libs/math/test/test_gamma_dist.cpp

   1 // Copyright John Maddock 2006.
   2 // Copyright Paul A. Bristow 2007, 2010.
   3
   4 // Use, modification and distribution are subject to the
   5 // Boost Software License, Version 1.0.
   6 // (See accompanying file LICENSE_1_0.txt
   7 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   8
   9 // test_gamma_dist.cpp
  10
  11 // http://en.wikipedia.org/wiki/Gamma_distribution
  12 // http://www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm
  13 // Also:
  14 // Weisstein, Eric W. "Gamma Distribution."
  15 // From MathWorld--A Wolfram Web Resource.
  16 // http://mathworld.wolfram.com/GammaDistribution.html
  17
  18 #include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
  19
  20 #include <boost/math/concepts/real_concept.hpp> // for real_concept
  21 #define BOOST_TEST_MAIN
  22 #include <boost/test/unit_test.hpp> // Boost.Test
  23 #include <boost/test/tools/floating_point_comparison.hpp>
  24
  25 #include <boost/math/distributions/gamma.hpp>
  26     using boost::math::gamma_distribution;
  27 #include <boost/math/tools/test.hpp>
  28 #include "test_out_of_range.hpp"
  29
  30 #include <iostream>
  31 #include <iomanip>
  32    using std::cout;
  33    using std::endl;
  34    using std::setprecision;
  35 #include <limits>
  36   using std::numeric_limits;
  37
  38 template <class RealType>
  39 RealType NaivePDF(RealType shape, RealType scale, RealType x)
  40 {
  41    // Deliberately naive PDF calculator again which
  42    // we'll compare our pdf function.  However some
  43    // published values to compare against would be better....
  44    using namespace std;
  45    RealType result = log(x) * (shape - 1) - x / scale - boost::math::lgamma(shape) - log(scale) * shape;
  46    return exp(result);
  47 }
  48
  49 template <class RealType>
  50 void check_gamma(RealType shape, RealType scale, RealType x, RealType p, RealType q, RealType tol)
  51 {
  52    BOOST_CHECK_CLOSE(
  53       ::boost::math::cdf(
  54          gamma_distribution<RealType>(shape, scale),    // distribution.
  55          x),                                            // random variable.
  56          p,                                             // probability.
  57          tol);                                          // %tolerance.
  58    BOOST_CHECK_CLOSE(
  59       ::boost::math::cdf(
  60          complement(
  61             gamma_distribution<RealType>(shape, scale), // distribution.
  62             x)),                                        // random variable.
  63          q,                                             // probability complement.
  64          tol);                                          // %tolerance.
  65    if(p < 0.999)
  66    {
  67       BOOST_CHECK_CLOSE(
  68          ::boost::math::quantile(
  69             gamma_distribution<RealType>(shape, scale),    // distribution.
  70             p),                                            // probability.
  71             x,                                             // random variable.
  72             tol);                                          // %tolerance.
  73    }
  74    if(q < 0.999)
  75    {
  76       BOOST_CHECK_CLOSE(
  77          ::boost::math::quantile(
  78             complement(
  79                gamma_distribution<RealType>(shape, scale), // distribution.
  80                q)),                                        // probability complement.
  81             x,                                             // random variable.
  82             tol);                                          // %tolerance.
  83    }
  84    // PDF:
  85    BOOST_CHECK_CLOSE(
  86       boost::math::pdf(
  87          gamma_distribution<RealType>(shape, scale),    // distribution.
  88          x),                                            // random variable.
  89          NaivePDF(shape, scale, x),                     // PDF
  90          tol);                                          // %tolerance.
  91 }
  92
  93 template <class RealType>
  94 void test_spots(RealType)
  95 {
  96    // Basic sanity checks
  97    //
  98    // 15 decimal places expressed as a persentage.
  99    // The first tests use values generated by MathCAD,
 100    // and should be accurate to around double precision.
 101    //
 102    RealType tolerance = (std::max)(RealType(5e-14f), std::numeric_limits<RealType>::epsilon() * 20) * 100;
 103    cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;
 104
 105    check_gamma(
 106       static_cast<RealType>(0.5),
 107       static_cast<RealType>(1),
 108       static_cast<RealType>(0.5),
 109       static_cast<RealType>(0.682689492137085),
 110       static_cast<RealType>(1-0.682689492137085),
 111       tolerance);
 112    check_gamma(
 113       static_cast<RealType>(2),
 114       static_cast<RealType>(1),
 115       static_cast<RealType>(0.5),
 116       static_cast<RealType>(0.090204010431050),
 117       static_cast<RealType>(1-0.090204010431050),
 118       tolerance);
 119    check_gamma(
 120       static_cast<RealType>(40),
 121       static_cast<RealType>(1),
 122       static_cast<RealType>(10),
 123       static_cast<RealType>(7.34163631456064E-13),
 124       static_cast<RealType>(1-7.34163631456064E-13),
 125       tolerance);
 126
 127    //
 128    // Some more test data generated by the online
 129    // calculator at http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
 130    // This has the advantage of supporting the scale parameter as well
 131    // as shape, but has only a few digits accuracy, and produces
 132    // some deeply suspect values if the shape parameter is < 1
 133    // (it doesn't agree with MathCAD or this implementation).
 134    // To be fair the incomplete gamma is tricky to get right in this area...
 135    //
 136    tolerance = 1e-5f * 100; // 5 decimal places as a persentage
 137    cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;
 138
 139    check_gamma(
 140       static_cast<RealType>(2),
 141       static_cast<RealType>(1)/5,
 142       static_cast<RealType>(0.1),
 143       static_cast<RealType>(0.090204),
 144       static_cast<RealType>(1-0.090204),
 145       tolerance);
 146    check_gamma(
 147       static_cast<RealType>(2),
 148       static_cast<RealType>(1)/5,
 149       static_cast<RealType>(0.5),
 150       static_cast<RealType>(1-0.287298),
 151       static_cast<RealType>(0.287298),
 152       tolerance);
 153    check_gamma(
 154       static_cast<RealType>(3),
 155       static_cast<RealType>(2),
 156       static_cast<RealType>(1),
 157       static_cast<RealType>(0.014388),
 158       static_cast<RealType>(1-0.014388),
 159       tolerance * 10); // one less decimal place in the test value
 160    check_gamma(
 161       static_cast<RealType>(3),
 162       static_cast<RealType>(2),
 163       static_cast<RealType>(5),
 164       static_cast<RealType>(0.456187),
 165       static_cast<RealType>(1-0.456187),
 166       tolerance);
 167
 168
 169     RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100;  // 5 eps as a persentage
 170     gamma_distribution<RealType> dist(8, 3);
 171     RealType x = static_cast<RealType>(0.125);
 172     using namespace std; // ADL of std names.
 173     // mean:
 174     BOOST_CHECK_CLOSE(
 175        mean(dist)
 176        , static_cast<RealType>(8*3), tol2);
 177     // variance:
 178     BOOST_CHECK_CLOSE(
 179        variance(dist)
 180        , static_cast<RealType>(8*3*3), tol2);
 181     // std deviation:
 182     BOOST_CHECK_CLOSE(
 183        standard_deviation(dist)
 184        , sqrt(static_cast<RealType>(8*3*3)), tol2);
 185     // hazard:
 186     BOOST_CHECK_CLOSE(
 187        hazard(dist, x)
 188        , pdf(dist, x) / cdf(complement(dist, x)), tol2);
 189     // cumulative hazard:
 190     BOOST_CHECK_CLOSE(
 191        chf(dist, x)
 192        , -log(cdf(complement(dist, x))), tol2);
 193     // coefficient_of_variation:
 194     BOOST_CHECK_CLOSE(
 195        coefficient_of_variation(dist)
 196        , standard_deviation(dist) / mean(dist), tol2);
 197     // mode:
 198     BOOST_CHECK_CLOSE(
 199        mode(dist)
 200        , static_cast<RealType>(7 * 3), tol2);
 201     // skewness:
 202     BOOST_CHECK_CLOSE(
 203        skewness(dist)
 204        , 2 / sqrt(static_cast<RealType>(8)), tol2);
 205     // kertosis:
 206     BOOST_CHECK_CLOSE(
 207        kurtosis(dist)
 208        , 3 + 6 / static_cast<RealType>(8), tol2);
 209     // kertosis excess:
 210     BOOST_CHECK_CLOSE(
 211        kurtosis_excess(dist)
 212        , 6 / static_cast<RealType>(8), tol2);
 213
 214     BOOST_CHECK_CLOSE(
 215        median(dist), static_cast<RealType>(23.007748327502412), // double precision test value
 216        (std::max)(tol2, static_cast<RealType>(std::numeric_limits<double>::epsilon() * 2 * 100))); // 2 eps as persent
 217     // Rely on default definition in derived accessors.
 218
 219    // error tests
 220    check_out_of_range<boost::math::gamma_distribution<RealType> >(1, 1);
 221    BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(0, 1), std::domain_error);
 222    BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(-1, 1), std::domain_error);
 223    BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, 0), std::domain_error);
 224    BOOST_MATH_CHECK_THROW(boost::math::gamma_distribution<RealType>(1, -1), std::domain_error);
 225
 226 } // template <class RealType>void test_spots(RealType)
 227
 228 BOOST_AUTO_TEST_CASE( test_main )
 229 {
 230    // Basic sanity-check spot values.
 231    // (Parameter value, arbitrarily zero, only communicates the floating point type).
 232   test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
 233   test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
 234 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 235   test_spots(0.0L); // Test long double.
 236 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
 237   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 238 #endif
 239 #else
 240    std::cout << "<note>The long double tests have been disabled on this platform "
 241       "either because the long double overloads of the usual math functions are "
 242       "not available at all, or because they are too inaccurate for these tests "
 243       "to pass.</note>" << std::endl;
 244 #endif
 245
 246
 247 } // BOOST_AUTO_TEST_CASE( test_main )
 248
 249
 250 /*
 251
 252 Output:
 253
 254 Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_gamma_dist.exe"
 255 Running 1 test case...
 256 Tolerance for type float is 0.000238419 %
 257 Tolerance for type float is 0.001 %
 258 Tolerance for type double is 5e-012 %
 259 Tolerance for type double is 0.001 %
 260 Tolerance for type long double is 5e-012 %
 261 Tolerance for type long double is 0.001 %
 262 Tolerance for type class boost::math::concepts::real_concept is 5e-012 %
 263 Tolerance for type class boost::math::concepts::real_concept is 0.001 %
 264 *** No errors detected
 265
 266 */
 267
 268