365 lines
12 KiB
C++
365 lines
12 KiB
C++
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// Copyright John Maddock 2006, 2007.
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// Copyright Paul A. Bristow 2008, 2010.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
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#define BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/special_functions/gamma.hpp> // for incomplete beta.
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#include <boost/math/distributions/complement.hpp> // complements
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#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
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#include <boost/math/special_functions/fpclassify.hpp>
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#include <utility>
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namespace boost{ namespace math{
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template <class RealType = double, class Policy = policies::policy<> >
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class chi_squared_distribution
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{
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public:
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typedef RealType value_type;
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typedef Policy policy_type;
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chi_squared_distribution(RealType i) : m_df(i)
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{
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RealType result;
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detail::check_df(
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"boost::math::chi_squared_distribution<%1%>::chi_squared_distribution", m_df, &result, Policy());
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} // chi_squared_distribution
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RealType degrees_of_freedom()const
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{
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return m_df;
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}
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// Parameter estimation:
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static RealType find_degrees_of_freedom(
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RealType difference_from_variance,
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RealType alpha,
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RealType beta,
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RealType variance,
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RealType hint = 100);
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private:
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//
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// Data member:
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//
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RealType m_df; // degrees of freedom is a positive real number.
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}; // class chi_squared_distribution
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typedef chi_squared_distribution<double> chi_squared;
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#ifdef BOOST_MSVC
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#pragma warning(push)
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#pragma warning(disable:4127)
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#endif
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const chi_squared_distribution<RealType, Policy>& /*dist*/)
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{ // Range of permissible values for random variable x.
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if (std::numeric_limits<RealType>::has_infinity)
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{
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return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()); // 0 to + infinity.
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}
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else
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{
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using boost::math::tools::max_value;
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return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max.
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}
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}
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#ifdef BOOST_MSVC
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#pragma warning(pop)
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#endif
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> support(const chi_squared_distribution<RealType, Policy>& /*dist*/)
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{ // Range of supported values for random variable x.
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// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
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return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity.
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}
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template <class RealType, class Policy>
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RealType pdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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RealType degrees_of_freedom = dist.degrees_of_freedom();
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// Error check:
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RealType error_result;
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static const char* function = "boost::math::pdf(const chi_squared_distribution<%1%>&, %1%)";
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if(false == detail::check_df(
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function, degrees_of_freedom, &error_result, Policy()))
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return error_result;
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if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
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{
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return policies::raise_domain_error<RealType>(
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function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
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}
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if(chi_square == 0)
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{
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// Handle special cases:
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if(degrees_of_freedom < 2)
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{
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return policies::raise_overflow_error<RealType>(
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function, 0, Policy());
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}
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else if(degrees_of_freedom == 2)
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{
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return 0.5f;
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}
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else
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{
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return 0;
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}
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}
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return gamma_p_derivative(degrees_of_freedom / 2, chi_square / 2, Policy()) / 2;
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} // pdf
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template <class RealType, class Policy>
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inline RealType cdf(const chi_squared_distribution<RealType, Policy>& dist, const RealType& chi_square)
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{
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RealType degrees_of_freedom = dist.degrees_of_freedom();
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// Error check:
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RealType error_result;
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static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)";
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if(false == detail::check_df(
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function, degrees_of_freedom, &error_result, Policy()))
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return error_result;
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if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
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{
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return policies::raise_domain_error<RealType>(
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function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
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}
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return boost::math::gamma_p(degrees_of_freedom / 2, chi_square / 2, Policy());
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} // cdf
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template <class RealType, class Policy>
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inline RealType quantile(const chi_squared_distribution<RealType, Policy>& dist, const RealType& p)
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{
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RealType degrees_of_freedom = dist.degrees_of_freedom();
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static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)";
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// Error check:
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RealType error_result;
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if(false ==
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(
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detail::check_df(function, degrees_of_freedom, &error_result, Policy())
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&& detail::check_probability(function, p, &error_result, Policy()))
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)
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return error_result;
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return 2 * boost::math::gamma_p_inv(degrees_of_freedom / 2, p, Policy());
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} // quantile
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c)
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{
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RealType const& degrees_of_freedom = c.dist.degrees_of_freedom();
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RealType const& chi_square = c.param;
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static const char* function = "boost::math::cdf(const chi_squared_distribution<%1%>&, %1%)";
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// Error check:
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RealType error_result;
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if(false == detail::check_df(
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function, degrees_of_freedom, &error_result, Policy()))
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return error_result;
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if((chi_square < 0) || !(boost::math::isfinite)(chi_square))
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{
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return policies::raise_domain_error<RealType>(
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function, "Chi Square parameter was %1%, but must be > 0 !", chi_square, Policy());
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}
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return boost::math::gamma_q(degrees_of_freedom / 2, chi_square / 2, Policy());
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}
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template <class RealType, class Policy>
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inline RealType quantile(const complemented2_type<chi_squared_distribution<RealType, Policy>, RealType>& c)
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{
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RealType const& degrees_of_freedom = c.dist.degrees_of_freedom();
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RealType const& q = c.param;
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static const char* function = "boost::math::quantile(const chi_squared_distribution<%1%>&, %1%)";
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// Error check:
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RealType error_result;
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if(false == (
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detail::check_df(function, degrees_of_freedom, &error_result, Policy())
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&& detail::check_probability(function, q, &error_result, Policy()))
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)
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return error_result;
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return 2 * boost::math::gamma_q_inv(degrees_of_freedom / 2, q, Policy());
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}
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template <class RealType, class Policy>
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inline RealType mean(const chi_squared_distribution<RealType, Policy>& dist)
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{ // Mean of Chi-Squared distribution = v.
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return dist.degrees_of_freedom();
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} // mean
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template <class RealType, class Policy>
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inline RealType variance(const chi_squared_distribution<RealType, Policy>& dist)
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{ // Variance of Chi-Squared distribution = 2v.
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return 2 * dist.degrees_of_freedom();
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} // variance
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template <class RealType, class Policy>
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inline RealType mode(const chi_squared_distribution<RealType, Policy>& dist)
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{
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RealType df = dist.degrees_of_freedom();
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static const char* function = "boost::math::mode(const chi_squared_distribution<%1%>&)";
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// Most sources only define mode for df >= 2,
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// but for 0 <= df <= 2, the pdf maximum actually occurs at random variate = 0;
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// So one could extend the definition of mode thus:
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//if(df < 0)
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//{
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// return policies::raise_domain_error<RealType>(
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// function,
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// "Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",
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// df, Policy());
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//}
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//return (df <= 2) ? 0 : df - 2;
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if(df < 2)
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return policies::raise_domain_error<RealType>(
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function,
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"Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
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df, Policy());
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return df - 2;
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}
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//template <class RealType, class Policy>
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//inline RealType median(const chi_squared_distribution<RealType, Policy>& dist)
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//{ // Median is given by Quantile[dist, 1/2]
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// RealType df = dist.degrees_of_freedom();
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// if(df <= 1)
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// return tools::domain_error<RealType>(
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// BOOST_CURRENT_FUNCTION,
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// "The Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
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// df);
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// return df - RealType(2)/3;
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//}
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// Now implemented via quantile(half) in derived accessors.
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template <class RealType, class Policy>
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inline RealType skewness(const chi_squared_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // For ADL
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RealType df = dist.degrees_of_freedom();
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return sqrt (8 / df); // == 2 * sqrt(2 / df);
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}
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template <class RealType, class Policy>
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inline RealType kurtosis(const chi_squared_distribution<RealType, Policy>& dist)
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{
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RealType df = dist.degrees_of_freedom();
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return 3 + 12 / df;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const chi_squared_distribution<RealType, Policy>& dist)
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{
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RealType df = dist.degrees_of_freedom();
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return 12 / df;
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}
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//
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// Parameter estimation comes last:
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//
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namespace detail
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{
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template <class RealType, class Policy>
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struct df_estimator
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{
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df_estimator(RealType a, RealType b, RealType variance, RealType delta)
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: alpha(a), beta(b), ratio(delta/variance)
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{ // Constructor
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}
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RealType operator()(const RealType& df)
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{
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if(df <= tools::min_value<RealType>())
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return 1;
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chi_squared_distribution<RealType, Policy> cs(df);
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RealType result;
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if(ratio > 0)
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{
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RealType r = 1 + ratio;
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result = cdf(cs, quantile(complement(cs, alpha)) / r) - beta;
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}
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else
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{ // ratio <= 0
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RealType r = 1 + ratio;
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result = cdf(complement(cs, quantile(cs, alpha) / r)) - beta;
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}
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return result;
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}
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private:
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RealType alpha;
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RealType beta;
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RealType ratio; // Difference from variance / variance, so fractional.
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};
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} // namespace detail
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template <class RealType, class Policy>
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RealType chi_squared_distribution<RealType, Policy>::find_degrees_of_freedom(
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RealType difference_from_variance,
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RealType alpha,
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RealType beta,
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RealType variance,
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RealType hint)
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{
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static const char* function = "boost::math::chi_squared_distribution<%1%>::find_degrees_of_freedom(%1%,%1%,%1%,%1%,%1%)";
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// Check for domain errors:
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RealType error_result;
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if(false ==
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detail::check_probability(function, alpha, &error_result, Policy())
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&& detail::check_probability(function, beta, &error_result, Policy()))
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{ // Either probability is outside 0 to 1.
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return error_result;
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}
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if(hint <= 0)
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{ // No hint given, so guess df = 1.
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hint = 1;
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}
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detail::df_estimator<RealType, Policy> f(alpha, beta, variance, difference_from_variance);
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tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
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boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
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std::pair<RealType, RealType> r =
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tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());
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RealType result = r.first + (r.second - r.first) / 2;
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if(max_iter >= policies::get_max_root_iterations<Policy>())
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{
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policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
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" either there is no answer to how many degrees of freedom are required"
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" or the answer is infinite. Current best guess is %1%", result, Policy());
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}
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return result;
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}
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} // namespace math
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} // namespace boost
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// This include must be at the end, *after* the accessors
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// for this distribution have been defined, in order to
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// keep compilers that support two-phase lookup happy.
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#include <boost/math/distributions/detail/derived_accessors.hpp>
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#endif // BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
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