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Boost-Commit : |
Subject: [Boost-commit] svn:boost r65659 - trunk/libs/math/test
From: pbristow_at_[hidden]
Date: 2010-09-29 05:08:09
Author: pbristow
Date: 2010-09-29 05:08:05 EDT (Wed, 29 Sep 2010)
New Revision: 65659
URL: http://svn.boost.org/trac/boost/changeset/65659
Log:
Tests for new distribution, including spot values from Mathematica.
Added:
trunk/libs/math/test/test_inverse_chi_squared_distribution.cpp (contents, props changed)
Added: trunk/libs/math/test/test_inverse_chi_squared_distribution.cpp
==============================================================================
--- (empty file)
+++ trunk/libs/math/test/test_inverse_chi_squared_distribution.cpp 2010-09-29 05:08:05 EDT (Wed, 29 Sep 2010)
@@ -0,0 +1,513 @@
+// test_inverse_chi_squared.cpp
+
+// 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)
+
+#ifdef _MSC_VER
+# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'type' was previously defined as a type
+// in Boost.test and lexical_cast
+# pragma warning (disable : 4310) // cast truncates constant value
+#endif
+
+// http://www.wolframalpha.com/input/?i=inverse+chisquare+distribution
+
+#include <boost/math/concepts/real_concept.hpp> // for real_concept
+using ::boost::math::concepts::real_concept;
+
+//#include <boost/math/tools/test.hpp>
+#include <boost/test/test_exec_monitor.hpp> // for test_main
+#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION
+
+#include <boost/math/distributions/inverse_chi_squared.hpp> // for inverse_chisquared_distribution
+using boost::math::inverse_chi_squared_distribution;
+using boost::math::cdf;
+using boost::math::pdf;
+
+// Use Inverse Gamma distribution to check their relationship:
+// inverse_chi_squared<>(v) == inverse_gamma<>(v / 2., 0.5)
+#include <boost/math/distributions/inverse_gamma.hpp> // for inverse_gamma_distribution
+using boost::math::inverse_gamma_distribution;
+using boost::math::inverse_gamma;
+// using ::boost::math::cdf;
+// using ::boost::math::pdf;
+
+#include <boost/math/special_functions/gamma.hpp>
+using boost::math::tgamma; // for naive pdf.
+
+#include <iostream>
+using std::cout;
+using std::endl;
+#include <limits>
+using std::numeric_limits; // for epsilon.
+
+template <class RealType>
+RealType naive_pdf(RealType df, RealType scale, RealType x)
+{ // Formula from Wikipedia
+ using namespace std; // For ADL of std functions.
+ using boost::math::tgamma;
+ RealType result = pow(scale * df/2, df/2) * exp(-df * scale/(2 * x));
+ result /= tgamma(df/2) * pow(x, 1 + df/2);
+ return result;
+}
+
+// Test using a spot value from some other reference source,
+// in this case test values from output from R provided by Thomas Mang,
+// and Wolfram Mathematica by Mark Coleman.
+
+template <class RealType>
+void test_spot(
+ RealType degrees_of_freedom, // degrees_of_freedom,
+ RealType scale, // scale,
+ RealType x, // random variate x,
+ RealType pd, // expected pdf,
+ RealType P, // expected CDF,
+ RealType Q, // expected complement of CDF,
+ RealType tol) // test tolerance.
+{
+ boost::math::inverse_chi_squared_distribution<RealType> dist(degrees_of_freedom, scale);
+
+ BOOST_CHECK_CLOSE_FRACTION
+ ( // Compare to expected PDF.
+ pdf(dist, x), // calculated.
+ pd, // expected
+ tol);
+
+ BOOST_CHECK_CLOSE_FRACTION( // Compare to naive pdf formula (probably less accurate).
+ pdf(dist, x), naive_pdf(dist.degrees_of_freedom(), dist.scale(), x), tol);
+
+ BOOST_CHECK_CLOSE_FRACTION( // Compare to expected CDF.
+ cdf(dist, x), P, tol);
+
+ if((P < 0.999) && (Q < 0.999))
+ { // We can only check this if P is not too close to 1,
+ // so that we can guarantee Q is accurate:
+ BOOST_CHECK_CLOSE_FRACTION(
+ cdf(complement(dist, x)), Q, tol); // 1 - cdf
+ BOOST_CHECK_CLOSE_FRACTION(
+ quantile(dist, P), x, tol); // quantile(cdf) = x
+ BOOST_CHECK_CLOSE_FRACTION(
+ quantile(complement(dist, Q)), x, tol); // quantile(1 - cdf) = x
+ }
+} // test_spot
+
+template <class RealType> // Any floating-point type RealType.
+void test_spots(RealType)
+{
+ // Basic sanity checks, some test data is to six decimal places only,
+ // so set tolerance to 0.000001 (expressed as a percentage = 0.0001%).
+
+ RealType tolerance = 0.000001f;
+ cout << "Tolerance = " << tolerance * 100 << "%." << endl;
+
+// This test values from output from geoR (17 decimal digits) guided by Thomas Mang.
+ test_spot(static_cast<RealType>(2), static_cast<RealType>(1./2.),
+ // degrees_of_freedom, default scale = 1/df.
+ static_cast<RealType>(1.L), // x.
+ static_cast<RealType>(0.30326532985631671L), // pdf.
+ static_cast<RealType>(0.60653065971263365L), // cdf.
+ static_cast<RealType>(1 - 0.606530659712633657L), // cdf complement.
+ tolerance // tol
+ );
+
+// Tests from Mark Coleman & Georgi Boshnakov using Wolfram Mathematica.
+ test_spot(static_cast<RealType>(10), static_cast<RealType>(0.1L), // degrees_of_freedom, scale
+ static_cast<RealType>(0.2), // x
+ static_cast<RealType>(1.6700235722635659824529759616528281217001163943570L), // pdf
+ static_cast<RealType>(0.89117801891415124234834646836872197623907651175353L), // cdf
+ static_cast<RealType>(1 - 0.89117801891415127L), // cdf complement
+ tolerance // tol
+ );
+
+ test_spot(static_cast<RealType>(10), static_cast<RealType>(0.1L), // degrees_of_freedom, scale
+ static_cast<RealType>(0.5), // x
+ static_cast<RealType>(0.03065662009762021L), // pdf
+ static_cast<RealType>(0.99634015317265628765454354418728984933240514654437L), // cdf
+ static_cast<RealType>(1 - 0.99634015317265628765454354418728984933240514654437L), // cdf complement
+ tolerance // tol
+ );
+
+
+ test_spot(static_cast<RealType>(10), static_cast<RealType>(2), // degrees_of_freedom, scale
+ static_cast<RealType>(0.5), // x
+ static_cast<RealType>(0.00054964096598361569L), // pdf
+ static_cast<RealType>(0.000016944743930067383903707995865261004246785511612700L), // cdf
+ static_cast<RealType>(1 - 0.000016944743930067383903707995865261004246785511612700L), // cdf complement
+ tolerance // tol
+ );
+
+ // Check some bad parameters to the distribution cause expected exception to be thrown.
+ BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution<RealType> ichsqbad1(-1), std::domain_error); // negative degrees_of_freedom.
+ BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution<RealType> ichsqbad2(1, -1), std::domain_error); // negative scale.
+ BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution<RealType> ichsqbad3(-1, -1), std::domain_error); // negative scale and degrees_of_freedom.
+
+ inverse_chi_squared_distribution<RealType> ichsq;
+
+ if(std::numeric_limits<RealType>::has_infinity)
+ {
+ BOOST_CHECK_THROW(pdf(ichsq, +std::numeric_limits<RealType>::infinity()), std::domain_error); // x = + infinity, pdf = 0
+ BOOST_CHECK_THROW(pdf(ichsq, -std::numeric_limits<RealType>::infinity()), std::domain_error); // x = - infinity, pdf = 0
+ BOOST_CHECK_THROW(cdf(ichsq, +std::numeric_limits<RealType>::infinity()),std::domain_error ); // x = + infinity, cdf = 1
+ BOOST_CHECK_THROW(cdf(ichsq, -std::numeric_limits<RealType>::infinity()), std::domain_error); // x = - infinity, cdf = 0
+ BOOST_CHECK_THROW(cdf(complement(ichsq, +std::numeric_limits<RealType>::infinity())), std::domain_error); // x = + infinity, c cdf = 0
+ BOOST_CHECK_THROW(cdf(complement(ichsq, -std::numeric_limits<RealType>::infinity())), std::domain_error); // x = - infinity, c cdf = 1
+ BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
+ BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean
+ BOOST_CHECK_THROW(boost::math::inverse_chi_squared_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
+ }
+
+ if (std::numeric_limits<RealType>::has_quiet_NaN)
+ { // If no longer allow x or p to be NaN, then these tests should throw.
+ BOOST_CHECK_THROW(pdf(ichsq, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
+ BOOST_CHECK_THROW(cdf(ichsq, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
+ BOOST_CHECK_THROW(cdf(complement(ichsq, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
+ BOOST_CHECK_THROW(quantile(ichsq, std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + quiet_NaN
+ BOOST_CHECK_THROW(quantile(complement(ichsq, std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + quiet_NaN
+ }
+ // Spot check for pdf using 'naive pdf' function
+ for(RealType x = 0.5; x < 5; x += 0.5)
+ {
+ BOOST_CHECK_CLOSE_FRACTION(
+ pdf(inverse_chi_squared_distribution<RealType>(5, 6), x),
+ naive_pdf(RealType(5), RealType(6), x),
+ tolerance);
+ } // Spot checks for parameters:
+
+ RealType tol_2eps = boost::math::tools::epsilon<RealType>() * 2; // 2 eps as a fraction.
+ inverse_chi_squared_distribution<RealType> dist51(5, 1);
+ inverse_chi_squared_distribution<RealType> dist52(5, 2);
+ inverse_chi_squared_distribution<RealType> dist31(3, 1);
+ inverse_chi_squared_distribution<RealType> dist111(11, 1);
+ // 11 mean 0.10000000000000001, variance 0.0011111111111111111, sd 0.033333333333333333
+
+ RealType x = static_cast<RealType>(0.125);
+ using namespace std; // ADL of std names.
+ using namespace boost::math;
+
+ inverse_chi_squared_distribution<RealType> dist10(10);
+ // mean, variance etc
+ BOOST_CHECK_CLOSE_FRACTION(mean(dist10), static_cast<RealType>(0.125), tol_2eps);
+ BOOST_CHECK_CLOSE_FRACTION(variance(dist10), static_cast<RealType>(0.0052083333333333333333333333333333333333333333333333L), tol_2eps);
+ BOOST_CHECK_CLOSE_FRACTION(mode(dist10), static_cast<RealType>(0.08333333333333333333333333333333333333333333333L), tol_2eps);
+ BOOST_CHECK_CLOSE_FRACTION(median(dist10), static_cast<RealType>(0.10704554778227709530244586234274024205738435512468L), tol_2eps);
+ BOOST_CHECK_CLOSE_FRACTION(cdf(dist10, median(dist10)), 0.5L, tol_2eps);
+ BOOST_CHECK_CLOSE_FRACTION(skewness(dist10), static_cast<RealType>(3.4641016151377545870548926830117447338856105076208L), tol_2eps);
+ BOOST_CHECK_CLOSE_FRACTION(kurtosis(dist10), static_cast<RealType>(45), tol_2eps);
+ BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(dist10), static_cast<RealType>(45-3), tol_2eps);
+
+ tol_2eps = boost::math::tools::epsilon<RealType>() * 2; // 2 eps as a percentage.
+
+ // Special and limit cases:
+
+ RealType mx = (std::numeric_limits<RealType>::max)();
+ RealType mi = (std::numeric_limits<RealType>::min)();
+
+ BOOST_CHECK_EQUAL(
+ pdf(inverse_chi_squared_distribution<RealType>(1),
+ static_cast<RealType>(mx)), // max()
+ static_cast<RealType>(0)
+ );
+
+ BOOST_CHECK_EQUAL(
+ pdf(inverse_chi_squared_distribution<RealType>(1),
+ static_cast<RealType>(mi)), // min()
+ static_cast<RealType>(0)
+ );
+
+ BOOST_CHECK_EQUAL(
+ pdf(inverse_chi_squared_distribution<RealType>(1), static_cast<RealType>(0)), static_cast<RealType>(0));
+ BOOST_CHECK_EQUAL(
+ pdf(inverse_chi_squared_distribution<RealType>(3), static_cast<RealType>(0))
+ , static_cast<RealType>(0.0f));
+ BOOST_CHECK_EQUAL(
+ cdf(inverse_chi_squared_distribution<RealType>(1), static_cast<RealType>(0))
+ , static_cast<RealType>(0.0f));
+ BOOST_CHECK_EQUAL(
+ cdf(inverse_chi_squared_distribution<RealType>(2), static_cast<RealType>(0))
+ , static_cast<RealType>(0.0f));
+ BOOST_CHECK_EQUAL(
+ cdf(inverse_chi_squared_distribution<RealType>(3), static_cast<RealType>(0))
+ , static_cast<RealType>(0.0f));
+ BOOST_CHECK_EQUAL(
+ cdf(complement(inverse_chi_squared_distribution<RealType>(1), static_cast<RealType>(0)))
+ , static_cast<RealType>(1));
+ BOOST_CHECK_EQUAL(
+ cdf(complement(inverse_chi_squared_distribution<RealType>(2), static_cast<RealType>(0)))
+ , static_cast<RealType>(1));
+ BOOST_CHECK_EQUAL(
+ cdf(complement(inverse_chi_squared_distribution<RealType>(3), static_cast<RealType>(0)))
+ , static_cast<RealType>(1));
+
+ BOOST_CHECK_THROW(
+ pdf(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(-1)), // degrees_of_freedom negative.
+ static_cast<RealType>(1)), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ pdf(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+ static_cast<RealType>(-1)), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ cdf(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(-1)),
+ static_cast<RealType>(1)), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ cdf(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+ static_cast<RealType>(-1)), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ cdf(complement(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(-1)),
+ static_cast<RealType>(1))), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ cdf(complement(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+ static_cast<RealType>(-1))), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ quantile(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(-1)),
+ static_cast<RealType>(0.5)), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ quantile(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+ static_cast<RealType>(-1)), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ quantile(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+ static_cast<RealType>(1.1)), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ quantile(complement(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(-1)),
+ static_cast<RealType>(0.5))), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ quantile(complement(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+ static_cast<RealType>(-1))), std::domain_error
+ );
+ BOOST_CHECK_THROW(
+ quantile(complement(
+ inverse_chi_squared_distribution<RealType>(static_cast<RealType>(8)),
+ static_cast<RealType>(1.1))), std::domain_error
+ );
+} // template <class RealType>void test_spots(RealType)
+
+
+int test_main(int, char* [])
+{
+ BOOST_MATH_CONTROL_FP;
+
+ double tol_few_eps = numeric_limits<double>::epsilon() * 4;
+
+ // Check that can generate inverse_chi_squared distribution using the two convenience methods:
+ // inverse_chi_squared_distribution; // with default parameters, degrees_of_freedom = 1, scale - 1
+ using boost::math::inverse_chi_squared;
+
+ // Some constructor tests using default double.
+ double tol4eps = boost::math::tools::epsilon<double>() * 4; // 4 eps as a fraction.
+
+ inverse_chi_squared ichsqdef; // Using typedef and both default parameters.
+
+ BOOST_CHECK_EQUAL(ichsqdef.degrees_of_freedom(), 1.); // df == 1
+ BOOST_CHECK_EQUAL(ichsqdef.scale(), 1); // scale == 1./df
+ BOOST_CHECK_CLOSE_FRACTION(pdf(ichsqdef, 1),0.2419707245191433L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(pdf(ichsqdef, 9),0.013977156581221969L, tol4eps);
+
+ inverse_chi_squared_distribution<double> ichisq102(10., 2); // Both parameters specified.
+ BOOST_CHECK_EQUAL(ichisq102.degrees_of_freedom(), 10.); // Check both parameters stored OK.
+ BOOST_CHECK_EQUAL(ichisq102.scale(), 2.); // Check both parameters stored OK.
+
+ inverse_chi_squared_distribution<double> ichisq10(10.); // Only df parameter specified (unscaled).
+ BOOST_CHECK_EQUAL(ichisq10.degrees_of_freedom(), 10.); // Check parameter stored.
+ BOOST_CHECK_EQUAL(ichisq10.scale(), 0.1); // Check default scale = 1/df = 1/10 = 0.1
+ BOOST_CHECK_CLOSE_FRACTION(pdf(ichisq10, 1), 0.00078975346316749169L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(pdf(ichisq10, 10), 0.0000000012385799798186384L, tol4eps);
+
+ BOOST_CHECK_CLOSE_FRACTION(mode(ichisq10), 0.0833333333333333333333333333333333333333L, tol4eps);
+ // nu * xi / nu + 2 = 10 * 0.1 / (10 + 2) = 1/12 = 0.0833333...
+ // mode is not defined in Mathematica.
+ // See Discussion section http://en.wikipedia.org/wiki/Talk:Scaled-inverse-chi-square_distribution
+ // for origin of this formula.
+
+ inverse_chi_squared_distribution<double> ichisq5(5.); // // Only df parameter specified.
+ BOOST_CHECK_EQUAL(ichisq5.degrees_of_freedom(), 5.); // check parameter stored.
+ BOOST_CHECK_EQUAL(ichisq5.scale(), 1./5.); // check default is 1/df
+ BOOST_CHECK_CLOSE_FRACTION(pdf(ichisq5, 0.2), 3.0510380337346841L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(cdf(ichisq5, 0.5), 0.84914503608460956l, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(cdf(complement(ichisq5, 0.5)), 1 - 0.84914503608460956l, tol4eps);
+
+ BOOST_CHECK_CLOSE_FRACTION(quantile(ichisq5, 0.84914503608460956L), 0.5, tol4eps*100);
+ BOOST_CHECK_CLOSE_FRACTION(quantile(complement(ichisq5, 1. - 0.84914503608460956L)), 0.5, tol4eps*100);
+
+ // Check mean, etc spot values.
+ inverse_chi_squared_distribution<double> ichisq81(8., 1.); // degrees_of_freedom = 5, scale = 1
+ BOOST_CHECK_CLOSE_FRACTION(mean(ichisq81),1.33333333333333333333333333333333333333333L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(variance(ichisq81), 0.888888888888888888888888888888888888888888888L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(skewness(ichisq81), 2 * std::sqrt(8.), tol4eps);
+ inverse_chi_squared_distribution<double> ichisq21(2., 1.);
+ BOOST_CHECK_CLOSE_FRACTION(mode(ichisq21), 0.5, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(median(ichisq21), 1.4426950408889634L, tol4eps);
+
+ inverse_chi_squared ichsq4(4.); // Using typedef and degrees_of_freedom parameter (and default scale = 1/df).
+ BOOST_CHECK_EQUAL(ichsq4.degrees_of_freedom(), 4.); // df == 4.
+ BOOST_CHECK_EQUAL(ichsq4.scale(), 0.25); // scale == 1 /df == 1/4.
+
+ inverse_chi_squared ichsq32(3, 2);
+ BOOST_CHECK_EQUAL(ichsq32.degrees_of_freedom(), 3.); // df == 3.
+ BOOST_CHECK_EQUAL(ichsq32.scale(), 2); // scale == 2
+
+ inverse_chi_squared ichsq11(1, 1); // Using explicit degrees_of_freedom parameter, and default scale = 1).
+ BOOST_CHECK_EQUAL(mode(ichsq11), 0.33333333333333333333333333333333333333333L);
+ // (1 * 1)/ (1 + 2) = 1/3 using Wikipedia nu * xi /(nu + 2)
+ BOOST_CHECK_EQUAL(ichsq11.degrees_of_freedom(), 1.); // df == 1 (default).
+ BOOST_CHECK_EQUAL(ichsq11.scale(), 1.); // scale == 1.
+ /*
+ // Used to find some 'exact' values for testing mean, variance ...
+ // First with scale fixed at unity (Wikipedia definition 1)
+ cout << "df scale mean variance sd median" << endl;
+ for (int degrees_of_freedom = 8; degrees_of_freedom < 30; degrees_of_freedom++)
+ {
+ inverse_chi_squared ichisq(degrees_of_freedom, 1);
+ cout.precision(17);
+ cout << degrees_of_freedom << " " << 1 << " " << mean(ichisq) << ' '
+ << variance(ichisq) << ' ' << standard_deviation(ichisq)
+ << ' ' << median(ichisq) << endl;
+ }
+
+ // Default scale = 1 / df
+ cout << "|\n" << "df scale mean variance sd median" << endl;
+ for (int degrees_of_freedom = 8; degrees_of_freedom < 30; degrees_of_freedom++)
+ {
+ inverse_chi_squared ichisq(degrees_of_freedom);
+ cout.precision(17);
+ cout << degrees_of_freedom << " " << 1./degrees_of_freedom << " " << mean(ichisq) << ' '
+ << variance(ichisq) << ' ' << standard_deviation(ichisq)
+ << ' ' << median(ichisq) << endl;
+ }
+ */
+ inverse_chi_squared_distribution<> ichisq14(14, 1); // Using default RealType double.
+ BOOST_CHECK_CLOSE_FRACTION(mean(ichisq14), 1.166666666666666666666666666666666666666666666L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(variance(ichisq14), 0.272222222222222222222222222222222222222222222L, tol4eps);
+
+ inverse_chi_squared_distribution<> ichisq121(12); // Using default RealType double.
+ BOOST_CHECK_CLOSE_FRACTION(mean(ichisq121), 0.1L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(variance(ichisq121), 0.0025L, tol4eps);
+ BOOST_CHECK_CLOSE_FRACTION(standard_deviation(ichisq121), 0.05L, tol4eps);
+
+ // and "using boost::math::inverse_chi_squared_distribution;".
+ inverse_chi_squared_distribution<> ichsq23(2., 3.); // Using default RealType double.
+ BOOST_CHECK_EQUAL(ichsq23.degrees_of_freedom(), 2.); //
+ BOOST_CHECK_EQUAL(ichsq23.scale(), 3.); //
+ BOOST_CHECK_THROW(mean(ichsq23), std::domain_error); // Degrees of freedom (nu) must be > 2
+ BOOST_CHECK_THROW(variance(ichsq23), std::domain_error); // Degrees of freedom (nu) must be > 4
+ BOOST_CHECK_THROW(skewness(ichsq23), std::domain_error); // Degrees of freedom (nu) must be > 6
+ BOOST_CHECK_THROW(kurtosis_excess(ichsq23), std::domain_error); // Degrees of freedom (nu) must be > 8
+
+ { // Check relationship between inverse gamma and inverse chi_squared distributions.
+ using boost::math::inverse_gamma_distribution;
+
+ double df = 2.;
+ double scale = 1.;
+ double alpha = df/2; // aka inv_gamma shape
+ double beta = scale /2; // inv_gamma scale.
+
+ inverse_gamma_distribution<> ig(alpha, beta);
+
+ inverse_chi_squared_distribution<> ichsq(df, 1./df); // == default scale.
+ BOOST_CHECK_EQUAL(pdf(ichsq, 0), 0); // Special case of zero x.
+
+ double x = 0.5;
+ BOOST_CHECK_EQUAL(pdf(ig, x), pdf(ichsq, x)); // inv_gamma compared to inv_chisq
+ BOOST_CHECK_EQUAL(cdf(ichsq, 0), 0); // Special case of zero.
+ BOOST_CHECK_EQUAL(cdf(ig, x), cdf(ichsq, x)); // invgamma == invchisq
+
+ // Test pdf by comparing using naive_pdf with relation to inverse gamma distribution
+ // wikipedia http://en.wikipedia.org/wiki/Scaled-inverse-chi-square_distribution related distributions.
+ // So if naive_pdf is correct, inverse_chi_squared_distribution should agree.
+ df = 1.; scale = 1.;
+ BOOST_CHECK_CLOSE_FRACTION(naive_pdf(df, scale, x), pdf(ichsq11, x), tol_few_eps);
+
+ //inverse_gamma_distribution<> igd(df/2, (df * scale)/2);
+ inverse_gamma_distribution<> igd11(df/2, df * scale/2);
+ BOOST_CHECK_CLOSE_FRACTION(naive_pdf(df, scale, x), pdf(igd11, x), tol_few_eps);
+ BOOST_CHECK_CLOSE_FRACTION(naive_pdf(df, scale, x), pdf(ichsq11, x), tol_few_eps);
+
+ df = 2; scale = 1;
+ inverse_gamma_distribution<> igd21(df/2, df * scale/2);
+ inverse_chi_squared_distribution<> ichsq21(df, scale);
+ BOOST_CHECK_CLOSE_FRACTION(naive_pdf(df, scale, x), pdf(igd21, x), tol_few_eps); // 0.54134113294645081 OK
+ BOOST_CHECK_CLOSE_FRACTION(naive_pdf(df, scale, x), pdf(ichsq21, x), tol_few_eps);
+
+ df = 2; scale = 2;
+ inverse_gamma_distribution<> igd22(df/2, df * scale/2);
+ inverse_chi_squared_distribution<> ichsq22(df, scale);
+ BOOST_CHECK_CLOSE_FRACTION(naive_pdf(df, scale, x), pdf(igd22, x), tol_few_eps);
+ BOOST_CHECK_CLOSE_FRACTION(naive_pdf(df, scale, x), pdf(ichsq22, x), tol_few_eps);
+ }
+
+ // Check using float.
+ inverse_chi_squared_distribution<float> igf23(1.f, 2.f); // Using explicit RealType float.
+ BOOST_CHECK_EQUAL(igf23.degrees_of_freedom(), 1.f); //
+ BOOST_CHECK_EQUAL(igf23.scale(), 2.f); //
+
+ // Check throws from bad parameters.
+ inverse_chi_squared ig051(0.5, 1.); // degrees_of_freedom < 1, so wrong for mean.
+ BOOST_CHECK_THROW(mean(ig051), std::domain_error);
+ inverse_chi_squared ig191(1.9999, 1.); // degrees_of_freedom < 2, so wrong for variance.
+ BOOST_CHECK_THROW(variance(ig191), std::domain_error);
+ inverse_chi_squared ig291(2.9999, 1.); // degrees_of_freedom < 3, so wrong for skewness.
+ BOOST_CHECK_THROW(skewness(ig291), std::domain_error);
+ inverse_chi_squared ig391(3.9999, 1.); // degrees_of_freedom < 1, so wrong for kurtosis and kurtosis_excess.
+ BOOST_CHECK_THROW(kurtosis(ig391), std::domain_error);
+ BOOST_CHECK_THROW(kurtosis_excess(ig391), std::domain_error);
+
+ inverse_chi_squared ig102(10, 2); // Wolfram.com/ page 2, quantile = 2.96859.
+ //http://reference.wolfram.com/mathematica/ref/InverseChiSquareDistribution.html
+ BOOST_CHECK_CLOSE_FRACTION(quantile(ig102, 0.75), 2.96859, 0.000001);
+ BOOST_CHECK_CLOSE_FRACTION(cdf(ig102, 2.96859), 0.75 , 0.000001);
+ BOOST_CHECK_CLOSE_FRACTION(cdf(complement(ig102, 2.96859)), 1 - 0.75 , 0.00001);
+ BOOST_CHECK_CLOSE_FRACTION(quantile(complement(ig102, 1 - 0.75)), 2.96859, 0.000001);
+
+ // Basic sanity-check spot values.
+ // (Parameter value, arbitrarily zero, only communicates the floating point type).
+ test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
+ test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+ test_spots(0.0L); // Test long double.
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
+ test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+#endif
+#else
+ std::cout << "<note>The long double tests have been disabled on this platform "
+ "either because the long double overloads of the usual math functions are "
+ "not available at all, or because they are too inaccurate for these tests "
+ "to pass.</note>" << std::cout;
+#endif
+
+ /* */
+ return 0;
+} // int test_main(int, char* [])
+
+/*
+
+Output:
+
+
+
+
+*/
+
+
+
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