| // inverse_gamma.hpp |
| |
| // Copyright Paul A. Bristow 2010. |
| // Copyright John Maddock 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_STATS_INVERSE_GAMMA_HPP |
| #define BOOST_STATS_INVERSE_GAMMA_HPP |
| |
| // Inverse Gamma Distribution is a two-parameter family |
| // of continuous probability distributions |
| // on the positive real line, which is the distribution of |
| // the reciprocal of a variable distributed according to the gamma distribution. |
| |
| // http://en.wikipedia.org/wiki/Inverse-gamma_distribution |
| // http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html |
| |
| // See also gamma distribution at gamma.hpp: |
| // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm |
| // http://mathworld.wolfram.com/GammaDistribution.html |
| // http://en.wikipedia.org/wiki/Gamma_distribution |
| |
| #include <boost/math/distributions/fwd.hpp> |
| #include <boost/math/special_functions/gamma.hpp> |
| #include <boost/math/distributions/detail/common_error_handling.hpp> |
| #include <boost/math/distributions/complement.hpp> |
| |
| #include <utility> |
| |
| namespace boost{ namespace math |
| { |
| namespace detail |
| { |
| |
| template <class RealType, class Policy> |
| inline bool check_inverse_gamma_shape( |
| const char* function, // inverse_gamma |
| RealType shape, // shape aka alpha |
| RealType* result, // to update, perhaps with NaN |
| const Policy& pol) |
| { // Sources say shape argument must be > 0 |
| // but seems logical to allow shape zero as special case, |
| // returning pdf and cdf zero (but not < 0). |
| // (Functions like mean, variance with other limits on shape are checked |
| // in version including an operator & limit below). |
| if((shape < 0) || !(boost::math::isfinite)(shape)) |
| { |
| *result = policies::raise_domain_error<RealType>( |
| function, |
| "Shape parameter is %1%, but must be >= 0 !", shape, pol); |
| return false; |
| } |
| return true; |
| } //bool check_inverse_gamma_shape |
| |
| template <class RealType, class Policy> |
| inline bool check_inverse_gamma_x( |
| const char* function, |
| RealType const& x, |
| RealType* result, const Policy& pol) |
| { |
| if((x < 0) || !(boost::math::isfinite)(x)) |
| { |
| *result = policies::raise_domain_error<RealType>( |
| function, |
| "Random variate is %1% but must be >= 0 !", x, pol); |
| return false; |
| } |
| return true; |
| } |
| |
| template <class RealType, class Policy> |
| inline bool check_inverse_gamma( |
| const char* function, // TODO swap these over, so shape is first. |
| RealType scale, // scale aka beta |
| RealType shape, // shape aka alpha |
| RealType* result, const Policy& pol) |
| { |
| return check_scale(function, scale, result, pol) |
| && check_inverse_gamma_shape(function, shape, result, pol); |
| } // bool check_inverse_gamma |
| |
| } // namespace detail |
| |
| template <class RealType = double, class Policy = policies::policy<> > |
| class inverse_gamma_distribution |
| { |
| public: |
| typedef RealType value_type; |
| typedef Policy policy_type; |
| |
| inverse_gamma_distribution(RealType shape = 1, RealType scale = 1) |
| : m_shape(shape), m_scale(scale) |
| { |
| RealType result; |
| detail::check_inverse_gamma( |
| "boost::math::inverse_gamma_distribution<%1%>::inverse_gamma_distribution", |
| scale, shape, &result, Policy()); |
| } |
| |
| RealType shape()const |
| { |
| return m_shape; |
| } |
| |
| RealType scale()const |
| { |
| return m_scale; |
| } |
| private: |
| // |
| // Data members: |
| // |
| RealType m_shape; // distribution shape |
| RealType m_scale; // distribution scale |
| }; |
| |
| typedef inverse_gamma_distribution<double> inverse_gamma; |
| // typedef - but potential clash with name of inverse gamma *function*. |
| // but there is a typedef for gamma |
| // typedef boost::math::gamma_distribution<Type, Policy> gamma; |
| |
| // Allow random variable x to be zero, treated as a special case (unlike some definitions). |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> range(const inverse_gamma_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>()); |
| } |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> support(const inverse_gamma_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. |
| using boost::math::tools::max_value; |
| using boost::math::tools::min_value; |
| return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType pdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::pdf(const inverse_gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) |
| { // distribution parameters bad. |
| return result; |
| } |
| if(x == 0) |
| { // Treat random variate zero as a special case. |
| return 0; |
| } |
| else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy())) |
| { // x bad. |
| return result; |
| } |
| result = scale / x; |
| if(result < tools::min_value<RealType>()) |
| return 0; // random variable is infinite or so close as to make no difference. |
| result = gamma_p_derivative(shape, result, Policy()) * scale; |
| if(0 != result) |
| { |
| if(x < 0) |
| { |
| // x * x may under or overflow, likewise our result, |
| // so be extra careful about the arithmetic: |
| RealType lim = tools::max_value<RealType>() * x; |
| if(lim < result) |
| return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy()); |
| result /= x; |
| if(lim < result) |
| return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy()); |
| result /= x; |
| } |
| result /= (x * x); |
| } |
| // better than naive |
| // result = (pow(scale, shape) * pow(x, (-shape -1)) * exp(-scale/x) ) / tgamma(shape); |
| return result; |
| } // pdf |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& x) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::cdf(const inverse_gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) |
| { // distribution parameters bad. |
| return result; |
| } |
| if (x == 0) |
| { // Treat zero as a special case. |
| return 0; |
| } |
| else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy())) |
| { // x bad |
| return result; |
| } |
| result = boost::math::gamma_q(shape, scale / x, Policy()); |
| // result = tgamma(shape, scale / x) / tgamma(shape); // naive using tgamma |
| return result; |
| } // cdf |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& p) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| using boost::math::gamma_q_inv; |
| |
| static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| if(false == detail::check_probability(function, p, &result, Policy())) |
| return result; |
| if(p == 1) |
| { |
| return policies::raise_overflow_error<RealType>(function, 0, Policy()); |
| } |
| result = gamma_q_inv(shape, p, Policy()); |
| if((result < 1) && (result * tools::max_value<RealType>() < scale)) |
| return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy()); |
| result = scale / result; |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = c.dist.shape(); |
| RealType scale = c.dist.scale(); |
| |
| RealType result = 0; |
| if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| if(false == detail::check_inverse_gamma_x(function, c.param, &result, Policy())) |
| return result; |
| |
| //result = 1. - gamma_q(shape, c.param / scale, Policy()); |
| result = gamma_p(shape, scale/c.param, Policy()); |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType quantile(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = c.dist.shape(); |
| RealType scale = c.dist.scale(); |
| RealType q = c.param; |
| |
| RealType result = 0; |
| if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| if(false == detail::check_probability(function, q, &result, Policy())) |
| return result; |
| |
| if(q == 0) |
| { |
| return policies::raise_overflow_error<RealType>(function, 0, Policy()); |
| } |
| result = gamma_p_inv(shape, q, Policy()); |
| if((result < 1) && (result * tools::max_value<RealType>() < scale)) |
| return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy()); |
| result = scale / result; |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType mean(const inverse_gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::mean(const inverse_gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| |
| if(false == detail::check_scale(function, scale, &result, Policy())) |
| { |
| return result; |
| } |
| if((shape <= 1) || !(boost::math::isfinite)(shape)) |
| { |
| result = policies::raise_domain_error<RealType>( |
| function, |
| "Shape parameter is %1%, but for a defined mean it must be > 1", shape, Policy()); |
| return result; |
| } |
| result = scale / (shape - 1); |
| return result; |
| } // mean |
| |
| template <class RealType, class Policy> |
| inline RealType variance(const inverse_gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::variance(const inverse_gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| if(false == detail::check_scale(function, scale, &result, Policy())) |
| { |
| return result; |
| } |
| if((shape <= 2) || !(boost::math::isfinite)(shape)) |
| { |
| result = policies::raise_domain_error<RealType>( |
| function, |
| "Shape parameter is %1%, but for a defined variance it must be > 2", shape, Policy()); |
| return result; |
| } |
| result = (scale * scale) / ((shape - 1) * (shape -1) * (shape -2)); |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType mode(const inverse_gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::mode(const inverse_gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy())) |
| { |
| return result; |
| } |
| // Only defined for shape >= 0, but is checked by check_inverse_gamma. |
| result = scale / (shape + 1); |
| return result; |
| } |
| |
| //template <class RealType, class Policy> |
| //inline RealType median(const gamma_distribution<RealType, Policy>& dist) |
| //{ // Wikipedia does not define median, |
| // so rely on default definition quantile(0.5) in derived accessors. |
| // return result. |
| //} |
| |
| template <class RealType, class Policy> |
| inline RealType skewness(const inverse_gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::skewness(const inverse_gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| RealType result = 0; |
| |
| if(false == detail::check_scale(function, scale, &result, Policy())) |
| { |
| return result; |
| } |
| if((shape <= 3) || !(boost::math::isfinite)(shape)) |
| { |
| result = policies::raise_domain_error<RealType>( |
| function, |
| "Shape parameter is %1%, but for a defined skewness it must be > 3", shape, Policy()); |
| return result; |
| } |
| result = (4 * sqrt(shape - 2) ) / (shape - 3); |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis_excess(const inverse_gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::kurtosis_excess(const inverse_gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| if(false == detail::check_scale(function, scale, &result, Policy())) |
| { |
| return result; |
| } |
| if((shape <= 4) || !(boost::math::isfinite)(shape)) |
| { |
| result = policies::raise_domain_error<RealType>( |
| function, |
| "Shape parameter is %1%, but for a defined kurtosis excess it must be > 4", shape, Policy()); |
| return result; |
| } |
| result = (30 * shape - 66) / ((shape - 3) * (shape - 4)); |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis(const inverse_gamma_distribution<RealType, Policy>& dist) |
| { |
| static const char* function = "boost::math::kurtosis(const inverse_gamma_distribution<%1%>&)"; |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result = 0; |
| |
| if(false == detail::check_scale(function, scale, &result, Policy())) |
| { |
| return result; |
| } |
| if((shape <= 4) || !(boost::math::isfinite)(shape)) |
| { |
| result = policies::raise_domain_error<RealType>( |
| function, |
| "Shape parameter is %1%, but for a defined kurtosis it must be > 4", shape, Policy()); |
| return result; |
| } |
| return kurtosis_excess(dist) + 3; |
| } |
| |
| } // 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_STATS_INVERSE_GAMMA_HPP |