| // Copyright John Maddock 2010. |
| // Copyright Paul A. Bristow 2010. |
| |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. |
| // (See accompanying file LICENSE_1_0.txt |
| // or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| #ifndef BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP |
| #define BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP |
| |
| #include <boost/math/distributions/fwd.hpp> |
| #include <boost/math/special_functions/gamma.hpp> // for incomplete beta. |
| #include <boost/math/distributions/complement.hpp> // for complements. |
| #include <boost/math/distributions/detail/common_error_handling.hpp> // for error checks. |
| #include <boost/math/special_functions/fpclassify.hpp> // for isfinite |
| |
| // See http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution |
| // for definitions of this scaled version. |
| // See http://en.wikipedia.org/wiki/Inverse-chi-square_distribution |
| // for unscaled version. |
| |
| // http://reference.wolfram.com/mathematica/ref/InverseChiSquareDistribution.html |
| // Weisstein, Eric W. "Inverse Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. |
| // http://mathworld.wolfram.com/InverseChi-SquaredDistribution.html |
| |
| #include <utility> |
| |
| namespace boost{ namespace math{ |
| |
| namespace detail |
| { |
| template <class RealType, class Policy> |
| inline bool check_inverse_chi_squared( // Check both distribution parameters. |
| const char* function, |
| RealType degrees_of_freedom, // degrees_of_freedom (aka nu). |
| RealType scale, // scale (aka sigma^2) |
| RealType* result, |
| const Policy& pol) |
| { |
| return check_scale(function, scale, result, pol) |
| && check_df(function, degrees_of_freedom, |
| result, pol); |
| } // bool check_inverse_chi_squared |
| } // namespace detail |
| |
| template <class RealType = double, class Policy = policies::policy<> > |
| class inverse_chi_squared_distribution |
| { |
| public: |
| typedef RealType value_type; |
| typedef Policy policy_type; |
| |
| inverse_chi_squared_distribution(RealType df, RealType scale) : m_df(df), m_scale (scale) |
| { |
| RealType result; |
| detail::check_df( |
| "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", |
| m_df, &result, Policy()) |
| && detail::check_scale( |
| "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", |
| m_scale, &result, Policy()); |
| } // inverse_chi_squared_distribution constructor |
| |
| inverse_chi_squared_distribution(RealType df = 1) : m_df(df) |
| { |
| RealType result; |
| m_scale = 1 / m_df ; // Default scale = 1 / degrees of freedom (Wikipedia definition 1). |
| detail::check_df( |
| "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", |
| m_df, &result, Policy()); |
| } // inverse_chi_squared_distribution |
| |
| RealType degrees_of_freedom()const |
| { |
| return m_df; // aka nu |
| } |
| RealType scale()const |
| { |
| return m_scale; // aka xi |
| } |
| |
| // Parameter estimation: NOT implemented yet. |
| //static RealType find_degrees_of_freedom( |
| // RealType difference_from_variance, |
| // RealType alpha, |
| // RealType beta, |
| // RealType variance, |
| // RealType hint = 100); |
| |
| private: |
| // Data members: |
| RealType m_df; // degrees of freedom are treated as a real number. |
| RealType m_scale; // distribution scale. |
| |
| }; // class chi_squared_distribution |
| |
| typedef inverse_chi_squared_distribution<double> inverse_chi_squared; |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> range(const inverse_chi_squared_distribution<RealType, Policy>& /*dist*/) |
| { // Range of permissible values for random variable x. |
| using boost::math::tools::max_value; |
| return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + infinity. |
| } |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> support(const inverse_chi_squared_distribution<RealType, Policy>& /*dist*/) |
| { // Range of supported values for random variable x. |
| // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. |
| return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity. |
| } |
| |
| template <class RealType, class Policy> |
| RealType pdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions. |
| RealType df = dist.degrees_of_freedom(); |
| RealType scale = dist.scale(); |
| RealType error_result; |
| |
| static const char* function = "boost::math::pdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; |
| |
| if(false == detail::check_inverse_chi_squared |
| (function, df, scale, &error_result, Policy()) |
| ) |
| { // Bad distribution. |
| return error_result; |
| } |
| if((x < 0) || !(boost::math::isfinite)(x)) |
| { // Bad x. |
| return policies::raise_domain_error<RealType>( |
| function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy()); |
| } |
| |
| if(x == 0) |
| { // Treat as special case. |
| return 0; |
| } |
| // Wikipedia scaled inverse chi sq (df, scale) related to inv gamma (df/2, df * scale /2) |
| // so use inverse gamma pdf with shape = df/2, scale df * scale /2 |
| // RealType shape = df /2; // inv_gamma shape |
| // RealType scale = df * scale/2; // inv_gamma scale |
| // RealType result = gamma_p_derivative(shape, scale / x, Policy()) * scale / (x * x); |
| RealType result = df * scale/2 / x; |
| if(result < tools::min_value<RealType>()) |
| return 0; // Random variable is near enough infinite. |
| result = gamma_p_derivative(df/2, result, Policy()) * df * scale/2; |
| if(result != 0) // prevent 0 / 0: |
| result /= (x * x); |
| return result; |
| } // pdf |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; |
| RealType df = dist.degrees_of_freedom(); |
| RealType scale = dist.scale(); |
| RealType error_result; |
| |
| if(false == |
| detail::check_inverse_chi_squared(function, df, scale, &error_result, Policy()) |
| ) |
| { // Bad distribution. |
| return error_result; |
| } |
| if((x < 0) || !(boost::math::isfinite)(x)) |
| { // Bad x. |
| return policies::raise_domain_error<RealType>( |
| function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy()); |
| } |
| if (x == 0) |
| { // Treat zero as a special case. |
| return 0; |
| } |
| // RealType shape = df /2; // inv_gamma shape, |
| // RealType scale = df * scale/2; // inv_gamma scale, |
| // result = boost::math::gamma_q(shape, scale / x, Policy()); // inverse_gamma code. |
| return boost::math::gamma_q(df / 2, (df * (scale / 2)) / x, Policy()); |
| } // cdf |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& p) |
| { |
| using boost::math::gamma_q_inv; |
| RealType df = dist.degrees_of_freedom(); |
| RealType scale = dist.scale(); |
| |
| static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)"; |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df, &error_result, Policy()) |
| && detail::check_probability( |
| function, p, &error_result, Policy())) |
| { |
| return error_result; |
| } |
| if(false == detail::check_probability( |
| function, p, &error_result, Policy())) |
| { |
| return error_result; |
| } |
| // RealType shape = df /2; // inv_gamma shape, |
| // RealType scale = df * scale/2; // inv_gamma scale, |
| // result = scale / gamma_q_inv(shape, p, Policy()); |
| RealType result = gamma_q_inv(df /2, p, Policy()); |
| if(result == 0) |
| return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy()); |
| result = df * (scale / 2) / result; |
| return result; |
| } // quantile |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c) |
| { |
| using boost::math::gamma_q_inv; |
| RealType const& df = c.dist.degrees_of_freedom(); |
| RealType const& scale = c.dist.scale(); |
| RealType const& x = c.param; |
| static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)"; |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df( |
| function, df, &error_result, Policy())) |
| { |
| return error_result; |
| } |
| if (x == 0) |
| { // Treat zero as a special case. |
| return 1; |
| } |
| if((x < 0) || !(boost::math::isfinite)(x)) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, "inverse Chi Square parameter was %1%, but must be > 0 !", x, Policy()); |
| } |
| // RealType shape = df /2; // inv_gamma shape, |
| // RealType scale = df * scale/2; // inv_gamma scale, |
| // result = gamma_p(shape, scale/c.param, Policy()); use inv_gamma. |
| |
| return gamma_p(df / 2, (df * scale/2) / x, Policy()); // OK |
| } // cdf(complemented |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c) |
| { |
| using boost::math::gamma_q_inv; |
| |
| RealType const& df = c.dist.degrees_of_freedom(); |
| RealType const& scale = c.dist.scale(); |
| RealType const& q = c.param; |
| static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)"; |
| // Error check: |
| RealType error_result; |
| if(false == detail::check_df(function, df, &error_result, Policy())) |
| { |
| return error_result; |
| } |
| if(false == detail::check_probability(function, q, &error_result, Policy())) |
| { |
| return error_result; |
| } |
| // RealType shape = df /2; // inv_gamma shape, |
| // RealType scale = df * scale/2; // inv_gamma scale, |
| // result = scale / gamma_p_inv(shape, q, Policy()); // using inv_gamma. |
| RealType result = gamma_p_inv(df/2, q, Policy()); |
| if(result == 0) |
| return policies::raise_overflow_error<RealType, Policy>(function, "Random variable is infinite.", Policy()); |
| result = (df * scale / 2) / result; |
| return result; |
| } // quantile(const complement |
| |
| template <class RealType, class Policy> |
| inline RealType mean(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
| { // Mean of inverse Chi-Squared distribution. |
| RealType df = dist.degrees_of_freedom(); |
| RealType scale = dist.scale(); |
| |
| static const char* function = "boost::math::mean(const inverse_chi_squared_distribution<%1%>&)"; |
| if(df <= 2) |
| return policies::raise_domain_error<RealType>( |
| function, |
| "inverse Chi-Squared distribution only has a mode for degrees of freedom > 2, but got degrees of freedom = %1%.", |
| df, Policy()); |
| return (df * scale) / (df - 2); |
| } // mean |
| |
| template <class RealType, class Policy> |
| inline RealType variance(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
| { // Variance of inverse Chi-Squared distribution. |
| RealType df = dist.degrees_of_freedom(); |
| RealType scale = dist.scale(); |
| static const char* function = "boost::math::variance(const inverse_chi_squared_distribution<%1%>&)"; |
| if(df <= 4) |
| { |
| return policies::raise_domain_error<RealType>( |
| function, |
| "inverse Chi-Squared distribution only has a variance for degrees of freedom > 4, but got degrees of freedom = %1%.", |
| df, Policy()); return 2 * dist.degrees_of_freedom(); |
| } |
| return 2 * df * df * scale * scale / ((df - 2)*(df - 2) * (df - 4)); |
| } // variance |
| |
| template <class RealType, class Policy> |
| inline RealType mode(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
| { // mode is not defined in Mathematica. |
| // See Discussion section http://en.wikipedia.org/wiki/Talk:Scaled-inverse-chi-square_distribution |
| // for origin of the formula used below. |
| |
| RealType df = dist.degrees_of_freedom(); |
| RealType scale = dist.scale(); |
| static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)"; |
| if(df < 0) |
| return policies::raise_domain_error<RealType>( |
| function, |
| "inverse Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.", |
| df, Policy()); |
| return (df * scale) / (df + 2); |
| } |
| |
| //template <class RealType, class Policy> |
| //inline RealType median(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
| //{ // Median is given by Quantile[dist, 1/2] |
| // RealType df = dist.degrees_of_freedom(); |
| // if(df <= 1) |
| // return tools::domain_error<RealType>( |
| // BOOST_CURRENT_FUNCTION, |
| // "The inverse_Chi-Squared distribution only has a median for degrees of freedom >= 0, but got degrees of freedom = %1%.", |
| // df); |
| // return df; |
| //} |
| // Now implemented via quantile(half) in derived accessors. |
| |
| template <class RealType, class Policy> |
| inline RealType skewness(const inverse_chi_squared_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // For ADL |
| 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 |