| // 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 |
| #include <boost/test/test_exec_monitor.hpp> // Boost.Test |
| #include <boost/test/floating_point_comparison.hpp> |
| |
| #include <boost/math/distributions/gamma.hpp> |
| using boost::math::gamma_distribution; |
| #include <boost/math/tools/test.hpp> |
| |
| #include <iostream> |
| 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. |
| |
| } // template <class RealType>void test_spots(RealType) |
| |
| int test_main(int, char* []) |
| { |
| // 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: |
| |
| 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 |
| |
| */ |
| |
| |
