SV platform dependency builds

//  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

// 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

// 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

// 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

// 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.