libs/math/test/test_extreme_value.cpp

   1 // Copyright John Maddock 2006.
   2
   3 // Use, modification and distribution are subject to the
   4 // Boost Software License, Version 1.0.
   5 // (See accompanying file LICENSE_1_0.txt
   6 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   7
   8 // test_extreme_value.cpp
   9
  10 #include <boost/math/tools/test.hpp>
  11 #include <boost/math/concepts/real_concept.hpp> // for real_concept
  12 #include <boost/math/distributions/extreme_value.hpp>
  13     using boost::math::extreme_value_distribution;
  14
  15 #define BOOST_TEST_MAIN
  16 #include <boost/test/unit_test.hpp> // Boost.Test
  17 #include <boost/test/tools/floating_point_comparison.hpp>
  18 #include "test_out_of_range.hpp"
  19
  20 #include <iostream>
  21    using std::cout;
  22    using std::endl;
  23    using std::setprecision;
  24
  25 template <class RealType>
  26 void test_spot(RealType a, RealType b, RealType x, RealType p, RealType q, RealType tolerance)
  27 {
  28    BOOST_CHECK_CLOSE(
  29       ::boost::math::cdf(
  30          extreme_value_distribution<RealType>(a, b),
  31          x),
  32          p,
  33          tolerance); // %
  34    BOOST_CHECK_CLOSE(
  35       ::boost::math::cdf(
  36          complement(extreme_value_distribution<RealType>(a, b),
  37          x)),
  38          q,
  39          tolerance); // %
  40    if((p < 0.999) && (p > 0))
  41    {
  42       BOOST_CHECK_CLOSE(
  43          ::boost::math::quantile(
  44             extreme_value_distribution<RealType>(a, b),
  45             p),
  46             x,
  47             tolerance); // %
  48    }
  49    if((q < 0.999) && (q > 0))
  50    {
  51       BOOST_CHECK_CLOSE(
  52          ::boost::math::quantile(
  53             complement(extreme_value_distribution<RealType>(a, b),
  54             q)),
  55             x,
  56             tolerance); // %
  57    }
  58 }
  59
  60 template <class RealType>
  61 void test_spots(RealType)
  62 {
  63    // Basic sanity checks.
  64    // 50eps as a percentage, up to a maximum of double precision
  65    // (that's the limit of our test data).
  66    RealType tolerance = (std::max)(
  67       static_cast<RealType>(boost::math::tools::epsilon<double>()),
  68       boost::math::tools::epsilon<RealType>());
  69    tolerance *= 50 * 100;
  70
  71    cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;
  72
  73    // Results calculated by punching numbers into a calculator,
  74    // and using the formula at http://mathworld.wolfram.com/ExtremeValueDistribution.html
  75    test_spot(
  76       static_cast<RealType>(0.5), // a
  77       static_cast<RealType>(1.5), // b
  78       static_cast<RealType>(0.125), // x
  79       static_cast<RealType>(0.27692033409990891617007608217222L), // p
  80       static_cast<RealType>(0.72307966590009108382992391782778L), //q
  81       tolerance);
  82    test_spot(
  83       static_cast<RealType>(0.5), // a
  84       static_cast<RealType>(2), // b
  85       static_cast<RealType>(-5), // x
  86       static_cast<RealType>(1.6087601139887776413169427645933e-7L), // p
  87       static_cast<RealType>(0.99999983912398860112223586830572L), //q
  88       tolerance);
  89    test_spot(
  90       static_cast<RealType>(0.5), // a
  91       static_cast<RealType>(0.25), // b
  92       static_cast<RealType>(0.75), // x
  93       static_cast<RealType>(0.69220062755534635386542199718279L), // p
  94       static_cast<RealType>(0.30779937244465364613457800281721), //q
  95       tolerance);
  96    test_spot(
  97       static_cast<RealType>(0.5), // a
  98       static_cast<RealType>(0.25), // b
  99       static_cast<RealType>(5), // x
 100       static_cast<RealType>(0.99999998477002037126351248727041L), // p
 101       static_cast<RealType>(1.5229979628736487512729586276294e-8L), //q
 102       tolerance);
 103
 104    BOOST_CHECK_CLOSE(
 105       ::boost::math::pdf(
 106          extreme_value_distribution<RealType>(0.5, 2),
 107          static_cast<RealType>(0.125)),              // x
 108          static_cast<RealType>(0.18052654830890205978204427757846L),                // probability.
 109          tolerance); // %
 110    BOOST_CHECK_CLOSE(
 111       ::boost::math::pdf(
 112          extreme_value_distribution<RealType>(1, 3),
 113          static_cast<RealType>(5)),              // x
 114          static_cast<RealType>(0.0675057324099851209129017326286L),                // probability.
 115          tolerance); // %
 116    BOOST_CHECK_CLOSE(
 117       ::boost::math::pdf(
 118          extreme_value_distribution<RealType>(1, 3),
 119          static_cast<RealType>(0)),              // x
 120          static_cast<RealType>(0.11522236828583456431277265757312L),                // probability.
 121          tolerance); // %
 122
 123    BOOST_CHECK_CLOSE(
 124       ::boost::math::mean(
 125          extreme_value_distribution<RealType>(2, 3)),
 126          static_cast<RealType>(3.731646994704598581819536270246L),
 127          tolerance); // %
 128    BOOST_CHECK_CLOSE(
 129       ::boost::math::standard_deviation(
 130          extreme_value_distribution<RealType>(1, 0.5)),
 131          static_cast<RealType>(0.6412749150809320477720181798355L),
 132          tolerance); // %
 133    BOOST_CHECK_CLOSE(
 134       ::boost::math::mode(
 135          extreme_value_distribution<RealType>(2, 3)),
 136          static_cast<RealType>(2),
 137          tolerance); // %
 138    BOOST_CHECK_CLOSE(
 139       ::boost::math::median(
 140          extreme_value_distribution<RealType>(0, 1)),
 141          static_cast<RealType>(+0.36651292058166432701243915823266946945426344783710526305367771367056),
 142          tolerance); // %
 143
 144    BOOST_CHECK_CLOSE(
 145       ::boost::math::skewness(
 146          extreme_value_distribution<RealType>(2, 3)),
 147          static_cast<RealType>(1.1395470994046486574927930193898461120875997958366L),
 148          tolerance); // %
 149    BOOST_CHECK_CLOSE(
 150       ::boost::math::kurtosis(
 151          extreme_value_distribution<RealType>(2, 3)),
 152          static_cast<RealType>(5.4),
 153          tolerance); // %
 154    BOOST_CHECK_CLOSE(
 155       ::boost::math::kurtosis_excess(
 156          extreme_value_distribution<RealType>(2, 3)),
 157          static_cast<RealType>(2.4),
 158          tolerance); // %
 159
 160    //
 161    // Things that are errors:
 162    //
 163    extreme_value_distribution<RealType> dist(0.5, 2);
 164    BOOST_MATH_CHECK_THROW(
 165        quantile(dist, RealType(1.0)),
 166        std::overflow_error);
 167    BOOST_MATH_CHECK_THROW(
 168        quantile(complement(dist, RealType(0.0))),
 169        std::overflow_error);
 170    BOOST_MATH_CHECK_THROW(
 171        quantile(dist, RealType(0.0)),
 172        std::overflow_error);
 173    BOOST_MATH_CHECK_THROW(
 174        quantile(complement(dist, RealType(1.0))),
 175        std::overflow_error);
 176    BOOST_MATH_CHECK_THROW(
 177        cdf(extreme_value_distribution<RealType>(0, -1), RealType(1)),
 178        std::domain_error);
 179    BOOST_MATH_CHECK_THROW(
 180        quantile(dist, RealType(-1)),
 181        std::domain_error);
 182    BOOST_MATH_CHECK_THROW(
 183        quantile(dist, RealType(2)),
 184        std::domain_error);
 185    check_out_of_range<extreme_value_distribution<RealType> >(1, 2);
 186    if(std::numeric_limits<RealType>::has_infinity)
 187    {
 188       RealType inf = std::numeric_limits<RealType>::infinity();
 189       BOOST_CHECK_EQUAL(pdf(extreme_value_distribution<RealType>(), -inf), 0);
 190       BOOST_CHECK_EQUAL(pdf(extreme_value_distribution<RealType>(), inf), 0);
 191       BOOST_CHECK_EQUAL(cdf(extreme_value_distribution<RealType>(), -inf), 0);
 192       BOOST_CHECK_EQUAL(cdf(extreme_value_distribution<RealType>(), inf), 1);
 193       BOOST_CHECK_EQUAL(cdf(complement(extreme_value_distribution<RealType>(), -inf)), 1);
 194       BOOST_CHECK_EQUAL(cdf(complement(extreme_value_distribution<RealType>(), inf)), 0);
 195    }
 196    //
 197    // Bug reports:
 198    //
 199    // https://svn.boost.org/trac/boost/ticket/10938:
 200    BOOST_CHECK_CLOSE(
 201    ::boost::math::pdf(
 202       extreme_value_distribution<RealType>(0, 1),
 203       static_cast<RealType>(-1000)),              // x
 204       static_cast<RealType>(0),                // probability.
 205       tolerance); // %
 206
 207 } // template <class RealType>void test_spots(RealType)
 208
 209 BOOST_AUTO_TEST_CASE( test_main )
 210 {
 211
 212   // Check that can generate extreme_value distribution using the two convenience methods:
 213    boost::math::extreme_value mycev1(1.); // Using typedef
 214    extreme_value_distribution<> myev2(1.); // Using default RealType double.
 215
 216     // Basic sanity-check spot values.
 217    // (Parameter value, arbitrarily zero, only communicates the floating point type).
 218   test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
 219   test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
 220 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 221   test_spots(0.0L); // Test long double.
 222 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
 223   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 224 #endif
 225 #else
 226    std::cout << "<note>The long double tests have been disabled on this platform "
 227       "either because the long double overloads of the usual math functions are "
 228       "not available at all, or because they are too inaccurate for these tests "
 229       "to pass.</note>" << std::endl;
 230 #endif
 231
 232
 233 } // BOOST_AUTO_TEST_CASE( test_main )
 234
 235 /*
 236
 237 Output is:
 238
 239 -Running 1 test case...
 240 Tolerance for type float is 0.000596046 %
 241 Tolerance for type double is 1.11022e-012 %
 242 Tolerance for type long double is 1.11022e-012 %
 243 Tolerance for type class boost::math::concepts::real_concept is 1.11022e-012 %
 244 *** No errors detected
 245 */
 246
 247