sigma * sigma * log(q)); - return result; -} // quantile complement - -template <class RealType, class Policy> -inline RealType mean(const rayleigh_distribution<RealType, Policy>& dist) -{ - RealType result = 0; - RealType sigma = dist.sigma(); - static const char* function = "boost::math::mean(const rayleigh_distribution<%1%>&, %1%)"; - if(false == detail::verify_sigma(function, sigma, &result, Policy())) - { - return result; - } - using boost::math::constants::root_half_pi; - return sigma * root_half_pi<RealType>(); -} // mean - -template <class RealType, class Policy> -inline RealType variance(const rayleigh_distribution<RealType, Policy>& dist) -{ - RealType result = 0; - RealType sigma = dist.sigma(); - static const char* function = "boost::math::variance(const rayleigh_distribution<%1%>&, %1%)"; - if(false == detail::verify_sigma(function, sigma, &result, Policy())) - { - return result; - } - using boost::math::constants::four_minus_pi; - return four_minus_pi<RealType>() * sigma * sigma / 2; -} // variance - -template <class RealType, class Policy> -inline RealType mode(const rayleigh_distribution<RealType, Policy>& dist) -{ - return dist.sigma(); -} - -template <class RealType, class Policy> -inline RealType median(const rayleigh_distribution<RealType, Policy>& dist) -{ - using boost::math::constants::root_ln_four; - return root_ln_four<RealType>() * dist.sigma(); -} - -template <class RealType, class Policy> -inline RealType skewness(const rayleigh_distribution<RealType, Policy>& /*dist*/) -{ - // using namespace boost::math::constants; - return static_cast<RealType>(0.63111065781893713819189935154422777984404221106391L); - // Computed using NTL at 150 bit, about 50 decimal digits. - // return 2 * root_pi<RealType>() * pi_minus_three<RealType>() / pow23_four_minus_pi<RealType>(); -} - -template <class RealType, class Policy> -inline RealType kurtosis(const rayleigh_distribution<RealType, Policy>& /*dist*/) -{ - // using namespace boost::math::constants; - return static_cast<RealType>(3.2450893006876380628486604106197544154170667057995L); - // Computed using NTL at 150 bit, about 50 decimal digits. - // return 3 - (6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) / - // (four_minus_pi<RealType>() * four_minus_pi<RealType>()); -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const rayleigh_distribution<RealType, Policy>& /*dist*/) -{ - //using namespace boost::math::constants; - // Computed using NTL at 150 bit, about 50 decimal digits. - return static_cast<RealType>(0.2450893006876380628486604106197544154170667057995L); - // return -(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) / - // (four_minus_pi<RealType>() * four_minus_pi<RealType>()); -} // kurtosis - -} // namespace math -} // namespace boost - -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_rayleigh_HPP
--- a/any/include/boost/math/distributions/skew_normal.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,719 +0,0 @@ -// Copyright Benjamin Sobotta 2012 - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_SKEW_NORMAL_HPP -#define BOOST_STATS_SKEW_NORMAL_HPP - -// http://en.wikipedia.org/wiki/Skew_normal_distribution -// http://azzalini.stat.unipd.it/SN/ -// Also: -// Azzalini, A. (1985). "A class of distributions which includes the normal ones". -// Scand. J. Statist. 12: 171-178. - -#include <boost/math/distributions/fwd.hpp> // TODO add skew_normal distribution to fwd.hpp! -#include <boost/math/special_functions/owens_t.hpp> // Owen's T function -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/normal.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/constants/constants.hpp> -#include <boost/math/tools/tuple.hpp> -#include <boost/math/tools/roots.hpp> // Newton-Raphson -#include <boost/assert.hpp> -#include <boost/math/distributions/detail/generic_mode.hpp> // pdf max finder. - -#include <utility> -#include <algorithm> // std::lower_bound, std::distance - -namespace boost{ namespace math{ - - namespace detail - { - template <class RealType, class Policy> - inline bool check_skew_normal_shape( - const char* function, - RealType shape, - RealType* result, - const Policy& pol) - { - if(!(boost::math::isfinite)(shape)) - { - *result = - policies::raise_domain_error<RealType>(function, - "Shape parameter is %1%, but must be finite!", - shape, pol); - return false; - } - return true; - } - - } // namespace detail - - template <class RealType = double, class Policy = policies::policy<> > - class skew_normal_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - skew_normal_distribution(RealType l_location = 0, RealType l_scale = 1, RealType l_shape = 0) - : location_(l_location), scale_(l_scale), shape_(l_shape) - { // Default is a 'standard' normal distribution N01. (shape=0 results in the normal distribution with no skew) - static const char* function = "boost::math::skew_normal_distribution<%1%>::skew_normal_distribution"; - - RealType result; - detail::check_scale(function, l_scale, &result, Policy()); - detail::check_location(function, l_location, &result, Policy()); - detail::check_skew_normal_shape(function, l_shape, &result, Policy()); - } - - RealType location()const - { - return location_; - } - - RealType scale()const - { - return scale_; - } - - RealType shape()const - { - return shape_; - } - - - private: - // - // Data members: - // - RealType location_; // distribution location. - RealType scale_; // distribution scale. - RealType shape_; // distribution shape. - }; // class skew_normal_distribution - - typedef skew_normal_distribution<double> skew_normal; - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const skew_normal_distribution<RealType, Policy>& /*dist*/) - { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>( - std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), - std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>()); // - to + max value. - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const skew_normal_distribution<RealType, Policy>& /*dist*/) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. - } - - template <class RealType, class Policy> - inline RealType pdf(const skew_normal_distribution<RealType, Policy>& dist, const RealType& x) - { - const RealType scale = dist.scale(); - const RealType location = dist.location(); - const RealType shape = dist.shape(); - - static const char* function = "boost::math::pdf(const skew_normal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, location, &result, Policy())) - { - return result; - } - if(false == detail::check_skew_normal_shape(function, shape, &result, Policy())) - { - return result; - } - if((boost::math::isinf)(x)) - { - return 0; // pdf + and - infinity is zero. - } - // Below produces MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity()) - //{ // pdf + and - infinity is zero. - // return 0; - //} - if(false == detail::check_x(function, x, &result, Policy())) - { - return result; - } - - const RealType transformed_x = (x-location)/scale; - - normal_distribution<RealType, Policy> std_normal; - - result = pdf(std_normal, transformed_x) * cdf(std_normal, shape*transformed_x) * 2 / scale; - - return result; - } // pdf - - template <class RealType, class Policy> - inline RealType cdf(const skew_normal_distribution<RealType, Policy>& dist, const RealType& x) - { - const RealType scale = dist.scale(); - const RealType location = dist.location(); - const RealType shape = dist.shape(); - - static const char* function = "boost::math::cdf(const skew_normal_distribution<%1%>&, %1%)"; - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - { - return result; - } - if(false == detail::check_location(function, location, &result, Policy())) - { - return result; - } - if(false == detail::check_skew_normal_shape(function, shape, &result, Policy())) - { - return result; - } - if((boost::math::isinf)(x)) - { - if(x < 0) return 0; // -infinity - return 1; // + infinity - } - // These produce MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) - //{ // cdf +infinity is unity. - // return 1; - //} - //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) - //{ // cdf -infinity is zero. - // return 0; - //} - if(false == detail::check_x(function, x, &result, Policy())) - { - return result; - } - - const RealType transformed_x = (x-location)/scale; - - normal_distribution<RealType, Policy> std_normal; - - result = cdf(std_normal, transformed_x) - owens_t(transformed_x, shape)*static_cast<RealType>(2); - - return result; - } // cdf - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<skew_normal_distribution<RealType, Policy>, RealType>& c) - { - const RealType scale = c.dist.scale(); - const RealType location = c.dist.location(); - const RealType shape = c.dist.shape(); - const RealType x = c.param; - - static const char* function = "boost::math::cdf(const complement(skew_normal_distribution<%1%>&), %1%)"; - - if((boost::math::isinf)(x)) - { - if(x < 0) return 1; // cdf complement -infinity is unity. - return 0; // cdf complement +infinity is zero - } - // These produce MSVC 4127 warnings, so the above used instead. - //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) - //{ // cdf complement +infinity is zero. - // return 0; - //} - //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) - //{ // cdf complement -infinity is unity. - // return 1; - //} - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, location, &result, Policy())) - return result; - if(false == detail::check_skew_normal_shape(function, shape, &result, Policy())) - return result; - if(false == detail::check_x(function, x, &result, Policy())) - return result; - - const RealType transformed_x = (x-location)/scale; - - normal_distribution<RealType, Policy> std_normal; - - result = cdf(complement(std_normal, transformed_x)) + owens_t(transformed_x, shape)*static_cast<RealType>(2); - return result; - } // cdf complement - - template <class RealType, class Policy> - inline RealType location(const skew_normal_distribution<RealType, Policy>& dist) - { - return dist.location(); - } - - template <class RealType, class Policy> - inline RealType scale(const skew_normal_distribution<RealType, Policy>& dist) - { - return dist.scale(); - } - - template <class RealType, class Policy> - inline RealType shape(const skew_normal_distribution<RealType, Policy>& dist) - { - return dist.shape(); - } - - template <class RealType, class Policy> - inline RealType mean(const skew_normal_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // for ADL of std functions - - using namespace boost::math::constants; - - //const RealType delta = dist.shape() / sqrt(static_cast<RealType>(1)+dist.shape()*dist.shape()); - - //return dist.location() + dist.scale() * delta * root_two_div_pi<RealType>(); - - return dist.location() + dist.scale() * dist.shape() / sqrt(pi<RealType>()+pi<RealType>()*dist.shape()*dist.shape()) * root_two<RealType>(); - } - - template <class RealType, class Policy> - inline RealType variance(const skew_normal_distribution<RealType, Policy>& dist) - { - using namespace boost::math::constants; - - const RealType delta2 = static_cast<RealType>(1) / (static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape())); - //const RealType inv_delta2 = static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape()); - - RealType variance = dist.scale()*dist.scale()*(static_cast<RealType>(1)-two_div_pi<RealType>()*delta2); - //RealType variance = dist.scale()*dist.scale()*(static_cast<RealType>(1)-two_div_pi<RealType>()/inv_delta2); - - return variance; - } - - namespace detail - { - /* - TODO No closed expression for mode, so use max of pdf. - */ - - template <class RealType, class Policy> - inline RealType mode_fallback(const skew_normal_distribution<RealType, Policy>& dist) - { // mode. - static const char* function = "mode(skew_normal_distribution<%1%> const&)"; - const RealType scale = dist.scale(); - const RealType location = dist.location(); - const RealType shape = dist.shape(); - - RealType result; - if(!detail::check_scale( - function, - scale, &result, Policy()) - || - !detail::check_skew_normal_shape( - function, - shape, - &result, - Policy())) - return result; - - if( shape == 0 ) - { - return location; - } - - if( shape < 0 ) - { - skew_normal_distribution<RealType, Policy> D(0, 1, -shape); - result = mode_fallback(D); - result = location-scale*result; - return result; - } - - BOOST_MATH_STD_USING - - // 21 elements - static const RealType shapes[] = { - 0.0, - 1.000000000000000e-004, - 2.069138081114790e-004, - 4.281332398719396e-004, - 8.858667904100824e-004, - 1.832980710832436e-003, - 3.792690190732250e-003, - 7.847599703514606e-003, - 1.623776739188722e-002, - 3.359818286283781e-002, - 6.951927961775606e-002, - 1.438449888287663e-001, - 2.976351441631319e-001, - 6.158482110660261e-001, - 1.274274985703135e+000, - 2.636650898730361e+000, - 5.455594781168514e+000, - 1.128837891684688e+001, - 2.335721469090121e+001, - 4.832930238571753e+001, - 1.000000000000000e+002}; - - // 21 elements - static const RealType guess[] = { - 0.0, - 5.000050000525391e-005, - 1.500015000148736e-004, - 3.500035000350010e-004, - 7.500075000752560e-004, - 1.450014500145258e-003, - 3.050030500305390e-003, - 6.250062500624765e-003, - 1.295012950129504e-002, - 2.675026750267495e-002, - 5.525055250552491e-002, - 1.132511325113255e-001, - 2.249522495224952e-001, - 3.992539925399257e-001, - 5.353553535535358e-001, - 4.954549545495457e-001, - 3.524535245352451e-001, - 2.182521825218249e-001, - 1.256512565125654e-001, - 6.945069450694508e-002, - 3.735037350373460e-002 - }; - - const RealType* result_ptr = std::lower_bound(shapes, shapes+21, shape); - - typedef typename std::iterator_traits<RealType*>::difference_type diff_type; - - const diff_type d = std::distance(shapes, result_ptr); - - BOOST_ASSERT(d > static_cast<diff_type>(0)); - - // refine - if(d < static_cast<diff_type>(21)) // shape smaller 100 - { - result = guess[d-static_cast<diff_type>(1)] - + (guess[d]-guess[d-static_cast<diff_type>(1)])/(shapes[d]-shapes[d-static_cast<diff_type>(1)]) - * (shape-shapes[d-static_cast<diff_type>(1)]); - } - else // shape greater 100 - { - result = 1e-4; - } - - skew_normal_distribution<RealType, Policy> helper(0, 1, shape); - - result = detail::generic_find_mode_01(helper, result, function); - - result = result*scale + location; - - return result; - } // mode_fallback - - - /* - * TODO No closed expression for mode, so use f'(x) = 0 - */ - template <class RealType, class Policy> - struct skew_normal_mode_functor - { - skew_normal_mode_functor(const boost::math::skew_normal_distribution<RealType, Policy> dist) - : distribution(dist) - { - } - - boost::math::tuple<RealType, RealType> operator()(RealType const& x) - { - normal_distribution<RealType, Policy> std_normal; - const RealType shape = distribution.shape(); - const RealType pdf_x = pdf(distribution, x); - const RealType normpdf_x = pdf(std_normal, x); - const RealType normpdf_ax = pdf(std_normal, x*shape); - RealType fx = static_cast<RealType>(2)*shape*normpdf_ax*normpdf_x - x*pdf_x; - RealType dx = static_cast<RealType>(2)*shape*x*normpdf_x*normpdf_ax*(static_cast<RealType>(1) + shape*shape) + pdf_x + x*fx; - // return both function evaluation difference f(x) and 1st derivative f'(x). - return boost::math::make_tuple(fx, -dx); - } - private: - const boost::math::skew_normal_distribution<RealType, Policy> distribution; - }; - - } // namespace detail - - template <class RealType, class Policy> - inline RealType mode(const skew_normal_distribution<RealType, Policy>& dist) - { - const RealType scale = dist.scale(); - const RealType location = dist.location(); - const RealType shape = dist.shape(); - - static const char* function = "boost::math::mode(const skew_normal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, location, &result, Policy())) - return result; - if(false == detail::check_skew_normal_shape(function, shape, &result, Policy())) - return result; - - if( shape == 0 ) - { - return location; - } - - if( shape < 0 ) - { - skew_normal_distribution<RealType, Policy> D(0, 1, -shape); - result = mode(D); - result = location-scale*result; - return result; - } - - // 21 elements - static const RealType shapes[] = { - 0.0, - static_cast<RealType>(1.000000000000000e-004), - static_cast<RealType>(2.069138081114790e-004), - static_cast<RealType>(4.281332398719396e-004), - static_cast<RealType>(8.858667904100824e-004), - static_cast<RealType>(1.832980710832436e-003), - static_cast<RealType>(3.792690190732250e-003), - static_cast<RealType>(7.847599703514606e-003), - static_cast<RealType>(1.623776739188722e-002), - static_cast<RealType>(3.359818286283781e-002), - static_cast<RealType>(6.951927961775606e-002), - static_cast<RealType>(1.438449888287663e-001), - static_cast<RealType>(2.976351441631319e-001), - static_cast<RealType>(6.158482110660261e-001), - static_cast<RealType>(1.274274985703135e+000), - static_cast<RealType>(2.636650898730361e+000), - static_cast<RealType>(5.455594781168514e+000), - static_cast<RealType>(1.128837891684688e+001), - static_cast<RealType>(2.335721469090121e+001), - static_cast<RealType>(4.832930238571753e+001), - static_cast<RealType>(1.000000000000000e+002) - }; - - // 21 elements - static const RealType guess[] = { - 0.0, - static_cast<RealType>(5.000050000525391e-005), - static_cast<RealType>(1.500015000148736e-004), - static_cast<RealType>(3.500035000350010e-004), - static_cast<RealType>(7.500075000752560e-004), - static_cast<RealType>(1.450014500145258e-003), - static_cast<RealType>(3.050030500305390e-003), - static_cast<RealType>(6.250062500624765e-003), - static_cast<RealType>(1.295012950129504e-002), - static_cast<RealType>(2.675026750267495e-002), - static_cast<RealType>(5.525055250552491e-002), - static_cast<RealType>(1.132511325113255e-001), - static_cast<RealType>(2.249522495224952e-001), - static_cast<RealType>(3.992539925399257e-001), - static_cast<RealType>(5.353553535535358e-001), - static_cast<RealType>(4.954549545495457e-001), - static_cast<RealType>(3.524535245352451e-001), - static_cast<RealType>(2.182521825218249e-001), - static_cast<RealType>(1.256512565125654e-001), - static_cast<RealType>(6.945069450694508e-002), - static_cast<RealType>(3.735037350373460e-002) - }; - - const RealType* result_ptr = std::lower_bound(shapes, shapes+21, shape); - - typedef typename std::iterator_traits<RealType*>::difference_type diff_type; - - const diff_type d = std::distance(shapes, result_ptr); - - BOOST_ASSERT(d > static_cast<diff_type>(0)); - - // TODO: make the search bounds smarter, depending on the shape parameter - RealType search_min = 0; // below zero was caught above - RealType search_max = 0.55f; // will never go above 0.55 - - // refine - if(d < static_cast<diff_type>(21)) // shape smaller 100 - { - // it is safe to assume that d > 0, because shape==0.0 is caught earlier - result = guess[d-static_cast<diff_type>(1)] - + (guess[d]-guess[d-static_cast<diff_type>(1)])/(shapes[d]-shapes[d-static_cast<diff_type>(1)]) - * (shape-shapes[d-static_cast<diff_type>(1)]); - } - else // shape greater 100 - { - result = 1e-4f; - search_max = guess[19]; // set 19 instead of 20 to have a safety margin because the table may not be exact @ shape=100 - } - - const int get_digits = policies::digits<RealType, Policy>();// get digits from policy, - boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); // and max iterations. - - skew_normal_distribution<RealType, Policy> helper(0, 1, shape); - - result = tools::newton_raphson_iterate(detail::skew_normal_mode_functor<RealType, Policy>(helper), result, - search_min, search_max, get_digits, m); - - result = result*scale + location; - - return result; - } - - - - template <class RealType, class Policy> - inline RealType skewness(const skew_normal_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // for ADL of std functions - using namespace boost::math::constants; - - static const RealType factor = four_minus_pi<RealType>()/static_cast<RealType>(2); - const RealType delta = dist.shape() / sqrt(static_cast<RealType>(1)+dist.shape()*dist.shape()); - - return factor * pow(root_two_div_pi<RealType>() * delta, 3) / - pow(static_cast<RealType>(1)-two_div_pi<RealType>()*delta*delta, static_cast<RealType>(1.5)); - } - - template <class RealType, class Policy> - inline RealType kurtosis(const skew_normal_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist)+static_cast<RealType>(3); - } - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const skew_normal_distribution<RealType, Policy>& dist) - { - using namespace boost::math::constants; - - static const RealType factor = pi_minus_three<RealType>()*static_cast<RealType>(2); - - const RealType delta2 = static_cast<RealType>(1) / (static_cast<RealType>(1)+static_cast<RealType>(1)/(dist.shape()*dist.shape())); - - const RealType x = static_cast<RealType>(1)-two_div_pi<RealType>()*delta2; - const RealType y = two_div_pi<RealType>() * delta2; - - return factor * y*y / (x*x); - } - - namespace detail - { - - template <class RealType, class Policy> - struct skew_normal_quantile_functor - { - skew_normal_quantile_functor(const boost::math::skew_normal_distribution<RealType, Policy> dist, RealType const& p) - : distribution(dist), prob(p) - { - } - - boost::math::tuple<RealType, RealType> operator()(RealType const& x) - { - RealType c = cdf(distribution, x); - RealType fx = c - prob; // Difference cdf - value - to minimize. - RealType dx = pdf(distribution, x); // pdf is 1st derivative. - // return both function evaluation difference f(x) and 1st derivative f'(x). - return boost::math::make_tuple(fx, dx); - } - private: - const boost::math::skew_normal_distribution<RealType, Policy> distribution; - RealType prob; - }; - - } // namespace detail - - template <class RealType, class Policy> - inline RealType quantile(const skew_normal_distribution<RealType, Policy>& dist, const RealType& p) - { - const RealType scale = dist.scale(); - const RealType location = dist.location(); - const RealType shape = dist.shape(); - - static const char* function = "boost::math::quantile(const skew_normal_distribution<%1%>&, %1%)"; - - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, location, &result, Policy())) - return result; - if(false == detail::check_skew_normal_shape(function, shape, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - - // Compute initial guess via Cornish-Fisher expansion. - RealType x = -boost::math::erfc_inv(2 * p, Policy()) * constants::root_two<RealType>(); - - // Avoid unnecessary computations if there is no skew. - if(shape != 0) - { - const RealType skew = skewness(dist); - const RealType exk = kurtosis_excess(dist); - - x = x + (x*x-static_cast<RealType>(1))*skew/static_cast<RealType>(6) - + x*(x*x-static_cast<RealType>(3))*exk/static_cast<RealType>(24) - - x*(static_cast<RealType>(2)*x*x-static_cast<RealType>(5))*skew*skew/static_cast<RealType>(36); - } // if(shape != 0) - - result = standard_deviation(dist)*x+mean(dist); - - // handle special case of non-skew normal distribution. - if(shape == 0) - return result; - - // refine the result by numerically searching the root of (p-cdf) - - const RealType search_min = range(dist).first; - const RealType search_max = range(dist).second; - - const int get_digits = policies::digits<RealType, Policy>();// get digits from policy, - boost::uintmax_t m = policies::get_max_root_iterations<Policy>(); // and max iterations. - - result = tools::newton_raphson_iterate(detail::skew_normal_quantile_functor<RealType, Policy>(dist, p), result, - search_min, search_max, get_digits, m); - - return result; - } // quantile - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<skew_normal_distribution<RealType, Policy>, RealType>& c) - { - const RealType scale = c.dist.scale(); - const RealType location = c.dist.location(); - const RealType shape = c.dist.shape(); - - static const char* function = "boost::math::quantile(const complement(skew_normal_distribution<%1%>&), %1%)"; - RealType result = 0; - if(false == detail::check_scale(function, scale, &result, Policy())) - return result; - if(false == detail::check_location(function, location, &result, Policy())) - return result; - if(false == detail::check_skew_normal_shape(function, shape, &result, Policy())) - return result; - RealType q = c.param; - if(false == detail::check_probability(function, q, &result, Policy())) - return result; - - skew_normal_distribution<RealType, Policy> D(-location, scale, -shape); - - result = -quantile(D, q); - - return result; - } // quantile - - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_SKEW_NORMAL_HPP - -
--- a/any/include/boost/math/distributions/students_t.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,493 +0,0 @@ -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2006, 2012, 2017. -// Copyright Thomas Mang 2012. - -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_STUDENTS_T_HPP -#define BOOST_STATS_STUDENTS_T_HPP - -// http://en.wikipedia.org/wiki/Student%27s_t_distribution -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3664.htm - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/beta.hpp> // for ibeta(a, b, x). -#include <boost/math/distributions/complement.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/normal.hpp> - -#include <utility> - -#ifdef BOOST_MSVC -# pragma warning(push) -# pragma warning(disable: 4702) // unreachable code (return after domain_error throw). -#endif - -namespace boost { namespace math { - -template <class RealType = double, class Policy = policies::policy<> > -class students_t_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - students_t_distribution(RealType df) : df_(df) - { // Constructor. - RealType result; - detail::check_df_gt0_to_inf( // Checks that df > 0 or df == inf. - "boost::math::students_t_distribution<%1%>::students_t_distribution", df_, &result, Policy()); - } // students_t_distribution - - RealType degrees_of_freedom()const - { - return df_; - } - - // Parameter estimation: - static RealType find_degrees_of_freedom( - RealType difference_from_mean, - RealType alpha, - RealType beta, - RealType sd, - RealType hint = 100); - -private: - // Data member: - RealType df_; // degrees of freedom is a real number > 0 or +infinity. -}; - -typedef students_t_distribution<double> students_t; // Convenience typedef for double version. - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const students_t_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - // Now including infinity. - using boost::math::tools::max_value; - //return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); - return std::pair<RealType, RealType>(((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>()), ((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? +std::numeric_limits<RealType>::infinity() : +max_value<RealType>())); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const students_t_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // Now including infinity. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - //return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); - return std::pair<RealType, RealType>(((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>()), ((::std::numeric_limits<RealType>::is_specialized & ::std::numeric_limits<RealType>::has_infinity) ? +std::numeric_limits<RealType>::infinity() : +max_value<RealType>())); -} - -template <class RealType, class Policy> -inline RealType pdf(const students_t_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_FPU_EXCEPTION_GUARD - BOOST_MATH_STD_USING // for ADL of std functions. - - RealType error_result; - if(false == detail::check_x_not_NaN( - "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", x, &error_result, Policy())) - return error_result; - RealType df = dist.degrees_of_freedom(); - if(false == detail::check_df_gt0_to_inf( // Check that df > 0 or == +infinity. - "boost::math::pdf(const students_t_distribution<%1%>&, %1%)", df, &error_result, Policy())) - return error_result; - - RealType result; - if ((boost::math::isinf)(x)) - { // - or +infinity. - result = static_cast<RealType>(0); - return result; - } - RealType limit = policies::get_epsilon<RealType, Policy>(); - // Use policies so that if policy requests lower precision, - // then get the normal distribution approximation earlier. - limit = static_cast<RealType>(1) / limit; // 1/eps - // for 64-bit double 1/eps = 4503599627370496 - if (df > limit) - { // Special case for really big degrees_of_freedom > 1 / eps - // - use normal distribution which is much faster and more accurate. - normal_distribution<RealType, Policy> n(0, 1); - result = pdf(n, x); - } - else - { // - RealType basem1 = x * x / df; - if(basem1 < 0.125) - { - result = exp(-boost::math::log1p(basem1, Policy()) * (1+df) / 2); - } - else - { - result = pow(1 / (1 + basem1), (df + 1) / 2); - } - result /= sqrt(df) * boost::math::beta(df / 2, RealType(0.5f), Policy()); - } - return result; -} // pdf - -template <class RealType, class Policy> -inline RealType cdf(const students_t_distribution<RealType, Policy>& dist, const RealType& x) -{ - RealType error_result; - // degrees_of_freedom > 0 or infinity check: - RealType df = dist.degrees_of_freedom(); - if (false == detail::check_df_gt0_to_inf( // Check that df > 0 or == +infinity. - "boost::math::cdf(const students_t_distribution<%1%>&, %1%)", df, &error_result, Policy())) - { - return error_result; - } - // Check for bad x first. - if(false == detail::check_x_not_NaN( - "boost::math::cdf(const students_t_distribution<%1%>&, %1%)", x, &error_result, Policy())) - { - return error_result; - } - if (x == 0) - { // Special case with exact result. - return static_cast<RealType>(0.5); - } - if ((boost::math::isinf)(x)) - { // x == - or + infinity, regardless of df. - return ((x < 0) ? static_cast<RealType>(0) : static_cast<RealType>(1)); - } - - RealType limit = policies::get_epsilon<RealType, Policy>(); - // Use policies so that if policy requests lower precision, - // then get the normal distribution approximation earlier. - limit = static_cast<RealType>(1) / limit; // 1/eps - // for 64-bit double 1/eps = 4503599627370496 - if (df > limit) - { // Special case for really big degrees_of_freedom > 1 / eps (perhaps infinite?) - // - use normal distribution which is much faster and more accurate. - normal_distribution<RealType, Policy> n(0, 1); - RealType result = cdf(n, x); - return result; - } - else - { // normal df case. - // - // Calculate probability of Student's t using the incomplete beta function. - // probability = ibeta(degrees_of_freedom / 2, 1/2, degrees_of_freedom / (degrees_of_freedom + t*t)) - // - // However when t is small compared to the degrees of freedom, that formula - // suffers from rounding error, use the identity formula to work around - // the problem: - // - // I[x](a,b) = 1 - I[1-x](b,a) - // - // and: - // - // x = df / (df + t^2) - // - // so: - // - // 1 - x = t^2 / (df + t^2) - // - RealType x2 = x * x; - RealType probability; - if(df > 2 * x2) - { - RealType z = x2 / (df + x2); - probability = ibetac(static_cast<RealType>(0.5), df / 2, z, Policy()) / 2; - } - else - { - RealType z = df / (df + x2); - probability = ibeta(df / 2, static_cast<RealType>(0.5), z, Policy()) / 2; - } - return (x > 0 ? 1 - probability : probability); - } -} // cdf - -template <class RealType, class Policy> -inline RealType quantile(const students_t_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - // - // Obtain parameters: - RealType probability = p; - - // Check for domain errors: - RealType df = dist.degrees_of_freedom(); - static const char* function = "boost::math::quantile(const students_t_distribution<%1%>&, %1%)"; - RealType error_result; - if(false == (detail::check_df_gt0_to_inf( // Check that df > 0 or == +infinity. - function, df, &error_result, Policy()) - && detail::check_probability(function, probability, &error_result, Policy()))) - return error_result; - // Special cases, regardless of degrees_of_freedom. - if (probability == 0) - return -policies::raise_overflow_error<RealType>(function, 0, Policy()); - if (probability == 1) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - if (probability == static_cast<RealType>(0.5)) - return 0; // - // -#if 0 - // This next block is disabled in favour of a faster method than - // incomplete beta inverse, but code retained for future reference: - // - // Calculate quantile of Student's t using the incomplete beta function inverse: - probability = (probability > 0.5) ? 1 - probability : probability; - RealType t, x, y; - x = ibeta_inv(degrees_of_freedom / 2, RealType(0.5), 2 * probability, &y); - if(degrees_of_freedom * y > tools::max_value<RealType>() * x) - t = tools::overflow_error<RealType>(function); - else - t = sqrt(degrees_of_freedom * y / x); - // - // Figure out sign based on the size of p: - // - if(p < 0.5) - t = -t; - - return t; -#endif - // - // Depending on how many digits RealType has, this may forward - // to the incomplete beta inverse as above. Otherwise uses a - // faster method that is accurate to ~15 digits everywhere - // and a couple of epsilon at double precision and in the central - // region where most use cases will occur... - // - return boost::math::detail::fast_students_t_quantile(df, probability, Policy()); -} // quantile - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<students_t_distribution<RealType, Policy>, RealType>& c) -{ - return cdf(c.dist, -c.param); -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<students_t_distribution<RealType, Policy>, RealType>& c) -{ - return -quantile(c.dist, c.param); -} - -// -// Parameter estimation follows: -// -namespace detail{ -// -// Functors for finding degrees of freedom: -// -template <class RealType, class Policy> -struct sample_size_func -{ - sample_size_func(RealType a, RealType b, RealType s, RealType d) - : alpha(a), beta(b), ratio(s*s/(d*d)) {} - - RealType operator()(const RealType& df) - { - if(df <= tools::min_value<RealType>()) - { // - return 1; - } - students_t_distribution<RealType, Policy> t(df); - RealType qa = quantile(complement(t, alpha)); - RealType qb = quantile(complement(t, beta)); - qa += qb; - qa *= qa; - qa *= ratio; - qa -= (df + 1); - return qa; - } - RealType alpha, beta, ratio; -}; - -} // namespace detail - -template <class RealType, class Policy> -RealType students_t_distribution<RealType, Policy>::find_degrees_of_freedom( - RealType difference_from_mean, - RealType alpha, - RealType beta, - RealType sd, - RealType hint) -{ - static const char* function = "boost::math::students_t_distribution<%1%>::find_degrees_of_freedom"; - // - // Check for domain errors: - // - RealType error_result; - if(false == detail::check_probability( - function, alpha, &error_result, Policy()) - && detail::check_probability(function, beta, &error_result, Policy())) - return error_result; - - if(hint <= 0) - hint = 1; - - detail::sample_size_func<RealType, Policy> f(alpha, beta, sd, difference_from_mean); - tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>()); - boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>(); - std::pair<RealType, RealType> r = tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy()); - RealType result = r.first + (r.second - r.first) / 2; - if(max_iter >= policies::get_max_root_iterations<Policy>()) - { - return policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:" - " either there is no answer to how many degrees of freedom are required" - " or the answer is infinite. Current best guess is %1%", result, Policy()); - } - return result; -} - -template <class RealType, class Policy> -inline RealType mode(const students_t_distribution<RealType, Policy>& /*dist*/) -{ - // Assume no checks on degrees of freedom are useful (unlike mean). - return 0; // Always zero by definition. -} - -template <class RealType, class Policy> -inline RealType median(const students_t_distribution<RealType, Policy>& /*dist*/) -{ - // Assume no checks on degrees of freedom are useful (unlike mean). - return 0; // Always zero by definition. -} - -// See section 5.1 on moments at http://en.wikipedia.org/wiki/Student%27s_t-distribution - -template <class RealType, class Policy> -inline RealType mean(const students_t_distribution<RealType, Policy>& dist) -{ // Revised for https://svn.boost.org/trac/boost/ticket/7177 - RealType df = dist.degrees_of_freedom(); - if(((boost::math::isnan)(df)) || (df <= 1) ) - { // mean is undefined for moment <= 1! - return policies::raise_domain_error<RealType>( - "boost::math::mean(students_t_distribution<%1%> const&, %1%)", - "Mean is undefined for degrees of freedom < 1 but got %1%.", df, Policy()); - return std::numeric_limits<RealType>::quiet_NaN(); - } - return 0; -} // mean - -template <class RealType, class Policy> -inline RealType variance(const students_t_distribution<RealType, Policy>& dist) -{ // http://en.wikipedia.org/wiki/Student%27s_t-distribution - // Revised for https://svn.boost.org/trac/boost/ticket/7177 - RealType df = dist.degrees_of_freedom(); - if ((boost::math::isnan)(df) || (df <= 2)) - { // NaN or undefined for <= 2. - return policies::raise_domain_error<RealType>( - "boost::math::variance(students_t_distribution<%1%> const&, %1%)", - "variance is undefined for degrees of freedom <= 2, but got %1%.", - df, Policy()); - return std::numeric_limits<RealType>::quiet_NaN(); // Undefined. - } - if ((boost::math::isinf)(df)) - { // +infinity. - return 1; - } - RealType limit = policies::get_epsilon<RealType, Policy>(); - // Use policies so that if policy requests lower precision, - // then get the normal distribution approximation earlier. - limit = static_cast<RealType>(1) / limit; // 1/eps - // for 64-bit double 1/eps = 4503599627370496 - if (df > limit) - { // Special case for really big degrees_of_freedom > 1 / eps. - return 1; - } - else - { - return df / (df - 2); - } -} // variance - -template <class RealType, class Policy> -inline RealType skewness(const students_t_distribution<RealType, Policy>& dist) -{ - RealType df = dist.degrees_of_freedom(); - if( ((boost::math::isnan)(df)) || (dist.degrees_of_freedom() <= 3)) - { // Undefined for moment k = 3. - return policies::raise_domain_error<RealType>( - "boost::math::skewness(students_t_distribution<%1%> const&, %1%)", - "Skewness is undefined for degrees of freedom <= 3, but got %1%.", - dist.degrees_of_freedom(), Policy()); - return std::numeric_limits<RealType>::quiet_NaN(); - } - return 0; // For all valid df, including infinity. -} // skewness - -template <class RealType, class Policy> -inline RealType kurtosis(const students_t_distribution<RealType, Policy>& dist) -{ - RealType df = dist.degrees_of_freedom(); - if(((boost::math::isnan)(df)) || (df <= 4)) - { // Undefined or infinity for moment k = 4. - return policies::raise_domain_error<RealType>( - "boost::math::kurtosis(students_t_distribution<%1%> const&, %1%)", - "Kurtosis is undefined for degrees of freedom <= 4, but got %1%.", - df, Policy()); - return std::numeric_limits<RealType>::quiet_NaN(); // Undefined. - } - if ((boost::math::isinf)(df)) - { // +infinity. - return 3; - } - RealType limit = policies::get_epsilon<RealType, Policy>(); - // Use policies so that if policy requests lower precision, - // then get the normal distribution approximation earlier. - limit = static_cast<RealType>(1) / limit; // 1/eps - // for 64-bit double 1/eps = 4503599627370496 - if (df > limit) - { // Special case for really big degrees_of_freedom > 1 / eps. - return 3; - } - else - { - //return 3 * (df - 2) / (df - 4); re-arranged to - return 6 / (df - 4) + 3; - } -} // kurtosis - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const students_t_distribution<RealType, Policy>& dist) -{ - // see http://mathworld.wolfram.com/Kurtosis.html - - RealType df = dist.degrees_of_freedom(); - if(((boost::math::isnan)(df)) || (df <= 4)) - { // Undefined or infinity for moment k = 4. - return policies::raise_domain_error<RealType>( - "boost::math::kurtosis_excess(students_t_distribution<%1%> const&, %1%)", - "Kurtosis_excess is undefined for degrees of freedom <= 4, but got %1%.", - df, Policy()); - return std::numeric_limits<RealType>::quiet_NaN(); // Undefined. - } - if ((boost::math::isinf)(df)) - { // +infinity. - return 0; - } - RealType limit = policies::get_epsilon<RealType, Policy>(); - // Use policies so that if policy requests lower precision, - // then get the normal distribution approximation earlier. - limit = static_cast<RealType>(1) / limit; // 1/eps - // for 64-bit double 1/eps = 4503599627370496 - if (df > limit) - { // Special case for really big degrees_of_freedom > 1 / eps. - return 0; - } - else - { - return 6 / (df - 4); - } -} - -} // namespace math -} // namespace boost - -#ifdef BOOST_MSVC -# pragma warning(pop) -#endif - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_STUDENTS_T_HPP
--- a/any/include/boost/math/distributions/triangular.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,531 +0,0 @@ -// Copyright John Maddock 2006, 2007. -// Copyright Paul A. Bristow 2006, 2007. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_TRIANGULAR_HPP -#define BOOST_STATS_TRIANGULAR_HPP - -// http://mathworld.wolfram.com/TriangularDistribution.html -// Note that the 'constructors' defined by Wolfram are difference from those here, -// for example -// N[variance[triangulardistribution{1, +2}, 1.5], 50] computes -// 0.041666666666666666666666666666666666666666666666667 -// TriangularDistribution{1, +2}, 1.5 is the analog of triangular_distribution(1, 1.5, 2) - -// http://en.wikipedia.org/wiki/Triangular_distribution - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/expm1.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> -#include <boost/math/constants/constants.hpp> - -#include <utility> - -namespace boost{ namespace math -{ - namespace detail - { - template <class RealType, class Policy> - inline bool check_triangular_lower( - const char* function, - RealType lower, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(lower)) - { // Any finite value is OK. - return true; - } - else - { // Not finite: infinity or NaN. - *result = policies::raise_domain_error<RealType>( - function, - "Lower parameter is %1%, but must be finite!", lower, pol); - return false; - } - } // bool check_triangular_lower( - - template <class RealType, class Policy> - inline bool check_triangular_mode( - const char* function, - RealType mode, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(mode)) - { // any finite value is OK. - return true; - } - else - { // Not finite: infinity or NaN. - *result = policies::raise_domain_error<RealType>( - function, - "Mode parameter is %1%, but must be finite!", mode, pol); - return false; - } - } // bool check_triangular_mode( - - template <class RealType, class Policy> - inline bool check_triangular_upper( - const char* function, - RealType upper, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(upper)) - { // any finite value is OK. - return true; - } - else - { // Not finite: infinity or NaN. - *result = policies::raise_domain_error<RealType>( - function, - "Upper parameter is %1%, but must be finite!", upper, pol); - return false; - } - } // bool check_triangular_upper( - - template <class RealType, class Policy> - inline bool check_triangular_x( - const char* function, - RealType const& x, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(x)) - { // Any finite value is OK - return true; - } - else - { // Not finite: infinity or NaN. - *result = policies::raise_domain_error<RealType>( - function, - "x parameter is %1%, but must be finite!", x, pol); - return false; - } - } // bool check_triangular_x - - template <class RealType, class Policy> - inline bool check_triangular( - const char* function, - RealType lower, - RealType mode, - RealType upper, - RealType* result, const Policy& pol) - { - if ((check_triangular_lower(function, lower, result, pol) == false) - || (check_triangular_mode(function, mode, result, pol) == false) - || (check_triangular_upper(function, upper, result, pol) == false)) - { // Some parameter not finite. - return false; - } - else if (lower >= upper) // lower == upper NOT useful. - { // lower >= upper. - *result = policies::raise_domain_error<RealType>( - function, - "lower parameter is %1%, but must be less than upper!", lower, pol); - return false; - } - else - { // Check lower <= mode <= upper. - if (mode < lower) - { - *result = policies::raise_domain_error<RealType>( - function, - "mode parameter is %1%, but must be >= than lower!", lower, pol); - return false; - } - if (mode > upper) - { - *result = policies::raise_domain_error<RealType>( - function, - "mode parameter is %1%, but must be <= than upper!", upper, pol); - return false; - } - return true; // All OK. - } - } // bool check_triangular - } // namespace detail - - template <class RealType = double, class Policy = policies::policy<> > - class triangular_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - triangular_distribution(RealType l_lower = -1, RealType l_mode = 0, RealType l_upper = 1) - : m_lower(l_lower), m_mode(l_mode), m_upper(l_upper) // Constructor. - { // Evans says 'standard triangular' is lower 0, mode 1/2, upper 1, - // has median sqrt(c/2) for c <=1/2 and 1 - sqrt(1-c)/2 for c >= 1/2 - // But this -1, 0, 1 is more useful in most applications to approximate normal distribution, - // where the central value is the most likely and deviations either side equally likely. - RealType result; - detail::check_triangular("boost::math::triangular_distribution<%1%>::triangular_distribution",l_lower, l_mode, l_upper, &result, Policy()); - } - // Accessor functions. - RealType lower()const - { - return m_lower; - } - RealType mode()const - { - return m_mode; - } - RealType upper()const - { - return m_upper; - } - private: - // Data members: - RealType m_lower; // distribution lower aka a - RealType m_mode; // distribution mode aka c - RealType m_upper; // distribution upper aka b - }; // class triangular_distribution - - typedef triangular_distribution<double> triangular; - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const triangular_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const triangular_distribution<RealType, Policy>& dist) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - return std::pair<RealType, RealType>(dist.lower(), dist.upper()); - } - - template <class RealType, class Policy> - RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x) - { - static const char* function = "boost::math::pdf(const triangular_distribution<%1%>&, %1%)"; - RealType lower = dist.lower(); - RealType mode = dist.mode(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_triangular_x(function, x, &result, Policy())) - { - return result; - } - if((x < lower) || (x > upper)) - { - return 0; - } - if (x == lower) - { // (mode - lower) == 0 which would lead to divide by zero! - return (mode == lower) ? 2 / (upper - lower) : RealType(0); - } - else if (x == upper) - { - return (mode == upper) ? 2 / (upper - lower) : RealType(0); - } - else if (x <= mode) - { - return 2 * (x - lower) / ((upper - lower) * (mode - lower)); - } - else - { // (x > mode) - return 2 * (upper - x) / ((upper - lower) * (upper - mode)); - } - } // RealType pdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x) - - template <class RealType, class Policy> - inline RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x) - { - static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)"; - RealType lower = dist.lower(); - RealType mode = dist.mode(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_triangular_x(function, x, &result, Policy())) - { - return result; - } - if((x <= lower)) - { - return 0; - } - if (x >= upper) - { - return 1; - } - // else lower < x < upper - if (x <= mode) - { - return ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower)); - } - else - { - return 1 - (upper - x) * (upper - x) / ((upper - lower) * (upper - mode)); - } - } // RealType cdf(const triangular_distribution<RealType, Policy>& dist, const RealType& x) - - template <class RealType, class Policy> - RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& p) - { - BOOST_MATH_STD_USING // for ADL of std functions (sqrt). - static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)"; - RealType lower = dist.lower(); - RealType mode = dist.mode(); - RealType upper = dist.upper(); - RealType result = 0; // of checks - if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_probability(function, p, &result, Policy())) - { - return result; - } - if(p == 0) - { - return lower; - } - if(p == 1) - { - return upper; - } - RealType p0 = (mode - lower) / (upper - lower); - RealType q = 1 - p; - if (p < p0) - { - result = sqrt((upper - lower) * (mode - lower) * p) + lower; - } - else if (p == p0) - { - result = mode; - } - else // p > p0 - { - result = upper - sqrt((upper - lower) * (upper - mode) * q); - } - return result; - - } // RealType quantile(const triangular_distribution<RealType, Policy>& dist, const RealType& q) - - template <class RealType, class Policy> - RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c) - { - static const char* function = "boost::math::cdf(const triangular_distribution<%1%>&, %1%)"; - RealType lower = c.dist.lower(); - RealType mode = c.dist.mode(); - RealType upper = c.dist.upper(); - RealType x = c.param; - RealType result = 0; // of checks. - if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_triangular_x(function, x, &result, Policy())) - { - return result; - } - if (x <= lower) - { - return 1; - } - if (x >= upper) - { - return 0; - } - if (x <= mode) - { - return 1 - ((x - lower) * (x - lower)) / ((upper - lower) * (mode - lower)); - } - else - { - return (upper - x) * (upper - x) / ((upper - lower) * (upper - mode)); - } - } // RealType cdf(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c) - - template <class RealType, class Policy> - RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c) - { - BOOST_MATH_STD_USING // Aid ADL for sqrt. - static const char* function = "boost::math::quantile(const triangular_distribution<%1%>&, %1%)"; - RealType l = c.dist.lower(); - RealType m = c.dist.mode(); - RealType u = c.dist.upper(); - RealType q = c.param; // probability 0 to 1. - RealType result = 0; // of checks. - if(false == detail::check_triangular(function, l, m, u, &result, Policy())) - { - return result; - } - if(false == detail::check_probability(function, q, &result, Policy())) - { - return result; - } - if(q == 0) - { - return u; - } - if(q == 1) - { - return l; - } - RealType lower = c.dist.lower(); - RealType mode = c.dist.mode(); - RealType upper = c.dist.upper(); - - RealType p = 1 - q; - RealType p0 = (mode - lower) / (upper - lower); - if(p < p0) - { - RealType s = (upper - lower) * (mode - lower); - s *= p; - result = sqrt((upper - lower) * (mode - lower) * p) + lower; - } - else if (p == p0) - { - result = mode; - } - else // p > p0 - { - result = upper - sqrt((upper - lower) * (upper - mode) * q); - } - return result; - } // RealType quantile(const complemented2_type<triangular_distribution<RealType, Policy>, RealType>& c) - - template <class RealType, class Policy> - inline RealType mean(const triangular_distribution<RealType, Policy>& dist) - { - static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)"; - RealType lower = dist.lower(); - RealType mode = dist.mode(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy())) - { - return result; - } - return (lower + upper + mode) / 3; - } // RealType mean(const triangular_distribution<RealType, Policy>& dist) - - - template <class RealType, class Policy> - inline RealType variance(const triangular_distribution<RealType, Policy>& dist) - { - static const char* function = "boost::math::mean(const triangular_distribution<%1%>&)"; - RealType lower = dist.lower(); - RealType mode = dist.mode(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_triangular(function, lower, mode, upper, &result, Policy())) - { - return result; - } - return (lower * lower + upper * upper + mode * mode - lower * upper - lower * mode - upper * mode) / 18; - } // RealType variance(const triangular_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType mode(const triangular_distribution<RealType, Policy>& dist) - { - static const char* function = "boost::math::mode(const triangular_distribution<%1%>&)"; - RealType mode = dist.mode(); - RealType result = 0; // of checks. - if(false == detail::check_triangular_mode(function, mode, &result, Policy())) - { // This should never happen! - return result; - } - return mode; - } // RealType mode - - template <class RealType, class Policy> - inline RealType median(const triangular_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // ADL of std functions. - static const char* function = "boost::math::median(const triangular_distribution<%1%>&)"; - RealType mode = dist.mode(); - RealType result = 0; // of checks. - if(false == detail::check_triangular_mode(function, mode, &result, Policy())) - { // This should never happen! - return result; - } - RealType lower = dist.lower(); - RealType upper = dist.upper(); - if (mode >= (upper + lower) / 2) - { - return lower + sqrt((upper - lower) * (mode - lower)) / constants::root_two<RealType>(); - } - else - { - return upper - sqrt((upper - lower) * (upper - mode)) / constants::root_two<RealType>(); - } - } // RealType mode - - template <class RealType, class Policy> - inline RealType skewness(const triangular_distribution<RealType, Policy>& dist) - { - BOOST_MATH_STD_USING // for ADL of std functions - using namespace boost::math::constants; // for root_two - static const char* function = "boost::math::skewness(const triangular_distribution<%1%>&)"; - - RealType lower = dist.lower(); - RealType mode = dist.mode(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == boost::math::detail::check_triangular(function,lower, mode, upper, &result, Policy())) - { - return result; - } - return root_two<RealType>() * (lower + upper - 2 * mode) * (2 * lower - upper - mode) * (lower - 2 * upper + mode) / - (5 * pow((lower * lower + upper * upper + mode * mode - - lower * upper - lower * mode - upper * mode), RealType(3)/RealType(2))); - // #11768: Skewness formula for triangular distribution is incorrect - corrected 29 Oct 2015 for release 1.61. - } // RealType skewness(const triangular_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis(const triangular_distribution<RealType, Policy>& dist) - { // These checks may be belt and braces as should have been checked on construction? - static const char* function = "boost::math::kurtosis(const triangular_distribution<%1%>&)"; - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType mode = dist.mode(); - RealType result = 0; // of checks. - if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy())) - { - return result; - } - return static_cast<RealType>(12)/5; // 12/5 = 2.4; - } // RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const triangular_distribution<RealType, Policy>& dist) - { // These checks may be belt and braces as should have been checked on construction? - static const char* function = "boost::math::kurtosis_excess(const triangular_distribution<%1%>&)"; - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType mode = dist.mode(); - RealType result = 0; // of checks. - if(false == detail::check_triangular(function,lower, mode, upper, &result, Policy())) - { - return result; - } - return static_cast<RealType>(-3)/5; // - 3/5 = -0.6 - // Assuming mathworld really means kurtosis excess? Wikipedia now corrected to match this. - } - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_TRIANGULAR_HPP - - -
--- a/any/include/boost/math/distributions/uniform.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,382 +0,0 @@ -// Copyright John Maddock 2006. -// Copyright Paul A. Bristow 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -// TODO deal with infinity as special better - or remove. -// - -#ifndef BOOST_STATS_UNIFORM_HPP -#define BOOST_STATS_UNIFORM_HPP - -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm -// http://mathworld.wolfram.com/UniformDistribution.html -// http://documents.wolfram.com/calculationcenter/v2/Functions/ListsMatrices/Statistics/UniformDistribution.html -// http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> - -#include <utility> - -namespace boost{ namespace math -{ - namespace detail - { - template <class RealType, class Policy> - inline bool check_uniform_lower( - const char* function, - RealType lower, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(lower)) - { // any finite value is OK. - return true; - } - else - { // Not finite. - *result = policies::raise_domain_error<RealType>( - function, - "Lower parameter is %1%, but must be finite!", lower, pol); - return false; - } - } // bool check_uniform_lower( - - template <class RealType, class Policy> - inline bool check_uniform_upper( - const char* function, - RealType upper, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(upper)) - { // Any finite value is OK. - return true; - } - else - { // Not finite. - *result = policies::raise_domain_error<RealType>( - function, - "Upper parameter is %1%, but must be finite!", upper, pol); - return false; - } - } // bool check_uniform_upper( - - template <class RealType, class Policy> - inline bool check_uniform_x( - const char* function, - RealType const& x, - RealType* result, const Policy& pol) - { - if((boost::math::isfinite)(x)) - { // Any finite value is OK - return true; - } - else - { // Not finite.. - *result = policies::raise_domain_error<RealType>( - function, - "x parameter is %1%, but must be finite!", x, pol); - return false; - } - } // bool check_uniform_x - - template <class RealType, class Policy> - inline bool check_uniform( - const char* function, - RealType lower, - RealType upper, - RealType* result, const Policy& pol) - { - if((check_uniform_lower(function, lower, result, pol) == false) - || (check_uniform_upper(function, upper, result, pol) == false)) - { - return false; - } - else if (lower >= upper) // If lower == upper then 1 / (upper-lower) = 1/0 = +infinity! - { // upper and lower have been checked before, so must be lower >= upper. - *result = policies::raise_domain_error<RealType>( - function, - "lower parameter is %1%, but must be less than upper!", lower, pol); - return false; - } - else - { // All OK, - return true; - } - } // bool check_uniform( - - } // namespace detail - - template <class RealType = double, class Policy = policies::policy<> > - class uniform_distribution - { - public: - typedef RealType value_type; - typedef Policy policy_type; - - uniform_distribution(RealType l_lower = 0, RealType l_upper = 1) // Constructor. - : m_lower(l_lower), m_upper(l_upper) // Default is standard uniform distribution. - { - RealType result; - detail::check_uniform("boost::math::uniform_distribution<%1%>::uniform_distribution", l_lower, l_upper, &result, Policy()); - } - // Accessor functions. - RealType lower()const - { - return m_lower; - } - - RealType upper()const - { - return m_upper; - } - private: - // Data members: - RealType m_lower; // distribution lower aka a. - RealType m_upper; // distribution upper aka b. - }; // class uniform_distribution - - typedef uniform_distribution<double> uniform; - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> range(const uniform_distribution<RealType, Policy>& /* dist */) - { // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + 'infinity'. - // Note RealType infinity is NOT permitted, only max_value. - } - - template <class RealType, class Policy> - inline const std::pair<RealType, RealType> support(const uniform_distribution<RealType, Policy>& dist) - { // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(dist.lower(), dist.upper()); - } - - template <class RealType, class Policy> - inline RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_uniform_x("boost::math::pdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy())) - { - return result; - } - - if((x < lower) || (x > upper) ) - { - return 0; - } - else - { - return 1 / (upper - lower); - } - } // RealType pdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) - - template <class RealType, class Policy> - inline RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy())) - { - return result; - } - if (x < lower) - { - return 0; - } - if (x > upper) - { - return 1; - } - return (x - lower) / (upper - lower); // lower <= x <= upper - } // RealType cdf(const uniform_distribution<RealType, Policy>& dist, const RealType& x) - - template <class RealType, class Policy> - inline RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks - if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)",lower, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", p, &result, Policy())) - { - return result; - } - if(p == 0) - { - return lower; - } - if(p == 1) - { - return upper; - } - return p * (upper - lower) + lower; - } // RealType quantile(const uniform_distribution<RealType, Policy>& dist, const RealType& p) - - template <class RealType, class Policy> - inline RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) - { - RealType lower = c.dist.lower(); - RealType upper = c.dist.upper(); - RealType x = c.param; - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_uniform_x("boost::math::cdf(const uniform_distribution<%1%>&, %1%)", x, &result, Policy())) - { - return result; - } - if (x < lower) - { - return 1; - } - if (x > upper) - { - return 0; - } - return (upper - x) / (upper - lower); - } // RealType cdf(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) - - template <class RealType, class Policy> - inline RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) - { - RealType lower = c.dist.lower(); - RealType upper = c.dist.upper(); - RealType q = c.param; - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", lower, upper, &result, Policy())) - { - return result; - } - if(false == detail::check_probability("boost::math::quantile(const uniform_distribution<%1%>&, %1%)", q, &result, Policy())) - { - return result; - } - if(q == 0) - { - return upper; - } - if(q == 1) - { - return lower; - } - return -q * (upper - lower) + upper; - } // RealType quantile(const complemented2_type<uniform_distribution<RealType, Policy>, RealType>& c) - - template <class RealType, class Policy> - inline RealType mean(const uniform_distribution<RealType, Policy>& dist) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::mean(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) - { - return result; - } - return (lower + upper ) / 2; - } // RealType mean(const uniform_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType variance(const uniform_distribution<RealType, Policy>& dist) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::variance(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) - { - return result; - } - return (upper - lower) * ( upper - lower) / 12; - // for standard uniform = 0.833333333333333333333333333333333333333333; - } // RealType variance(const uniform_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType mode(const uniform_distribution<RealType, Policy>& dist) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::mode(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) - { - return result; - } - result = lower; // Any value [lower, upper] but arbitrarily choose lower. - return result; - } - - template <class RealType, class Policy> - inline RealType median(const uniform_distribution<RealType, Policy>& dist) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::median(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) - { - return result; - } - return (lower + upper) / 2; // - } - template <class RealType, class Policy> - inline RealType skewness(const uniform_distribution<RealType, Policy>& dist) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::skewness(const uniform_distribution<%1%>&)",lower, upper, &result, Policy())) - { - return result; - } - return 0; - } // RealType skewness(const uniform_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist) - { - RealType lower = dist.lower(); - RealType upper = dist.upper(); - RealType result = 0; // of checks. - if(false == detail::check_uniform("boost::math::kurtosis_execess(const uniform_distribution<%1%>&)", lower, upper, &result, Policy())) - { - return result; - } - return static_cast<RealType>(-6)/5; // -6/5 = -1.2; - } // RealType kurtosis_excess(const uniform_distribution<RealType, Policy>& dist) - - template <class RealType, class Policy> - inline RealType kurtosis(const uniform_distribution<RealType, Policy>& dist) - { - return kurtosis_excess(dist) + 3; - } - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_UNIFORM_HPP - - -
--- a/any/include/boost/math/distributions/weibull.hpp Sat Feb 16 16:31:25 2019 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,395 +0,0 @@ -// Copyright John Maddock 2006. -// Use, modification and distribution are subject to the -// Boost Software License, Version 1.0. (See accompanying file -// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) - -#ifndef BOOST_STATS_WEIBULL_HPP -#define BOOST_STATS_WEIBULL_HPP - -// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm -// http://mathworld.wolfram.com/WeibullDistribution.html - -#include <boost/math/distributions/fwd.hpp> -#include <boost/math/special_functions/gamma.hpp> -#include <boost/math/special_functions/log1p.hpp> -#include <boost/math/special_functions/expm1.hpp> -#include <boost/math/distributions/detail/common_error_handling.hpp> -#include <boost/math/distributions/complement.hpp> - -#include <utility> - -namespace boost{ namespace math -{ -namespace detail{ - -template <class RealType, class Policy> -inline bool check_weibull_shape( - const char* function, - RealType shape, - RealType* result, const Policy& pol) -{ - if((shape <= 0) || !(boost::math::isfinite)(shape)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Shape parameter is %1%, but must be > 0 !", shape, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_weibull_x( - const char* function, - RealType const& x, - RealType* result, const Policy& pol) -{ - if((x < 0) || !(boost::math::isfinite)(x)) - { - *result = policies::raise_domain_error<RealType>( - function, - "Random variate is %1% but must be >= 0 !", x, pol); - return false; - } - return true; -} - -template <class RealType, class Policy> -inline bool check_weibull( - const char* function, - RealType scale, - RealType shape, - RealType* result, const Policy& pol) -{ - return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol); -} - -} // namespace detail - -template <class RealType = double, class Policy = policies::policy<> > -class weibull_distribution -{ -public: - typedef RealType value_type; - typedef Policy policy_type; - - weibull_distribution(RealType l_shape, RealType l_scale = 1) - : m_shape(l_shape), m_scale(l_scale) - { - RealType result; - detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy()); - } - - RealType shape()const - { - return m_shape; - } - - RealType scale()const - { - return m_scale; - } -private: - // - // Data members: - // - RealType m_shape; // distribution shape - RealType m_scale; // distribution scale -}; - -typedef weibull_distribution<double> weibull; - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/) -{ // Range of permissible values for random variable x. - using boost::math::tools::max_value; - return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); -} - -template <class RealType, class Policy> -inline const std::pair<RealType, RealType> support(const weibull_distribution<RealType, Policy>& /*dist*/) -{ // Range of supported values for random variable x. - // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. - using boost::math::tools::max_value; - using boost::math::tools::min_value; - return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>()); - // A discontinuity at x == 0, so only support down to min_value. -} - -template <class RealType, class Policy> -inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_weibull_x(function, x, &result, Policy())) - return result; - - if(x == 0) - { - if(shape == 1) - { - return 1 / scale; - } - if(shape > 1) - { - return 0; - } - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - } - result = exp(-pow(x / scale, shape)); - result *= pow(x / scale, shape - 1) * shape / scale; - - return result; -} - -template <class RealType, class Policy> -inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_weibull_x(function, x, &result, Policy())) - return result; - - result = -boost::math::expm1(-pow(x / scale, shape), Policy()); - - return result; -} - -template <class RealType, class Policy> -inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_probability(function, p, &result, Policy())) - return result; - - if(p == 1) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape); - - return result; -} - -template <class RealType, class Policy> -inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)"; - - RealType shape = c.dist.shape(); - RealType scale = c.dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_weibull_x(function, c.param, &result, Policy())) - return result; - - result = exp(-pow(c.param / scale, shape)); - - return result; -} - -template <class RealType, class Policy> -inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)"; - - RealType shape = c.dist.shape(); - RealType scale = c.dist.scale(); - RealType q = c.param; - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - return result; - if(false == detail::check_probability(function, q, &result, Policy())) - return result; - - if(q == 0) - return policies::raise_overflow_error<RealType>(function, 0, Policy()); - - result = scale * pow(-log(q), 1 / shape); - - return result; -} - -template <class RealType, class Policy> -inline RealType mean(const weibull_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::mean(const weibull_distribution<%1%>)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - return result; - - result = scale * boost::math::tgamma(1 + 1 / shape, Policy()); - return result; -} - -template <class RealType, class Policy> -inline RealType variance(const weibull_distribution<RealType, Policy>& dist) -{ - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - static const char* function = "boost::math::variance(const weibull_distribution<%1%>)"; - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - { - return result; - } - result = boost::math::tgamma(1 + 1 / shape, Policy()); - result *= -result; - result += boost::math::tgamma(1 + 2 / shape, Policy()); - result *= scale * scale; - return result; -} - -template <class RealType, class Policy> -inline RealType mode(const weibull_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std function pow. - - static const char* function = "boost::math::mode(const weibull_distribution<%1%>)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - { - return result; - } - if(shape <= 1) - return 0; - result = scale * pow((shape - 1) / shape, 1 / shape); - return result; -} - -template <class RealType, class Policy> -inline RealType median(const weibull_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std function pow. - - static const char* function = "boost::math::median(const weibull_distribution<%1%>)"; - - RealType shape = dist.shape(); // Wikipedia k - RealType scale = dist.scale(); // Wikipedia lambda - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - { - return result; - } - using boost::math::constants::ln_two; - result = scale * pow(ln_two<RealType>(), 1 / shape); - return result; -} - -template <class RealType, class Policy> -inline RealType skewness(const weibull_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - { - return result; - } - RealType g1, g2, g3, d; - - g1 = boost::math::tgamma(1 + 1 / shape, Policy()); - g2 = boost::math::tgamma(1 + 2 / shape, Policy()); - g3 = boost::math::tgamma(1 + 3 / shape, Policy()); - d = pow(g2 - g1 * g1, RealType(1.5)); - - result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d; - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist) -{ - BOOST_MATH_STD_USING // for ADL of std functions - - static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)"; - - RealType shape = dist.shape(); - RealType scale = dist.scale(); - - RealType result = 0; - if(false == detail::check_weibull(function, scale, shape, &result, Policy())) - return result; - - RealType g1, g2, g3, g4, d, g1_2, g1_4; - - g1 = boost::math::tgamma(1 + 1 / shape, Policy()); - g2 = boost::math::tgamma(1 + 2 / shape, Policy()); - g3 = boost::math::tgamma(1 + 3 / shape, Policy()); - g4 = boost::math::tgamma(1 + 4 / shape, Policy()); - g1_2 = g1 * g1; - g1_4 = g1_2 * g1_2; - d = g2 - g1_2; - d *= d; - - result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4; - result /= d; - return result; -} - -template <class RealType, class Policy> -inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist) -{ - return kurtosis_excess(dist) + 3; -} - -} // namespace math -} // namespace boost - -// This include must be at the end, *after* the accessors -// for this distribution have been defined, in order to -// keep compilers that support two-phase lookup happy. -#include <boost/math/distributions/detail/derived_accessors.hpp> - -#endif // BOOST_STATS_WEIBULL_HPP - -