| // Copyright John Maddock 2006. |
| // 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 <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_gamma_shape( |
| const char* function, |
| RealType shape, |
| RealType* result, const Policy& pol) |
| { |
| 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; |
| } |
| |
| template <class RealType, class Policy> |
| 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<RealType>( |
| function, |
| "Random variate is %1% but must be >= 0 !", x, pol); |
| return false; |
| } |
| return true; |
| } |
| |
| template <class RealType, class Policy> |
| 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 RealType = double, class Policy = policies::policy<> > |
| class gamma_distribution |
| { |
| public: |
| typedef RealType value_type; |
| typedef Policy policy_type; |
| |
| gamma_distribution(RealType shape, RealType scale = 1) |
| : m_shape(shape), m_scale(scale) |
| { |
| RealType result; |
| detail::check_gamma("boost::math::gamma_distribution<%1%>::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 |
| }; |
| |
| // NO typedef because of clash with name of gamma function. |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> range(const gamma_distribution<RealType, Policy>& /* dist */) |
| { // Range of permissible values for random variable x. |
| using boost::math::tools::max_value; |
| return std::pair<RealType, RealType>(0, max_value<RealType>()); |
| } |
| |
| template <class RealType, class Policy> |
| inline const std::pair<RealType, RealType> support(const 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>(min_value<RealType>(), max_value<RealType>()); |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType pdf(const 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 gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| 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 <class RealType, class Policy> |
| inline RealType cdf(const 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 gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| 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 <class RealType, class Policy> |
| inline RealType quantile(const gamma_distribution<RealType, Policy>& dist, const RealType& p) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| 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<RealType>(function, 0, Policy()); |
| |
| result = gamma_p_inv(shape, p, Policy()) * scale; |
| |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType cdf(const complemented2_type<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; |
| 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 <class RealType, class Policy> |
| inline RealType quantile(const complemented2_type<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 q = c.param; |
| |
| RealType result; |
| 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<RealType>(function, 0, Policy()); |
| |
| result = gamma_q_inv(shape, q, Policy()) * scale; |
| |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType mean(const gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::mean(const gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| if(false == detail::check_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| |
| result = shape * scale; |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType variance(const gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::variance(const gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| if(false == detail::check_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| |
| result = shape * scale * scale; |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType mode(const gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::mode(const gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| if(false == detail::check_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| |
| if(shape < 1) |
| return policies::raise_domain_error<RealType>( |
| 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 <class RealType, class Policy> |
| //inline RealType median(const gamma_distribution<RealType, Policy>& dist) |
| //{ // Rely on default definition in derived accessors. |
| //} |
| |
| template <class RealType, class Policy> |
| inline RealType skewness(const gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::skewness(const gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| if(false == detail::check_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| |
| result = 2 / sqrt(shape); |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis_excess(const gamma_distribution<RealType, Policy>& dist) |
| { |
| BOOST_MATH_STD_USING // for ADL of std functions |
| |
| static const char* function = "boost::math::kurtosis_excess(const gamma_distribution<%1%>&)"; |
| |
| RealType shape = dist.shape(); |
| RealType scale = dist.scale(); |
| |
| RealType result; |
| if(false == detail::check_gamma(function, scale, shape, &result, Policy())) |
| return result; |
| |
| result = 6 / shape; |
| return result; |
| } |
| |
| template <class RealType, class Policy> |
| inline RealType kurtosis(const gamma_distribution<RealType, Policy>& dist) |
| { |
| 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_GAMMA_HPP |
| |
| |