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// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007, 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)
// test_gamma_dist.cpp
// http://en.wikipedia.org/wiki/Gamma_distribution
// http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
// Also:
// Weisstein, Eric W. "Gamma Distribution."
// From MathWorld--A Wolfram Web Resource.
// http://mathworld.wolfram.com/GammaDistribution.html
#include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
#include <boost/math/concepts/real_concept.hpp> // for real_concept
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // Boost.Test
#include <boost/test/tools/floating_point_comparison.hpp>
#include <boost/math/distributions/gamma.hpp>
using boost::math::gamma_distribution;
#include <boost/math/tools/test.hpp>
#include "test_out_of_range.hpp"
#include <iostream>
#include <iomanip>
using std::cout;
using std::endl;
using std::setprecision;
#include <limits>
using std::numeric_limits;
template <class RealType>
RealType NaivePDF(RealType shape, RealType scale, RealType x)
{
// Deliberately naive PDF calculator again which
// we'll compare our pdf function. However some
// published values to compare against would be better....
using namespace std;
RealType result = log(x) * (shape - 1) - x / scale - boost::math::lgamma(shape) - log(scale) * shape;
return exp(result);
}
template <class RealType>
void check_gamma(RealType shape, RealType scale, RealType x, RealType p, RealType q, RealType tol)
{
BOOST_CHECK_CLOSE(
::boost::math::cdf(
gamma_distribution<RealType>(shape, scale), // distribution.
x), // random variable.
p, // probability.
tol); // %tolerance.
BOOST_CHECK_CLOSE(
::boost::math::cdf(
complement(
gamma_distribution<RealType>(shape, scale), // distribution.
x)), // random variable.
q, // probability complement.
tol); // %tolerance.
if(p < 0.999)
{
BOOST_CHECK_CLOSE(
::boost::math::quantile(
gamma_distribution<RealType>(shape, scale), // distribution.
p), // probability.
x, // random variable.
tol); // %tolerance.
}
if(q < 0.999)
{
BOOST_CHECK_CLOSE(
::boost::math::quantile(
complement(
gamma_distribution<RealType>(shape, scale), // distribution.
q)), // probability complement.
x, // random variable.
tol); // %tolerance.
}
// PDF:
BOOST_CHECK_CLOSE(
boost::math::pdf(
gamma_distribution<RealType>(shape, scale), // distribution.
x), // random variable.
NaivePDF(shape, scale, x), // PDF
tol); // %tolerance.
}
template <class RealType>
void test_spots(RealType)
{
// Basic sanity checks
//
// 15 decimal places expressed as a percentage.
// The first tests use values generated by MathCAD,
// and should be accurate to around double precision.
//
RealType tolerance = (std::max)(RealType(5e-14f), std::numeric_limits<RealType>::epsilon() * 20) * 100;
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
check_gamma(
static_cast<RealType>(0.5),
static_cast<RealType>(1),
static_cast<RealType>(0.5),
static_cast<RealType>(0.682689492137085),
static_cast<RealType>(1-0.682689492137085),
tolerance);
check_gamma(
static_cast<RealType>(2),
static_cast<RealType>(1),
static_cast<RealType>(0.5),
static_cast<RealType>(0.090204010431050),
static_cast<RealType>(1-0.090204010431050),
tolerance);
check_gamma(
static_cast<RealType>(40),
static_cast<RealType>(1),
static_cast<RealType>(10),
static_cast<RealType>(7.34163631456064E-13),
static_cast<RealType>(1-7.34163631456064E-13),
tolerance);
//
// Some more test data generated by the online
// calculator at http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
// This has the advantage of supporting the scale parameter as well
// as shape, but has only a few digits accuracy, and produces
// some deeply suspect values if the shape parameter is < 1
// (it doesn't agree with MathCAD or this implementation).
// To be fair the incomplete gamma is tricky to get right in this area...
//
tolerance = 1e-5f * 100; // 5 decimal places as a percentage
cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
check_gamma(
static_cast<RealType>(2),
static_cast<RealType>(1)/5,
static_cast<RealType>(0.1),
static_cast<RealType>(0.090204),
static_cast<RealType>(1-0.090204),
tolerance);
check_gamma(
static_cast<RealType>(2),
static_cast<RealType>(1)/5,
static_cast<RealType>(0.5),
static_cast<RealType>(1-0.287298),
static_cast<RealType>(0.287298),
tolerance);
check_gamma(
static_cast<RealType>(3),
static_cast<RealType>(2),
static_cast<RealType>(1),
static_cast<RealType>(0.014388),
static_cast<RealType>(1-0.014388),
tolerance * 10); // one less decimal place in the test value
check_gamma(
static_cast<RealType>(3),
static_cast<RealType>(2),
static_cast<RealType>(5),
static_cast<RealType>(0.456187),
static_cast<RealType>(1-0.456187),
tolerance);
RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
gamma_distribution<RealType> dist(8, 3);
RealType x = static_cast<RealType>(0.125);
using namespace std; // ADL of std names.
// mean:
BOOST_CHECK_CLOSE(
mean(dist)
, static_cast<RealType>(8*3), tol2);
// variance:
BOOST_CHECK_CLOSE(
variance(dist)
, static_cast<RealType>(8*3*3), tol2);
// std deviation:
BOOST_CHECK_CLOSE(
standard_deviation(dist)
, sqrt(static_cast<RealType>(8*3*3)), tol2);
// hazard:
BOOST_CHECK_CLOSE(
hazard(dist, x)
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
// cumulative hazard:
BOOST_CHECK_CLOSE(
chf(dist, x)
, -log(cdf(complement(dist, x))), tol2);
// coefficient_of_variation:
BOOST_CHECK_CLOSE(
coefficient_of_variation(dist)
, standard_deviation(dist) / mean(dist), tol2);
// mode:
BOOST_CHECK_CLOSE(
mode(dist)
, static_cast<RealType>(7 * 3), tol2);
// skewness:
BOOST_CHECK_CLOSE(
skewness(dist)
, 2 / sqrt(static_cast<RealType>(8)), tol2);
// kurtosis:
BOOST_CHECK_CLOSE(
kurtosis(dist)
, 3 + 6 / static_cast<RealType>(8), tol2);
// kurtosis excess:
BOOST_CHECK_CLOSE(
kurtosis_excess(dist)
, 6 / static_cast<RealType>(8), tol2);
BOOST_CHECK_CLOSE(
median(dist), static_cast<RealType>(23.007748327502412), // double precision test value
(std::max)(tol2, static_cast<RealType>(std::numeric_limits<double>::epsilon() * 2 * 100))); // 2 eps as percent
using std::log;
RealType expected_entropy = RealType(8) + log(RealType(3)) + boost::math::lgamma(RealType(8)) - 7*boost::math::digamma(RealType(8));
BOOST_CHECK_CLOSE(
entropy(dist), expected_entropy, tol2);
// Rely on default definition in derived accessors.
// error tests
check_out_of_range<boost::math::gamma_distribution<RealType> >(1, 1);
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(0, 1), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(-1, 1), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, 0), std::domain_error);
BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, -1), std::domain_error);
} // template <class RealType>void test_spots(RealType)
BOOST_AUTO_TEST_CASE( test_main )
{
// 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.
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
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::endl;
#endif
} // BOOST_AUTO_TEST_CASE( test_main )
/*
Output:
Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_gamma_dist.exe"
Running 1 test case...
Tolerance for type float is 0.000238419 %
Tolerance for type float is 0.001 %
Tolerance for type double is 5e-012 %
Tolerance for type double is 0.001 %
Tolerance for type long double is 5e-012 %
Tolerance for type long double is 0.001 %
Tolerance for type class boost::math::concepts::real_concept is 5e-012 %
Tolerance for type class boost::math::concepts::real_concept is 0.001 %
*** No errors detected
*/
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