462 lines
16 KiB
Plaintext
462 lines
16 KiB
Plaintext
// inverse_gamma.hpp
|
|
|
|
// Copyright Paul A. Bristow 2010.
|
|
// Copyright John Maddock 2010.
|
|
// 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_INVERSE_GAMMA_HPP
|
|
#define BOOST_STATS_INVERSE_GAMMA_HPP
|
|
|
|
// Inverse Gamma Distribution is a two-parameter family
|
|
// of continuous probability distributions
|
|
// on the positive real line, which is the distribution of
|
|
// the reciprocal of a variable distributed according to the gamma distribution.
|
|
|
|
// http://en.wikipedia.org/wiki/Inverse-gamma_distribution
|
|
// http://rss.acs.unt.edu/Rdoc/library/pscl/html/igamma.html
|
|
|
|
// See also gamma distribution at 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_inverse_gamma_shape(
|
|
const char* function, // inverse_gamma
|
|
RealType shape, // shape aka alpha
|
|
RealType* result, // to update, perhaps with NaN
|
|
const Policy& pol)
|
|
{ // Sources say shape argument must be > 0
|
|
// but seems logical to allow shape zero as special case,
|
|
// returning pdf and cdf zero (but not < 0).
|
|
// (Functions like mean, variance with other limits on shape are checked
|
|
// in version including an operator & limit below).
|
|
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;
|
|
} //bool check_inverse_gamma_shape
|
|
|
|
template <class RealType, class Policy>
|
|
inline bool check_inverse_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_inverse_gamma(
|
|
const char* function, // TODO swap these over, so shape is first.
|
|
RealType scale, // scale aka beta
|
|
RealType shape, // shape aka alpha
|
|
RealType* result, const Policy& pol)
|
|
{
|
|
return check_scale(function, scale, result, pol)
|
|
&& check_inverse_gamma_shape(function, shape, result, pol);
|
|
} // bool check_inverse_gamma
|
|
|
|
} // namespace detail
|
|
|
|
template <class RealType = double, class Policy = policies::policy<> >
|
|
class inverse_gamma_distribution
|
|
{
|
|
public:
|
|
typedef RealType value_type;
|
|
typedef Policy policy_type;
|
|
|
|
inverse_gamma_distribution(RealType l_shape = 1, RealType l_scale = 1)
|
|
: m_shape(l_shape), m_scale(l_scale)
|
|
{
|
|
RealType result;
|
|
detail::check_inverse_gamma(
|
|
"boost::math::inverse_gamma_distribution<%1%>::inverse_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
|
|
};
|
|
|
|
typedef inverse_gamma_distribution<double> inverse_gamma;
|
|
// typedef - but potential clash with name of inverse gamma *function*.
|
|
// but there is a typedef for gamma
|
|
// typedef boost::math::gamma_distribution<Type, Policy> gamma;
|
|
|
|
// Allow random variable x to be zero, treated as a special case (unlike some definitions).
|
|
|
|
template <class RealType, class Policy>
|
|
inline const std::pair<RealType, RealType> range(const inverse_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 const std::pair<RealType, RealType> support(const inverse_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>(static_cast<RealType>(0), max_value<RealType>());
|
|
}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType pdf(const inverse_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 inverse_gamma_distribution<%1%>&, %1%)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
|
|
{ // distribution parameters bad.
|
|
return result;
|
|
}
|
|
if(x == 0)
|
|
{ // Treat random variate zero as a special case.
|
|
return 0;
|
|
}
|
|
else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
|
|
{ // x bad.
|
|
return result;
|
|
}
|
|
result = scale / x;
|
|
if(result < tools::min_value<RealType>())
|
|
return 0; // random variable is infinite or so close as to make no difference.
|
|
result = gamma_p_derivative(shape, result, Policy()) * scale;
|
|
if(0 != result)
|
|
{
|
|
if(x < 0)
|
|
{
|
|
// x * x may under or overflow, likewise our result,
|
|
// so be extra careful about the arithmetic:
|
|
RealType lim = tools::max_value<RealType>() * x;
|
|
if(lim < result)
|
|
return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
|
|
result /= x;
|
|
if(lim < result)
|
|
return policies::raise_overflow_error<RealType, Policy>(function, "PDF is infinite.", Policy());
|
|
result /= x;
|
|
}
|
|
result /= (x * x);
|
|
}
|
|
// better than naive
|
|
// result = (pow(scale, shape) * pow(x, (-shape -1)) * exp(-scale/x) ) / tgamma(shape);
|
|
return result;
|
|
} // pdf
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType cdf(const inverse_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 inverse_gamma_distribution<%1%>&, %1%)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
|
|
{ // distribution parameters bad.
|
|
return result;
|
|
}
|
|
if (x == 0)
|
|
{ // Treat zero as a special case.
|
|
return 0;
|
|
}
|
|
else if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
|
|
{ // x bad
|
|
return result;
|
|
}
|
|
result = boost::math::gamma_q(shape, scale / x, Policy());
|
|
// result = tgamma(shape, scale / x) / tgamma(shape); // naive using tgamma
|
|
return result;
|
|
} // cdf
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType quantile(const inverse_gamma_distribution<RealType, Policy>& dist, const RealType& p)
|
|
{
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
|
using boost::math::gamma_q_inv;
|
|
|
|
static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
if(false == detail::check_inverse_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_q_inv(shape, p, Policy());
|
|
if((result < 1) && (result * tools::max_value<RealType>() < scale))
|
|
return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
|
|
result = scale / result;
|
|
return result;
|
|
}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType cdf(const complemented2_type<inverse_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_inverse_gamma(function, scale, shape, &result, Policy()))
|
|
return result;
|
|
if(false == detail::check_inverse_gamma_x(function, c.param, &result, Policy()))
|
|
return result;
|
|
|
|
if(c.param == 0)
|
|
return 1; // Avoid division by zero
|
|
|
|
//result = 1. - gamma_q(shape, c.param / scale, Policy());
|
|
result = gamma_p(shape, scale/c.param, Policy());
|
|
return result;
|
|
}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType quantile(const complemented2_type<inverse_gamma_distribution<RealType, Policy>, RealType>& c)
|
|
{
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
|
|
|
static const char* function = "boost::math::quantile(const inverse_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_inverse_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_p_inv(shape, q, Policy());
|
|
if((result < 1) && (result * tools::max_value<RealType>() < scale))
|
|
return policies::raise_overflow_error<RealType, Policy>(function, "Value of random variable in inverse gamma distribution quantile is infinite.", Policy());
|
|
result = scale / result;
|
|
return result;
|
|
}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType mean(const inverse_gamma_distribution<RealType, Policy>& dist)
|
|
{
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
|
|
|
static const char* function = "boost::math::mean(const inverse_gamma_distribution<%1%>&)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
|
|
if(false == detail::check_scale(function, scale, &result, Policy()))
|
|
{
|
|
return result;
|
|
}
|
|
if((shape <= 1) || !(boost::math::isfinite)(shape))
|
|
{
|
|
result = policies::raise_domain_error<RealType>(
|
|
function,
|
|
"Shape parameter is %1%, but for a defined mean it must be > 1", shape, Policy());
|
|
return result;
|
|
}
|
|
result = scale / (shape - 1);
|
|
return result;
|
|
} // mean
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType variance(const inverse_gamma_distribution<RealType, Policy>& dist)
|
|
{
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
|
|
|
static const char* function = "boost::math::variance(const inverse_gamma_distribution<%1%>&)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
if(false == detail::check_scale(function, scale, &result, Policy()))
|
|
{
|
|
return result;
|
|
}
|
|
if((shape <= 2) || !(boost::math::isfinite)(shape))
|
|
{
|
|
result = policies::raise_domain_error<RealType>(
|
|
function,
|
|
"Shape parameter is %1%, but for a defined variance it must be > 2", shape, Policy());
|
|
return result;
|
|
}
|
|
result = (scale * scale) / ((shape - 1) * (shape -1) * (shape -2));
|
|
return result;
|
|
}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType mode(const inverse_gamma_distribution<RealType, Policy>& dist)
|
|
{
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
|
|
|
static const char* function = "boost::math::mode(const inverse_gamma_distribution<%1%>&)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
|
|
{
|
|
return result;
|
|
}
|
|
// Only defined for shape >= 0, but is checked by check_inverse_gamma.
|
|
result = scale / (shape + 1);
|
|
return result;
|
|
}
|
|
|
|
//template <class RealType, class Policy>
|
|
//inline RealType median(const gamma_distribution<RealType, Policy>& dist)
|
|
//{ // Wikipedia does not define median,
|
|
// so rely on default definition quantile(0.5) in derived accessors.
|
|
// return result.
|
|
//}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType skewness(const inverse_gamma_distribution<RealType, Policy>& dist)
|
|
{
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
|
|
|
static const char* function = "boost::math::skewness(const inverse_gamma_distribution<%1%>&)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
RealType result = 0;
|
|
|
|
if(false == detail::check_scale(function, scale, &result, Policy()))
|
|
{
|
|
return result;
|
|
}
|
|
if((shape <= 3) || !(boost::math::isfinite)(shape))
|
|
{
|
|
result = policies::raise_domain_error<RealType>(
|
|
function,
|
|
"Shape parameter is %1%, but for a defined skewness it must be > 3", shape, Policy());
|
|
return result;
|
|
}
|
|
result = (4 * sqrt(shape - 2) ) / (shape - 3);
|
|
return result;
|
|
}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType kurtosis_excess(const inverse_gamma_distribution<RealType, Policy>& dist)
|
|
{
|
|
BOOST_MATH_STD_USING // for ADL of std functions
|
|
|
|
static const char* function = "boost::math::kurtosis_excess(const inverse_gamma_distribution<%1%>&)";
|
|
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
if(false == detail::check_scale(function, scale, &result, Policy()))
|
|
{
|
|
return result;
|
|
}
|
|
if((shape <= 4) || !(boost::math::isfinite)(shape))
|
|
{
|
|
result = policies::raise_domain_error<RealType>(
|
|
function,
|
|
"Shape parameter is %1%, but for a defined kurtosis excess it must be > 4", shape, Policy());
|
|
return result;
|
|
}
|
|
result = (30 * shape - 66) / ((shape - 3) * (shape - 4));
|
|
return result;
|
|
}
|
|
|
|
template <class RealType, class Policy>
|
|
inline RealType kurtosis(const inverse_gamma_distribution<RealType, Policy>& dist)
|
|
{
|
|
static const char* function = "boost::math::kurtosis(const inverse_gamma_distribution<%1%>&)";
|
|
RealType shape = dist.shape();
|
|
RealType scale = dist.scale();
|
|
|
|
RealType result = 0;
|
|
|
|
if(false == detail::check_scale(function, scale, &result, Policy()))
|
|
{
|
|
return result;
|
|
}
|
|
if((shape <= 4) || !(boost::math::isfinite)(shape))
|
|
{
|
|
result = policies::raise_domain_error<RealType>(
|
|
function,
|
|
"Shape parameter is %1%, but for a defined kurtosis it must be > 4", shape, Policy());
|
|
return result;
|
|
}
|
|
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_INVERSE_GAMMA_HPP
|