summaryrefslogtreecommitdiffstats
path: root/src/boost/libs/math/test/test_gamma_dist.cpp
diff options
context:
space:
mode:
Diffstat (limited to 'src/boost/libs/math/test/test_gamma_dist.cpp')
-rw-r--r--src/boost/libs/math/test/test_gamma_dist.cpp268
1 files changed, 268 insertions, 0 deletions
diff --git a/src/boost/libs/math/test/test_gamma_dist.cpp b/src/boost/libs/math/test/test_gamma_dist.cpp
new file mode 100644
index 00000000..7ee1ee5d
--- /dev/null
+++ b/src/boost/libs/math/test/test_gamma_dist.cpp
@@ -0,0 +1,268 @@
+// 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 persentage.
+ // 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 persentage
+ 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 persentage
+ 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);
+ // kertosis:
+ BOOST_CHECK_CLOSE(
+ kurtosis(dist)
+ , 3 + 6 / static_cast<RealType>(8), tol2);
+ // kertosis 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 persent
+ // 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
+
+*/
+
+