350 lines
10 KiB
Plaintext
350 lines
10 KiB
Plaintext
// Copyright John Maddock 2006.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_STATS_GAMMA_HPP
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#define BOOST_STATS_GAMMA_HPP
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// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
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// http://mathworld.wolfram.com/GammaDistribution.html
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// http://en.wikipedia.org/wiki/Gamma_distribution
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#include <boost/math/distributions/fwd.hpp>
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#include <boost/math/special_functions/gamma.hpp>
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#include <boost/math/distributions/detail/common_error_handling.hpp>
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#include <boost/math/distributions/complement.hpp>
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#include <utility>
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namespace boost{ namespace math
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{
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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_gamma_shape(
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const char* function,
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RealType shape,
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RealType* result, const Policy& pol)
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{
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if((shape <= 0) || !(boost::math::isfinite)(shape))
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"Shape parameter is %1%, but must be > 0 !", shape, pol);
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return false;
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}
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return true;
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}
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template <class RealType, class Policy>
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inline bool check_gamma_x(
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const char* function,
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RealType const& x,
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RealType* result, const Policy& pol)
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{
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if((x < 0) || !(boost::math::isfinite)(x))
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{
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*result = policies::raise_domain_error<RealType>(
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function,
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"Random variate is %1% but must be >= 0 !", x, pol);
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return false;
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}
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return true;
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}
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template <class RealType, class Policy>
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inline bool check_gamma(
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const char* function,
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RealType scale,
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RealType shape,
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RealType* result, const Policy& pol)
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{
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return check_scale(function, scale, result, pol) && check_gamma_shape(function, shape, result, pol);
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}
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} // namespace detail
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template <class RealType = double, class Policy = policies::policy<> >
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class gamma_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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gamma_distribution(RealType l_shape, RealType l_scale = 1)
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: m_shape(l_shape), m_scale(l_scale)
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{
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RealType result;
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detail::check_gamma("boost::math::gamma_distribution<%1%>::gamma_distribution", l_scale, l_shape, &result, Policy());
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}
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RealType shape()const
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{
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return m_shape;
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}
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RealType scale()const
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{
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return m_scale;
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}
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private:
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//
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// Data members:
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//
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RealType m_shape; // distribution shape
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RealType m_scale; // distribution scale
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};
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// NO typedef because of clash with name of gamma function.
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template <class RealType, class Policy>
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inline const std::pair<RealType, RealType> range(const gamma_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>());
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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 gamma_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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using boost::math::tools::max_value;
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using boost::math::tools::min_value;
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return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>());
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}
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template <class RealType, class Policy>
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inline RealType pdf(const gamma_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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static const char* function = "boost::math::pdf(const gamma_distribution<%1%>&, %1%)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_gamma_x(function, x, &result, Policy()))
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return result;
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if(x == 0)
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{
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return 0;
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}
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result = gamma_p_derivative(shape, x / scale, Policy()) / scale;
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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 gamma_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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static const char* function = "boost::math::cdf(const gamma_distribution<%1%>&, %1%)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_gamma_x(function, x, &result, Policy()))
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return result;
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result = boost::math::gamma_p(shape, x / scale, Policy());
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return result;
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} // cdf
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template <class RealType, class Policy>
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inline RealType quantile(const gamma_distribution<RealType, Policy>& dist, const RealType& p)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_probability(function, p, &result, Policy()))
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return result;
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if(p == 1)
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return policies::raise_overflow_error<RealType>(function, 0, Policy());
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result = gamma_p_inv(shape, p, Policy()) * scale;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType cdf(const complemented2_type<gamma_distribution<RealType, Policy>, RealType>& c)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";
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RealType shape = c.dist.shape();
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RealType scale = c.dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_gamma_x(function, c.param, &result, Policy()))
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return result;
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result = gamma_q(shape, c.param / scale, Policy());
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return result;
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}
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template <class RealType, class Policy>
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inline RealType quantile(const complemented2_type<gamma_distribution<RealType, Policy>, RealType>& c)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";
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RealType shape = c.dist.shape();
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RealType scale = c.dist.scale();
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RealType q = c.param;
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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if(false == detail::check_probability(function, q, &result, Policy()))
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return result;
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if(q == 0)
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return policies::raise_overflow_error<RealType>(function, 0, Policy());
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result = gamma_q_inv(shape, q, Policy()) * scale;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType mean(const gamma_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::mean(const gamma_distribution<%1%>&)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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result = shape * scale;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType variance(const gamma_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::variance(const gamma_distribution<%1%>&)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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result = shape * scale * scale;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType mode(const gamma_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::mode(const gamma_distribution<%1%>&)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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if(shape < 1)
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return policies::raise_domain_error<RealType>(
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function,
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"The mode of the gamma distribution is only defined for values of the shape parameter >= 1, but got %1%.",
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shape, Policy());
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result = (shape - 1) * scale;
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return result;
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}
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//template <class RealType, class Policy>
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//inline RealType median(const gamma_distribution<RealType, Policy>& dist)
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//{ // Rely on default definition in derived accessors.
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//}
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template <class RealType, class Policy>
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inline RealType skewness(const gamma_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::skewness(const gamma_distribution<%1%>&)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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result = 2 / sqrt(shape);
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return result;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis_excess(const gamma_distribution<RealType, Policy>& dist)
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{
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BOOST_MATH_STD_USING // for ADL of std functions
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static const char* function = "boost::math::kurtosis_excess(const gamma_distribution<%1%>&)";
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RealType shape = dist.shape();
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RealType scale = dist.scale();
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RealType result = 0;
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if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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return result;
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result = 6 / shape;
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return result;
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}
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template <class RealType, class Policy>
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inline RealType kurtosis(const gamma_distribution<RealType, Policy>& dist)
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{
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return kurtosis_excess(dist) + 3;
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}
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} // namespace math
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} // namespace boost
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// This include must be at the end, *after* the accessors
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// for this distribution have been defined, in order to
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// keep compilers that support two-phase lookup happy.
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#include <boost/math/distributions/detail/derived_accessors.hpp>
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#endif // BOOST_STATS_GAMMA_HPP
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