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Subject: [Boost-commit] svn:boost r64969 - trunk/boost/math/distributions
From: pbristow_at_[hidden]
Date: 2010-08-23 07:58:47


Author: pbristow
Date: 2010-08-23 07:58:39 EDT (Mon, 23 Aug 2010)
New Revision: 64969
URL: http://svn.boost.org/trac/boost/changeset/64969

Log:
new inverse gamma distribution
Added:
   trunk/boost/math/distributions/inverse_gamma.hpp (contents, props changed)

Added: trunk/boost/math/distributions/inverse_gamma.hpp
==============================================================================
--- (empty file)
+++ trunk/boost/math/distributions/inverse_gamma.hpp 2010-08-23 07:58:39 EDT (Mon, 23 Aug 2010)
@@ -0,0 +1,423 @@
+// inverse_gamma.hpp
+
+// Copyright John Maddock 2006 - 2010.
+// Copyright Paul A. Bristow 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
+{
+
+ // Previous version without op and limit
+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;
+} //
+
+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,
+ 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);
+}
+
+} // 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 shape = 1, RealType scale = 1)
+ : m_shape(shape), m_scale(scale)
+ {
+ RealType result;
+ detail::check_inverse_gamma(
+ "boost::math::inverse_gamma_distribution<%1%>::inverse_gamma_distribution",
+ scale, 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;\
+
+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>(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>(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;
+ if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+ return result;
+ if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
+ return result;
+
+ if(x == 0)
+ {
+ return 0;
+ }
+
+ result = gamma_p_derivative(shape, scale / x, Policy()) * scale / (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;
+ if(false == detail::check_inverse_gamma(function, scale, shape, &result, Policy()))
+ return result;
+ if(false == detail::check_inverse_gamma_x(function, x, &result, Policy()))
+ return result;
+
+ result = boost::math::gamma_q(shape, scale / x, Policy());
+ // result = tgamma(shape, scale / x) / tgamma(shape);
+ 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
+
+ static const char* function = "boost::math::quantile(const inverse_gamma_distribution<%1%>&, %1%)";
+
+ RealType shape = dist.shape();
+ RealType scale = dist.scale();
+
+ RealType result;
+ 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 = scale / gamma_q_inv(shape, p, Policy());
+ 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;
+ 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;
+
+ //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;
+ 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 = scale / gamma_p_inv(shape, q, Policy());
+ 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;
+
+ 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 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;
+ 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 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;
+ 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;
+
+ 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 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;
+ 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 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;
+
+ 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 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


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