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// Copyright John Maddock 2006. // Copyright Matt Borland 2024. // 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_GAMMA_HPP #define BOOST_STATS_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 #include #include #include #include #include #include #include namespace boost{ namespace math { namespace detail { template BOOST_MATH_GPU_ENABLED inline bool check_gamma_shape( const char* function, RealType shape, RealType* result, const Policy& pol) { if((shape <= 0) || !(boost::math::isfinite)(shape)) { *result = policies::raise_domain_error( function, "Shape parameter is %1%, but must be > 0 !", shape, pol); return false; } return true; } template BOOST_MATH_GPU_ENABLED inline bool check_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( function, "Random variate is %1% but must be >= 0 !", x, pol); return false; } return true; } template BOOST_MATH_GPU_ENABLED inline bool check_gamma( const char* function, RealType scale, RealType shape, RealType* result, const Policy& pol) { return check_scale(function, scale, result, pol) && check_gamma_shape(function, shape, result, pol); } } // namespace detail template > class gamma_distribution { public: using value_type = RealType; using policy_type = Policy; BOOST_MATH_GPU_ENABLED explicit gamma_distribution(RealType l_shape, RealType l_scale = 1) : m_shape(l_shape), m_scale(l_scale) { RealType result; detail::check_gamma("boost::math::gamma_distribution<%1%>::gamma_distribution", l_scale, l_shape, &result, Policy()); } BOOST_MATH_GPU_ENABLED RealType shape()const { return m_shape; } BOOST_MATH_GPU_ENABLED RealType scale()const { return m_scale; } private: // // Data members: // RealType m_shape; // distribution shape RealType m_scale; // distribution scale }; // NO typedef because of clash with name of gamma function. #ifdef __cpp_deduction_guides template gamma_distribution(RealType)->gamma_distribution::type>; template gamma_distribution(RealType,RealType)->gamma_distribution::type>; #endif template BOOST_MATH_GPU_ENABLED inline boost::math::pair range(const gamma_distribution& /* dist */) { // Range of permissible values for random variable x. using boost::math::tools::max_value; return boost::math::pair(static_cast(0), max_value()); } template BOOST_MATH_GPU_ENABLED inline boost::math::pair support(const gamma_distribution& /* 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 boost::math::pair(min_value(), max_value()); } template BOOST_MATH_GPU_ENABLED inline RealType pdf(const gamma_distribution& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::pdf(const gamma_distribution<%1%>&, %1%)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_gamma(function, scale, shape, &result, Policy())) return result; if(false == detail::check_gamma_x(function, x, &result, Policy())) return result; if(x == 0) { return 0; } result = gamma_p_derivative(shape, x / scale, Policy()) / scale; return result; } // pdf template BOOST_MATH_GPU_ENABLED inline RealType logpdf(const gamma_distribution& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions using boost::math::lgamma; constexpr auto function = "boost::math::logpdf(const gamma_distribution<%1%>&, %1%)"; RealType k = dist.shape(); RealType theta = dist.scale(); RealType result = -boost::math::numeric_limits::infinity(); if(false == detail::check_gamma(function, theta, k, &result, Policy())) return result; if(false == detail::check_gamma_x(function, x, &result, Policy())) return result; if(x == 0) { return boost::math::numeric_limits::quiet_NaN(); } result = -k*log(theta) + (k-1)*log(x) - lgamma(k) - (x/theta); return result; } // logpdf template BOOST_MATH_GPU_ENABLED inline RealType cdf(const gamma_distribution& dist, const RealType& x) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::cdf(const gamma_distribution<%1%>&, %1%)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_gamma(function, scale, shape, &result, Policy())) return result; if(false == detail::check_gamma_x(function, x, &result, Policy())) return result; result = boost::math::gamma_p(shape, x / scale, Policy()); return result; } // cdf template BOOST_MATH_GPU_ENABLED inline RealType quantile(const gamma_distribution& dist, const RealType& p) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_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(function, 0, Policy()); result = gamma_p_inv(shape, p, Policy()) * scale; return result; } template BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type, RealType>& c) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto 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_gamma(function, scale, shape, &result, Policy())) return result; if(false == detail::check_gamma_x(function, c.param, &result, Policy())) return result; result = gamma_q(shape, c.param / scale, Policy()); return result; } template BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type, RealType>& c) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::quantile(const 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_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(function, 0, Policy()); result = gamma_q_inv(shape, q, Policy()) * scale; return result; } template BOOST_MATH_GPU_ENABLED inline RealType mean(const gamma_distribution& dist) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::mean(const gamma_distribution<%1%>&)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_gamma(function, scale, shape, &result, Policy())) return result; result = shape * scale; return result; } template BOOST_MATH_GPU_ENABLED inline RealType variance(const gamma_distribution& dist) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::variance(const gamma_distribution<%1%>&)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_gamma(function, scale, shape, &result, Policy())) return result; result = shape * scale * scale; return result; } template BOOST_MATH_GPU_ENABLED inline RealType mode(const gamma_distribution& dist) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::mode(const gamma_distribution<%1%>&)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_gamma(function, scale, shape, &result, Policy())) return result; if(shape < 1) return policies::raise_domain_error( function, "The mode of the gamma distribution is only defined for values of the shape parameter >= 1, but got %1%.", shape, Policy()); result = (shape - 1) * scale; return result; } //template //inline RealType median(const gamma_distribution& dist) //{ // Rely on default definition in derived accessors. //} template BOOST_MATH_GPU_ENABLED inline RealType skewness(const gamma_distribution& dist) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::skewness(const gamma_distribution<%1%>&)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_gamma(function, scale, shape, &result, Policy())) return result; result = 2 / sqrt(shape); return result; } template BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const gamma_distribution& dist) { BOOST_MATH_STD_USING // for ADL of std functions constexpr auto function = "boost::math::kurtosis_excess(const gamma_distribution<%1%>&)"; RealType shape = dist.shape(); RealType scale = dist.scale(); RealType result = 0; if(false == detail::check_gamma(function, scale, shape, &result, Policy())) return result; result = 6 / shape; return result; } template BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const gamma_distribution& dist) { return kurtosis_excess(dist) + 3; } template BOOST_MATH_GPU_ENABLED inline RealType entropy(const gamma_distribution& dist) { BOOST_MATH_STD_USING RealType k = dist.shape(); RealType theta = dist.scale(); return k + log(theta) + boost::math::lgamma(k) + (1-k)*digamma(k); } } // 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 #endif // BOOST_STATS_GAMMA_HPP