boost/math/distributions/gamma.hpp
// 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/special_functions/digamma.hpp>
#include <boost/math/distributions/detail/common_error_handling.hpp>
#include <boost/math/distributions/complement.hpp>
#include <utility>
#include <type_traits>
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:
using value_type = RealType;
using policy_type = Policy;
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());
}
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.
#ifdef __cpp_deduction_guides
template <class RealType>
gamma_distribution(RealType)->gamma_distribution<typename boost::math::tools::promote_args<RealType>::type>;
template <class RealType>
gamma_distribution(RealType,RealType)->gamma_distribution<typename boost::math::tools::promote_args<RealType>::type>;
#endif
template <class RealType, class Policy>
inline 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>(static_cast<RealType>(0), max_value<RealType>());
}
template <class RealType, class Policy>
inline 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 = 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 <class RealType, class Policy>
inline RealType logpdf(const gamma_distribution<RealType, Policy>& dist, const RealType& x)
{
BOOST_MATH_STD_USING // for ADL of std functions
using boost::math::lgamma;
static const char* function = "boost::math::logpdf(const gamma_distribution<%1%>&, %1%)";
RealType k = dist.shape();
RealType theta = dist.scale();
RealType result = -std::numeric_limits<RealType>::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 std::numeric_limits<RealType>::quiet_NaN();
}
result = -k*log(theta) + (k-1)*log(x) - lgamma(k) - (x/theta);
return result;
} // logpdf
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 = 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 <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 = 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<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 = 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 <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 = 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<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 = 0;
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 = 0;
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 = 0;
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 = 0;
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 = 0;
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;
}
template <class RealType, class Policy>
inline RealType entropy(const gamma_distribution<RealType, Policy>& dist)
{
RealType k = dist.shape();
RealType theta = dist.scale();
using std::log;
return k + log(theta) + 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 <boost/math/distributions/detail/derived_accessors.hpp>
#endif // BOOST_STATS_GAMMA_HPP