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