Subject: [Boost-commit] svn:boost r65424 - trunk/boost/math/distributions
From: pbristow_at_[hidden]
Date: 2010-09-15 11:39:45
Author: pbristow
Date: 2010-09-15 11:39:43 EDT (Wed, 15 Sep 2010)
New Revision: 65424
URL: http://svn.boost.org/trac/boost/changeset/65424
Log:
1st draft
Added:
trunk/boost/math/distributions/inverse_chi_squared.hpp (contents, props changed)
Added: trunk/boost/math/distributions/inverse_chi_squared.hpp
==============================================================================
--- (empty file)
+++ trunk/boost/math/distributions/inverse_chi_squared.hpp 2010-09-15 11:39:43 EDT (Wed, 15 Sep 2010)
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+// Copyright John Maddock 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_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP
+#define BOOST_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP
+
+#include <boost/math/distributions/fwd.hpp>
+#include <boost/math/special_functions/gamma.hpp> // for incomplete beta.
+#include <boost/math/distributions/complement.hpp> // complements
+#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
+#include <boost/math/special_functions/fpclassify.hpp>
+
+// See http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution
+// for definitions of this scaled version.
+
+// http://reference.wolfram.com/mathematica/ref/InverseChiSquareDistribution.html
+// Weisstein, Eric W. "Inverse Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource.
+// http://mathworld.wolfram.com/InverseChi-SquaredDistribution.html
+
+#include <utility>
+
+namespace boost{ namespace math{
+
+namespace detail
+{
+ template <class RealType, class Policy>
+ inline bool check_inverse_chi_squared( // Check distribution parameters.
+ const char* function,
+ RealType degrees_of_freedom, // degrees_of_freedom (aka nu).
+ RealType scale, // scale (aka sigma^2)
+ RealType* result,
+ const Policy& pol)
+ {
+ return check_scale(function, scale, result, pol)
+ && check_df(function, degrees_of_freedom,
+ result, pol);
+ } // bool check_inverse_chi_squared
+} // namespace detail
+
+template <class RealType = double, class Policy = policies::policy<> >
+class inverse_chi_squared_distribution
+{
+public:
+ typedef RealType value_type;
+ typedef Policy policy_type;
+
+ inverse_chi_squared_distribution(RealType df, RealType scale) : m_df(df), m_scale (scale)
+ {
+ RealType result;
+ detail::check_df(
+ "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", m_df, &result, Policy());
+ } // inverse_chi_squared_distribution constructor
+
+ inverse_chi_squared_distribution(RealType df = 1) : m_df(df)
+ {
+ RealType result;
+ m_scale = 1 / m_df ; // Default scale = 1 / degrees of freedom (Wikipedia definition 1).
+ detail::check_df(
+ "boost::math::inverse_chi_squared_distribution<%1%>::inverse_chi_squared_distribution", m_df, &result, Policy());
+ } // inverse_chi_squared_distribution
+
+ RealType degrees_of_freedom()const
+ {
+ return m_df;
+ }
+ RealType scale()const
+ {
+ return m_scale; // aka nu
+ }
+
+ // Parameter estimation:
+ static RealType find_degrees_of_freedom(
+ RealType difference_from_variance,
+ RealType alpha,
+ RealType beta,
+ RealType variance,
+ RealType hint = 100);
+
+private:
+ // Data members:
+ RealType m_df; // degrees of freedom are treated as a real number.
+ RealType m_scale; // distribution scale
+
+}; // class chi_squared_distribution
+
+typedef inverse_chi_squared_distribution<double> inverse_chi_squared;
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> range(const inverse_chi_squared_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>()); // 0 to + infinity.
+}
+
+template <class RealType, class Policy>
+inline const std::pair<RealType, RealType> support(const inverse_chi_squared_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.
+ return std::pair<RealType, RealType>(static_cast<RealType>(0), tools::max_value<RealType>()); // 0 to + infinity.
+}
+
+template <class RealType, class Policy>
+RealType pdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)
+{
+ BOOST_MATH_STD_USING // for ADL of std functions.
+ RealType df = dist.degrees_of_freedom();
+ RealType scale = dist.scale();
+ RealType error_result;
+
+ static const char* function = "boost::math::pdf(const inverse_chi_squared_distribution<%1%>&, %1%)";
+
+ if(false == detail::check_inverse_chi_squared
+ (function, df, scale, &error_result, Policy())
+ )
+ { // Bad distribution.
+ return error_result;
+ }
+
+ if((x < 0) || !(boost::math::isfinite)(x))
+ { // Bad x.
+ return policies::raise_domain_error<RealType>(
+ function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy());
+ }
+
+ if(x == 0)
+ { // Treat as special case.
+ return 0;
+ }
+ // Wikipedia scaled inverse chi sq (df, scale) related to inv gamma (df/2, df * scale /2)
+ // so use inverse gamma pdf with shape = df/2, scale df * scale /2
+ // RealType shape = df /2; // inv_gamma shape
+ // RealType scale = df * scale/2; // inv_gamma scale
+ //RealType result = gamma_p_derivative(shape, scale / x, Policy()) * scale / (x * x);
+ RealType result = gamma_p_derivative(df/2, df * scale/2 / x, Policy()) * df * scale/2 / (x * x);
+ return result;
+} // pdf
+
+template <class RealType, class Policy>
+inline RealType cdf(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& x)
+{
+ static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)";
+ RealType df = dist.degrees_of_freedom();
+ RealType scale = dist.scale();
+ RealType error_result;
+
+ if(false ==
+ detail::check_inverse_chi_squared(function, df, scale, &error_result, Policy())
+ )
+ { // Bad distribution.
+ return error_result;
+ }
+ if((x < 0) || !(boost::math::isfinite)(x))
+ { // Bad x.
+ return policies::raise_domain_error<RealType>(
+ function, "inverse Chi Square parameter was %1%, but must be >= 0 !", x, Policy());
+ }
+ if (x == 0)
+ { // Treat zero as a special case.
+ return 0;
+ }
+ // RealType shape = df /2; // inv_gamma shape
+ // RealType scale = df * scale/2; // inv_gamma scale
+ // result = boost::math::gamma_q(shape, scale / x, Policy()); // inverse_gamma code
+ return boost::math::gamma_q(df / 2, (df * (scale / 2)) / x, Policy());
+} // cdf
+
+template <class RealType, class Policy>
+inline RealType quantile(const inverse_chi_squared_distribution<RealType, Policy>& dist, const RealType& p)
+{
+ using boost::math::gamma_q_inv;
+ RealType df = dist.degrees_of_freedom();
+ RealType scale = dist.scale();
+
+ static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)";
+ // Error check:
+ RealType error_result;
+ if(false == detail::check_df(
+ function, df, &error_result, Policy())
+ && detail::check_probability(
+ function, p, &error_result, Policy()))
+ return error_result;
+ // RealType shape = df /2; // inv_gamma shape
+ // RealType scale = df * scale/2; // inv_gamma scale
+ // result = scale / gamma_q_inv(shape, p, Policy());
+ RealType result = df * scale/2 / gamma_q_inv(df /2, p, Policy());
+ return result;
+} // quantile
+
+template <class RealType, class Policy>
+inline RealType cdf(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c)
+{
+ using boost::math::gamma_q_inv;
+ RealType const& df = c.dist.degrees_of_freedom();
+ RealType const& scale = c.dist.scale();
+ RealType const& x = c.param;
+ static const char* function = "boost::math::cdf(const inverse_chi_squared_distribution<%1%>&, %1%)";
+ // Error check:
+ RealType error_result;
+ if(false == detail::check_df(
+ function, degrees_of_freedom, &error_result, Policy()))
+ return error_result;
+
+ if((x < 0) || !(boost::math::isfinite)(x))
+ {
+ return policies::raise_domain_error<RealType>(
+ function, "inverse Chi Square parameter was %1%, but must be > 0 !", x, Policy());
+ }
+ // RealType shape = df /2; // inv_gamma shape
+ // RealType scale = df * scale/2; // inv_gamma scale
+ // result = gamma_p(shape, scale/c.param, Policy()); inv_gamma
+
+ return gamma_q(df / 2, (df * scale/2)/ x, Policy());
+}
+
+template <class RealType, class Policy>
+inline RealType quantile(const complemented2_type<inverse_chi_squared_distribution<RealType, Policy>, RealType>& c)
+{
+ using boost::math::gamma_q_inv;
+
+ RealType const& df = c.dist.degrees_of_freedom();
+ RealType const& scale = c.dist.scale();
+ RealType const& q = c.param;
+ static const char* function = "boost::math::quantile(const inverse_chi_squared_distribution<%1%>&, %1%)";
+ // Error check:
+ RealType error_result;
+ if(false == detail::check_df(
+ function, df, &error_result, Policy())
+ && detail::check_probability(
+ function, q, &error_result, Policy()))
+ return error_result;
+ // RealType shape = df /2; // inv_gamma shape
+ // RealType scale = df * scale/2; // inv_gamma scale
+ // result = scale / gamma_p_inv(shape, q, Policy()); // inv_gamma
+ return df * scale/2 * gamma_p_inv(df /2, q, Policy());
+}
+/**/
+
+template <class RealType, class Policy>
+inline RealType mean(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{ // Mean of inverse Chi-Squared distribution.
+ RealType df = dist.degrees_of_freedom();
+ RealType scale = dist.scale();
+
+ static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)";
+ if(df <= 2)
+ return policies::raise_domain_error<RealType>(
+ function,
+ "inverse Chi-Squared distribution only has a mode for degrees of freedom > 2, but got degrees of freedom = %1%.",
+ df, Policy());
+ return (df * scale) / (df - 2);
+} // mean
+
+template <class RealType, class Policy>
+inline RealType variance(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{ // Variance of inverse Chi-Squared distribution..
+ RealType df = dist.degrees_of_freedom();
+ RealType scale = dist.scale();
+ static const char* function = "boost::math::variance(const inverse_chi_squared_distribution<%1%>&)";
+ if(df <= 4)
+ {
+ return policies::raise_domain_error<RealType>(
+ function,
+ "inverse Chi-Squared distribution only has a variance for degrees of freedom > 4, but got degrees of freedom = %1%.",
+ df, Policy()); return 2 * dist.degrees_of_freedom();
+ }
+ return 2 * df * df * scale * scale / ((df - 2)*(df - 2) * (df - 4));
+
+} // variance
+
+template <class RealType, class Policy>
+inline RealType mode(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{
+ RealType df = dist.degrees_of_freedom();
+ RealType scale = dist.scale();
+ static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)";
+ if(df < 0)
+ return policies::raise_domain_error<RealType>(
+ function,
+ "inverse Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",
+ df, Policy());
+ return (df * scale) / (df + 2);
+}
+
+//template <class RealType, class Policy>
+//inline RealType median(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+//{ // Median is given by Quantile[dist, 1/2]
+// RealType df = dist.degrees_of_freedom();
+// if(df <= 1)
+// return tools::domain_error<RealType>(
+// BOOST_CURRENT_FUNCTION,
+// "The inverse_Chi-Squared distribution only has a median for degrees of freedom >= 0, but got degrees of freedom = %1%.",
+// df);
+// return df;
+//}
+// Now implemented via quantile(half) in derived accessors.
+
+template <class RealType, class Policy>
+inline RealType skewness(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{
+ BOOST_MATH_STD_USING // For ADL
+ RealType df = dist.degrees_of_freedom();
+ static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)";
+ if(df <= 6)
+ return policies::raise_domain_error<RealType>(
+ function,
+ "inverse Chi-Squared distribution only has a skewness for degrees of freedom > 6, but got degrees of freedom = %1%.",
+ df, Policy());
+
+ return 4 * sqrt (2 * (df - 4)) / (df - 6); // Not a function of scale.
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{
+ RealType df = dist.degrees_of_freedom();
+ static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)";
+ if(df <= 8)
+ return policies::raise_domain_error<RealType>(
+ function,
+ "inverse Chi-Squared distribution only has a kurtosis for degrees of freedom > 8, but got degrees of freedom = %1%.",
+ df, Policy());
+
+ return kurtosis_excess(dist) + 3;
+}
+
+template <class RealType, class Policy>
+inline RealType kurtosis_excess(const inverse_chi_squared_distribution<RealType, Policy>& dist)
+{
+ RealType df = dist.degrees_of_freedom();
+ static const char* function = "boost::math::mode(const inverse_chi_squared_distribution<%1%>&)";
+ if(df <= 8)
+ return policies::raise_domain_error<RealType>(
+ function,
+ "inverse Chi-Squared distribution only has a kurtosis excess for degrees of freedom > 8, but got degrees of freedom = %1%.",
+ df, Policy());
+
+ return 12 * (5 * df - 22) / ((df - 6 )*(df - 8)); // Not a function of scale.
+}
+
+/*
+//
+// Parameter estimation comes last:
+//
+namespace detail
+{
+
+template <class RealType, class Policy>
+struct df_estimator
+{
+ df_estimator(RealType a, RealType b, RealType variance, RealType delta)
+ : alpha(a), beta(b), ratio(delta/variance) {}
+
+ RealType operator()(const RealType& df)
+ {
+ if(df <= tools::min_value<RealType>())
+ return 1;
+ inverse_chi_squared_distribution<RealType, Policy> cs(df);
+
+ RealType result;
+ if(ratio > 0)
+ {
+ RealType r = 1 + ratio;
+ result = cdf(cs, quantile(complement(cs, alpha)) / r) - beta;
+ }
+ else
+ {
+ RealType r = 1 + ratio;
+ result = cdf(complement(cs, quantile(cs, alpha) / r)) - beta;
+ }
+ return result;
+ }
+private:
+ RealType alpha, beta, ratio;
+};
+
+} // namespace detail
+
+template <class RealType, class Policy>
+RealType inverse_chi_squared_distribution<RealType, Policy>::find_degrees_of_freedom(
+ RealType difference_from_variance,
+ RealType alpha,
+ RealType beta,
+ RealType variance,
+ RealType hint)
+{
+ static const char* function = "boost::math::inverse_chi_squared_distribution<%1%>::find_degrees_of_freedom(%1%,%1%,%1%,%1%,%1%)";
+ // Check for domain errors:
+ RealType error_result;
+ if(false == detail::check_probability(
+ function, alpha, &error_result, Policy())
+ && detail::check_probability(function, beta, &error_result, Policy()))
+ return error_result;
+
+ if(hint <= 0)
+ hint = 1;
+
+ detail::df_estimator<RealType, Policy> f(alpha, beta, variance, difference_from_variance);
+ tools::eps_tolerance<RealType> tol(policies::digits<RealType, Policy>());
+ boost::uintmax_t max_iter = policies::get_max_root_iterations<Policy>();
+ std::pair<RealType, RealType> r = tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());
+ RealType result = r.first + (r.second - r.first) / 2;
+ if(max_iter >= policies::get_max_root_iterations<Policy>())
+ {
+ policies::raise_evaluation_error<RealType>(function, "Unable to locate solution in a reasonable time:"
+ " either there is no answer to how many degrees of freedom are required"
+ " or the answer is infinite. Current best guess is %1%", result, Policy());
+ }
+ return result;
+}
+
+*/
+
+} // 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_MATH_DISTRIBUTIONS_INVERSE_CHI_SQUARED_HPP