392 lines
15 KiB
Plaintext
392 lines
15 KiB
Plaintext
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// 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 l_scale) : m_df(df), m_scale (l_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();
|
||
|
|
static const char* function = "boost::math::skewness(const inverse_chi_squared_distribution<%1%>&)";
|
||
|
|
if(df <= 6)
|
||
|
|
return policies::raise_domain_error<RealType>(
|
||
|
|
function,
|
||
|
|
"inverse Chi-Squared distribution only has a skewness for degrees of freedom > 6, but got degrees of freedom = %1%.",
|
||
|
|
df, Policy());
|
||
|
|
|
||
|
|
return 4 * sqrt (2 * (df - 4)) / (df - 6); // Not a function of scale.
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis(const inverse_chi_squared_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
RealType df = dist.degrees_of_freedom();
|
||
|
|
static const char* function = "boost::math::kurtosis(const inverse_chi_squared_distribution<%1%>&)";
|
||
|
|
if(df <= 8)
|
||
|
|
return policies::raise_domain_error<RealType>(
|
||
|
|
function,
|
||
|
|
"inverse Chi-Squared distribution only has a kurtosis for degrees of freedom > 8, but got degrees of freedom = %1%.",
|
||
|
|
df, Policy());
|
||
|
|
|
||
|
|
return kurtosis_excess(dist) + 3;
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class RealType, class Policy>
|
||
|
|
inline RealType kurtosis_excess(const inverse_chi_squared_distribution<RealType, Policy>& dist)
|
||
|
|
{
|
||
|
|
RealType df = dist.degrees_of_freedom();
|
||
|
|
static const char* function = "boost::math::kurtosis(const inverse_chi_squared_distribution<%1%>&)";
|
||
|
|
if(df <= 8)
|
||
|
|
return policies::raise_domain_error<RealType>(
|
||
|
|
function,
|
||
|
|
"inverse Chi-Squared distribution only has a kurtosis excess for degrees of freedom > 8, but got degrees of freedom = %1%.",
|
||
|
|
df, Policy());
|
||
|
|
|
||
|
|
return 12 * (5 * df - 22) / ((df - 6 )*(df - 8)); // Not a function of scale.
|
||
|
|
}
|
||
|
|
|
||
|
|
//
|
||
|
|
// Parameter estimation comes last:
|
||
|
|
//
|
||
|
|
|
||
|
|
} // 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_INVERSE_CHI_SQUARED_HPP
|