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391 lines
15 KiB
391 lines
15 KiB
// Copyright John Maddock 2010. |
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// Copyright Paul A. Bristow 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_INVERSE_CHI_SQUARED_HPP |
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#define BOOST_MATH_DISTRIBUTIONS_INVERSE_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> // for complements. |
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#include <boost/math/distributions/detail/common_error_handling.hpp> // for error checks. |
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#include <boost/math/special_functions/fpclassify.hpp> // for isfinite |
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// See http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution |
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// for definitions of this scaled version. |
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// See http://en.wikipedia.org/wiki/Inverse-chi-square_distribution |
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// for unscaled version. |
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// http://reference.wolfram.com/mathematica/ref/InverseChiSquareDistribution.html |
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// Weisstein, Eric W. "Inverse Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. |
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// http://mathworld.wolfram.com/InverseChi-SquaredDistribution.html |
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#include <utility> |
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namespace boost{ namespace math{ |
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namespace detail |
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{ |
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template <class RealType, class Policy> |
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inline bool check_inverse_chi_squared( // Check both distribution parameters. |
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const char* function, |
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RealType degrees_of_freedom, // degrees_of_freedom (aka nu). |
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RealType scale, // scale (aka sigma^2) |
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RealType* result, |
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const Policy& pol) |
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{ |
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return check_scale(function, scale, result, pol) |
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&& check_df(function, degrees_of_freedom, |
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result, pol); |
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} // bool check_inverse_chi_squared |
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} // namespace detail |
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template <class RealType = double, class Policy = policies::policy<> > |
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class inverse_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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inverse_chi_squared_distribution(RealType df, RealType scale) : m_df(df), m_scale (scale) |
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{ |
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RealType result; |
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detail::check_df( |
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"boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", |
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m_df, &result, Policy()) |
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&& detail::check_scale( |
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"boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", |
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m_scale, &result, Policy()); |
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} // inverse_chi_squared_distribution constructor |
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inverse_chi_squared_distribution(RealType df = 1) : m_df(df) |
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{ |
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RealType result; |
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m_scale = 1 / m_df ; // Default scale = 1 / degrees of freedom (Wikipedia definition 1). |
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detail::check_df( |
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"boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", |
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m_df, &result, Policy()); |
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} // inverse_chi_squared_distribution |
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RealType degrees_of_freedom()const |
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{ |
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return m_df; // aka nu |
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} |
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RealType scale()const |
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{ |
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return m_scale; // aka xi |
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} |
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// Parameter estimation: NOT implemented yet. |
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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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// Data members: |
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RealType m_df; // degrees of freedom are treated as a real number. |
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RealType m_scale; // distribution scale. |
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}; // class chi_squared_distribution |
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typedef inverse_chi_squared_distribution<double> inverse_chi_squared; |
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template <class RealType, class Policy> |
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inline const std::pair<RealType, RealType> range(const inverse_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 inverse_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 inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) |
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{ |
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BOOST_MATH_STD_USING // for ADL of std functions. |
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RealType df = dist.degrees_of_freedom(); |
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RealType scale = dist.scale(); |
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RealType error_result; |
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static const char* function = "boost::math::pdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; |
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if(false == detail::check_inverse_chi_squared |
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(function, df, scale, &error_result, Policy()) |
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) |
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{ // Bad distribution. |
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return error_result; |
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} |
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if((x < 0) || !(boost::math::isfinite)(x)) |
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{ // Bad x. |
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return policies::raise_domain_error<RealType>( |
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function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy()); |
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} |
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if(x == 0) |
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{ // Treat as special case. |
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return 0; |
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} |
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// Wikipedia scaled inverse chi sq (df, scale) related to inv gamma (df/2, df * scale /2) |
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// so use inverse gamma pdf with shape = df/2, scale df * scale /2 |
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// RealType shape = df /2; // inv_gamma shape |
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// RealType scale = df * scale/2; // inv_gamma scale |
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// RealType result = gamma_p_derivative(shape, scale / x, Policy()) * scale / (x * x); |
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RealType result = df * scale/2 / x; |
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if(result < tools::min_value<RealType>()) |
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return 0; // Random variable is near enough infinite. |
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result = gamma_p_derivative(df/2, result, Policy()) * df * scale/2; |
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if(result != 0) // prevent 0 / 0, gamma_p_derivative -> 0 faster than x^2 |
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result /= (x * x); |
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return result; |
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} // pdf |
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template <class RealType, class Policy> |
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inline RealType cdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) |
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{ |
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static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; |
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RealType df = dist.degrees_of_freedom(); |
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RealType scale = dist.scale(); |
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RealType error_result; |
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if(false == |
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detail::check_inverse_chi_squared(function, df, scale, &error_result, Policy()) |
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) |
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{ // Bad distribution. |
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return error_result; |
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} |
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if((x < 0) || !(boost::math::isfinite)(x)) |
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{ // Bad x. |
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return policies::raise_domain_error<RealType>( |
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function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy()); |
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} |
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if (x == 0) |
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{ // Treat zero as a special case. |
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return 0; |
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} |
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// RealType shape = df /2; // inv_gamma shape, |
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// RealType scale = df * scale/2; // inv_gamma scale, |
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// result = boost::math::gamma_q(shape, scale / x, Policy()); // inverse_gamma code. |
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return boost::math::gamma_q(df / 2, (df * (scale / 2)) / x, Policy()); |
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} // cdf |
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template <class RealType, class Policy> |
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inline RealType quantile(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& p) |
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{ |
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using boost::math::gamma_q_inv; |
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RealType df = dist.degrees_of_freedom(); |
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RealType scale = dist.scale(); |
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static const char* function = "boost::math::quantile(const inverse_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, df, &error_result, Policy()) |
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&& detail::check_probability( |
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function, p, &error_result, Policy())) |
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{ |
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return error_result; |
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} |
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if(false == detail::check_probability( |
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function, p, &error_result, Policy())) |
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{ |
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return error_result; |
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} |
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// RealType shape = df /2; // inv_gamma shape, |
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// RealType scale = df * scale/2; // inv_gamma scale, |
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// result = scale / gamma_q_inv(shape, p, Policy()); |
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RealType result = gamma_q_inv(df /2, p, Policy()); |
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if(result == 0) |
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return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy()); |
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result = df * (scale / 2) / result; |
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return result; |
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} // quantile |
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template <class RealType, class Policy> |
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inline RealType cdf(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c) |
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{ |
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using boost::math::gamma_q_inv; |
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RealType const& df = c.dist.degrees_of_freedom(); |
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RealType const& scale = c.dist.scale(); |
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RealType const& x = c.param; |
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static const char* function = "boost::math::cdf(const inverse_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, df, &error_result, Policy())) |
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{ |
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return error_result; |
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} |
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if (x == 0) |
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{ // Treat zero as a special case. |
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return 1; |
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} |
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if((x < 0) || !(boost::math::isfinite)(x)) |
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{ |
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return policies::raise_domain_error<RealType>( |
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function, "inverse Chi Square parameter was %1%, but must be > 0 !", x, Policy()); |
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} |
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// RealType shape = df /2; // inv_gamma shape, |
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// RealType scale = df * scale/2; // inv_gamma scale, |
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// result = gamma_p(shape, scale/c.param, Policy()); use inv_gamma. |
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return gamma_p(df / 2, (df * scale/2) / x, Policy()); // OK |
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} // cdf(complemented |
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template <class RealType, class Policy> |
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inline RealType quantile(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c) |
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{ |
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using boost::math::gamma_q_inv; |
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RealType const& df = c.dist.degrees_of_freedom(); |
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RealType const& scale = c.dist.scale(); |
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RealType const& q = c.param; |
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static const char* function = "boost::math::quantile(const inverse_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(function, df, &error_result, Policy())) |
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{ |
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return error_result; |
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} |
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if(false == detail::check_probability(function, q, &error_result, Policy())) |
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{ |
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return error_result; |
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} |
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// RealType shape = df /2; // inv_gamma shape, |
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// RealType scale = df * scale/2; // inv_gamma scale, |
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// result = scale / gamma_p_inv(shape, q, Policy()); // using inv_gamma. |
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RealType result = gamma_p_inv(df/2, q, Policy()); |
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if(result == 0) |
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return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy()); |
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result = (df * scale / 2) / result; |
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return result; |
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} // quantile(const complement |
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template <class RealType, class Policy> |
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inline RealType mean(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
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{ // Mean of inverse Chi-Squared distribution. |
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RealType df = dist.degrees_of_freedom(); |
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RealType scale = dist.scale(); |
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static const char* function = "boost::math::mean(const inverse_chi_squared_distribution<%1%>&)"; |
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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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"inverse 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 * scale) / (df - 2); |
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} // mean |
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template <class RealType, class Policy> |
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inline RealType variance(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
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{ // Variance of inverse Chi-Squared distribution. |
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RealType df = dist.degrees_of_freedom(); |
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RealType scale = dist.scale(); |
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static const char* function = "boost::math::variance(const inverse_chi_squared_distribution<%1%>&)"; |
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if(df <= 4) |
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{ |
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return policies::raise_domain_error<RealType>( |
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function, |
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"inverse Chi-Squared distribution only has a variance for degrees of freedom > 4, but got degrees of freedom = %1%.", |
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df, Policy()); |
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} |
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return 2 * df * df * scale * scale / ((df - 2)*(df - 2) * (df - 4)); |
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} // variance |
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template <class RealType, class Policy> |
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inline RealType mode(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
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{ // mode is not defined in Mathematica. |
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// See Discussion section http://en.wikipedia.org/wiki/Talk:Scaled-inverse-chi-square_distribution |
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// for origin of the formula used below. |
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RealType df = dist.degrees_of_freedom(); |
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RealType scale = dist.scale(); |
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static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)"; |
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if(df < 0) |
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return policies::raise_domain_error<RealType>( |
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function, |
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"inverse 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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return (df * scale) / (df + 2); |
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} |
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//template <class RealType, class Policy> |
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//inline RealType median(const inverse_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 inverse_Chi-Squared distribution only has a median for degrees of freedom >= 0, but got degrees of freedom = %1%.", |
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// df); |
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// return df; |
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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 inverse_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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static const char* function = "boost::math::skewness(const inverse_chi_squared_distribution<%1%>&)"; |
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if(df <= 6) |
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return policies::raise_domain_error<RealType>( |
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function, |
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"inverse Chi-Squared distribution only has a skewness for degrees of freedom > 6, but got degrees of freedom = %1%.", |
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df, Policy()); |
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return 4 * sqrt (2 * (df - 4)) / (df - 6); // Not a function of scale. |
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} |
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template <class RealType, class Policy> |
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inline RealType kurtosis(const inverse_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::kurtosis(const inverse_chi_squared_distribution<%1%>&)"; |
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if(df <= 8) |
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return policies::raise_domain_error<RealType>( |
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function, |
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"inverse Chi-Squared distribution only has a kurtosis for degrees of freedom > 8, but got degrees of freedom = %1%.", |
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df, Policy()); |
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return kurtosis_excess(dist) + 3; |
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} |
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template <class RealType, class Policy> |
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inline RealType kurtosis_excess(const inverse_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::kurtosis(const inverse_chi_squared_distribution<%1%>&)"; |
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if(df <= 8) |
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return policies::raise_domain_error<RealType>( |
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function, |
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"inverse Chi-Squared distribution only has a kurtosis excess for degrees of freedom > 8, but got degrees of freedom = %1%.", |
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df, Policy()); |
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return 12 * (5 * df - 22) / ((df - 6 )*(df - 8)); // Not a function of scale. |
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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 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_INVERSE_CHI_SQUARED_HPP
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