FM / distributions

/usr/include/boost/math/distributions

Name	Size	Mode	Actions
detail/	-	0755	rm
arcsine.hpp	18797	0644	edit dl rm
bernoulli.hpp	12143	0644	edit dl rm
beta.hpp	18807	0644	edit dl rm
binomial.hpp	28654	0644	edit dl rm
cauchy.hpp	12310	0644	edit dl rm
chi_squared.hpp	12242	0644	edit dl rm
complement.hpp	5978	0644	edit dl rm
empirical_cumulative_distribution_function.hpp	1886	0644	edit dl rm
exponential.hpp	8944	0644	edit dl rm
extreme_value.hpp	10491	0644	edit dl rm
find_location.hpp	6713	0644	edit dl rm
find_scale.hpp	9674	0644	edit dl rm
fisher_f.hpp	14391	0644	edit dl rm
fwd.hpp	5461	0644	edit dl rm
gamma.hpp	10660	0644	edit dl rm
geometric.hpp	21156	0644	edit dl rm
hyperexponential.hpp	21887	0644	edit dl rm
hypergeometric.hpp	12220	0644	edit dl rm
inverse_chi_squared.hpp	15202	0644	edit dl rm
inverse_gamma.hpp	15389	0644	edit dl rm
inverse_gaussian.hpp	19760	0644	edit dl rm
laplace.hpp	10580	0644	edit dl rm
logistic.hpp	11273	0644	edit dl rm
lognormal.hpp	11714	0644	edit dl rm
negative_binomial.hpp	26139	0644	edit dl rm
non_central_beta.hpp	35837	0644	edit dl rm
non_central_chi_squared.hpp	40704	0644	edit dl rm
non_central_f.hpp	15848	0644	edit dl rm
non_central_t.hpp	47973	0644	edit dl rm
normal.hpp	10768	0644	edit dl rm
pareto.hpp	15516	0644	edit dl rm
poisson.hpp	20267	0644	edit dl rm
rayleigh.hpp	10344	0644	edit dl rm
skew_normal.hpp	25646	0644	edit dl rm
students_t.hpp	18476	0644	edit dl rm
triangular.hpp	18407	0644	edit dl rm
uniform.hpp	12963	0644	edit dl rm
weibull.hpp	12081	0644	edit dl rm

Edit: /usr/include/boost/math/distributions/chi_squared.hpp (12242B)

// 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;

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;

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

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