comparison DEPENDENCIES/generic/include/boost/math/distributions/chi_squared.hpp @ 16:2665513ce2d3

Add boost headers

+// 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;
+
+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.
+  }
+}
+
+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