| // 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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|
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| #include <utility>
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|
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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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|
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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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|
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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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|
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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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|
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| } // namespace detail
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|
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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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|
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| gamma_distribution(RealType shape, RealType scale = 1)
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| : m_shape(shape), m_scale(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", scale, shape, &result, Policy());
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| }
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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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|
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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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|
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| // NO typedef because of clash with name of gamma function.
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|
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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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|
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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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|
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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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|
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| static const char* function = "boost::math::pdf(const gamma_distribution<%1%>&, %1%)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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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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|
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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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|
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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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|
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| static const char* function = "boost::math::cdf(const gamma_distribution<%1%>&, %1%)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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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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|
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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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|
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| static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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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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|
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| result = gamma_p_inv(shape, p, Policy()) * scale;
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|
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| return result;
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| }
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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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|
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| static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";
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|
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| RealType shape = c.dist.shape();
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| RealType scale = c.dist.scale();
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|
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| RealType result;
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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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|
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| result = gamma_q(shape, c.param / scale, Policy());
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|
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| return result;
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| }
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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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|
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| static const char* function = "boost::math::quantile(const gamma_distribution<%1%>&, %1%)";
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|
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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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|
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| RealType result;
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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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|
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| if(q == 0)
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| return policies::raise_overflow_error<RealType>(function, 0, Policy());
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|
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| result = gamma_q_inv(shape, q, Policy()) * scale;
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|
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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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|
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| static const char* function = "boost::math::mean(const gamma_distribution<%1%>&)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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| if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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| return result;
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|
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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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|
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| static const char* function = "boost::math::variance(const gamma_distribution<%1%>&)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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| if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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| return result;
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|
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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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|
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| static const char* function = "boost::math::mode(const gamma_distribution<%1%>&)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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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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|
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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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|
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| static const char* function = "boost::math::skewness(const gamma_distribution<%1%>&)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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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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|
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| static const char* function = "boost::math::kurtosis_excess(const gamma_distribution<%1%>&)";
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|
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| RealType shape = dist.shape();
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| RealType scale = dist.scale();
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|
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| RealType result;
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| if(false == detail::check_gamma(function, scale, shape, &result, Policy()))
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| return result;
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|
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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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|
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|
|