123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268 |
- // 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
- */
|