| // 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
|
| #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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|
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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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|
|
| // 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 are a 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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|
|
| 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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| using boost::math::tools::max_value;
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| return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + infinity.
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| }
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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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|
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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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|
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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 == detail::check_df(
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| function, degrees_of_freedom, &error_result, Policy())
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| && detail::check_probability(
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| function, p, &error_result, Policy()))
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| return error_result;
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|
|
| return 2 * boost::math::gamma_p_inv(degrees_of_freedom / 2, p, Policy());
|
| } // 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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| 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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|
|
| 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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| 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 == detail::check_df(
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| function, degrees_of_freedom, &error_result, Policy())
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| && detail::check_probability(
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| function, q, &error_result, Policy()))
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| return error_result;
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|
|
| return 2 * boost::math::gamma_q_inv(degrees_of_freedom / 2, q, Policy());
|
| }
|
|
|
| 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
|
|
|
| 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();
|
| } // variance
|
|
|
| template <class RealType, class Policy>
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| inline RealType mode(const chi_squared_distribution<RealType, Policy>& dist)
|
| {
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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;
|
| }
|
|
|
| //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>(
|
| // 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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| //}
|
| // Now implemented via quantile(half) in derived accessors.
|
|
|
| template <class RealType, class Policy>
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| inline RealType skewness(const chi_squared_distribution<RealType, Policy>& dist)
|
| {
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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);
|
| }
|
|
|
| template <class RealType, class Policy>
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| inline RealType kurtosis(const chi_squared_distribution<RealType, Policy>& dist)
|
| {
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| RealType df = dist.degrees_of_freedom();
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| return 3 + 12 / df;
|
| }
|
|
|
| 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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| // Parameter estimation comes last:
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| //
|
| namespace detail
|
| {
|
|
|
| template <class RealType, class Policy>
|
| struct df_estimator
|
| {
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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)
|
| { // Constructor
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| }
|
|
|
| RealType operator()(const RealType& df)
|
| {
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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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| RealType r = 1 + ratio;
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| result = cdf(cs, quantile(complement(cs, alpha)) / r) - beta;
|
| }
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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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| return result;
|
| }
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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.
|
| };
|
|
|
| } // namespace detail
|
|
|
| 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)
|
| {
|
| static const char* function = "boost::math::chi_squared_distribution<%1%>::find_degrees_of_freedom(%1%,%1%,%1%,%1%,%1%)";
|
| // 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()))
|
| { // Either probability is outside 0 to 1.
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| return error_result;
|
| }
|
|
|
| if(hint <= 0)
|
| { // No hint given, so guess df = 1.
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| hint = 1;
|
| }
|
|
|
| detail::df_estimator<RealType, Policy> f(alpha, beta, variance, difference_from_variance);
|
| 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;
|
| if(max_iter >= policies::get_max_root_iterations<Policy>())
|
| {
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| 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"
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| " or the answer is infinite. Current best guess is %1%", result, Policy());
|
| }
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| return result;
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| }
|
|
|
| } // namespace math
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| } // 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>
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|
|
| #endif // BOOST_MATH_DISTRIBUTIONS_CHI_SQUARED_HPP
|