libs/math/test/test_logistic_dist.cpp

   1 // Copyright 2008 Gautam Sewani
   2 // Copyright 2013 Paul A. Bristow
   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 #ifdef _MSC_VER
  10 #  pragma warning (disable : 4127) // conditional expression is constant.
  11 #  pragma warning (disable : 4512) // assignment operator could not be generated.
  12 #endif
  13
  14 #include <boost/config.hpp>
  15 #ifndef BOOST_NO_EXCEPTIONS
  16 #define BOOST_MATH_UNDERFLOW_ERROR_POLICY throw_on_error
  17 #define BOOST_MATH_OVERFLOW_ERROR_POLICY throw_on_error
  18 #endif
  19 #include <boost/math/tools/test.hpp>
  20 #include <boost/math/concepts/real_concept.hpp> // for real_concept
  21 #include <boost/math/distributions/logistic.hpp>
  22     using boost::math::logistic_distribution;
  23
  24 #define BOOST_TEST_MAIN
  25 #include <boost/test/unit_test.hpp> // Boost.Test
  26 #include <boost/test/tools/floating_point_comparison.hpp>
  27 #include "test_out_of_range.hpp"
  28
  29 #include <iostream>
  30    using std::cout;
  31    using std::endl;
  32    using std::setprecision;
  33
  34 template <class RealType>
  35 void test_spot(RealType location, RealType scale, RealType x, RealType p, RealType q, RealType tolerance)
  36 {
  37    BOOST_CHECK_CLOSE(
  38       ::boost::math::cdf(
  39       logistic_distribution<RealType>(location,scale),
  40       x),
  41       p,
  42       tolerance); // %
  43    BOOST_CHECK_CLOSE(
  44       ::boost::math::cdf(
  45       complement(logistic_distribution<RealType>(location,scale),
  46       x)),
  47       q,
  48       tolerance); // %
  49    if(p < 0.999)
  50    {
  51       BOOST_CHECK_CLOSE(
  52          ::boost::math::quantile(
  53          logistic_distribution<RealType>(location,scale),
  54          p),
  55          x,
  56          tolerance); // %
  57    }
  58    if(q < 0.999)
  59    {
  60       BOOST_CHECK_CLOSE(
  61          ::boost::math::quantile(
  62          complement(logistic_distribution<RealType>(location,scale),
  63          q)),
  64          x,
  65          2 * tolerance); // %
  66    }
  67 }
  68
  69
  70 template <class RealType>
  71 void test_spots(RealType T)
  72 {
  73    // Basic sanity checks.
  74    // 50 eps as a percentage, up to a maximum of double precision
  75    // Test data taken from Mathematica 6
  76    RealType tolerance = (std::max)(
  77       static_cast<RealType>(1e-33L),
  78       boost::math::tools::epsilon<RealType>());
  79    cout<<"Absolute tolerance:"<<tolerance<<endl;
  80
  81    tolerance *= 50 * 100;
  82    // #  pragma warning(disable: 4100) // unreferenced formal parameter.
  83    // prevent his spurious warning.
  84    if (T != 0)
  85    {
  86       cout << "Expect parameter T == 0!" << endl;
  87    }
  88    cout << "Tolerance for type " << typeid(T).name()  << " is " << tolerance << " %" << endl;
  89
  90    test_spot(
  91       static_cast<RealType>(1), // location
  92       static_cast<RealType>(0.5L), // scale
  93       static_cast<RealType>(0.1L), // x
  94       static_cast<RealType>(0.141851064900487789594278108470953L), // p
  95       static_cast<RealType>(0.858148935099512210405721891529047L), //q
  96       tolerance);
  97
  98    test_spot(
  99       static_cast<RealType>(5), // location
 100       static_cast<RealType>(2), // scale
 101       static_cast<RealType>(3.123123123L),//x
 102       static_cast<RealType>(0.281215878622547904873088053477813L), // p
 103       static_cast<RealType>(0.718784121377452095126911946522187L), //q
 104       tolerance);
 105
 106    test_spot(
 107       static_cast<RealType>(1.2345L), // location
 108       static_cast<RealType>(0.12345L), // scale
 109       static_cast<RealType>(3.123123123L),//x
 110       static_cast<RealType>(0.999999773084685079723328282229357L), // p
 111       static_cast<RealType>(2.26915314920276671717770643005212e-7L), //q
 112       tolerance);
 113
 114
 115    //High probability
 116    test_spot(
 117       static_cast<RealType>(1), // location
 118       static_cast<RealType>(0.5L), // scale
 119       static_cast<RealType>(10), // x
 120       static_cast<RealType>(0.99999998477002048723965105559179L), // p
 121       static_cast<RealType>(1.5229979512760348944408208801237e-8L), //q
 122       tolerance);
 123
 124    //negative x
 125    test_spot(
 126       static_cast<RealType>(5), // location
 127       static_cast<RealType>(2), // scale
 128       static_cast<RealType>(-0.1L), // scale
 129       static_cast<RealType>(0.0724264853615177178439235061476928L), // p
 130       static_cast<RealType>(0.927573514638482282156076493852307L), //q
 131       tolerance);
 132
 133
 134    test_spot(
 135       static_cast<RealType>(5), // location
 136       static_cast<RealType>(2), // scale
 137       static_cast<RealType>(-20), // x
 138       static_cast<RealType>(3.72663928418656138608800947863869e-6L), // p
 139       static_cast<RealType>(0.999996273360715813438613911990521L), //q
 140       tolerance);
 141
 142
 143    // Test value to check cancellation error in straight/complemented quantile.
 144    // The subtraction in the formula location-scale*log term introduces catastrophic
 145    // cancellation error if location and scale*log term are close.
 146    // For these values, the tests fail at tolerance, but work at 100*tolerance.
 147    test_spot(
 148       static_cast<RealType>(-1.2345L), // location
 149       static_cast<RealType>(1.4555L), // scale
 150       static_cast<RealType>(-0.00125796420642514024493852425918807L),// x
 151       static_cast<RealType>(0.7L), // p
 152       static_cast<RealType>(0.3L), //q
 153       80*tolerance);
 154
 155    test_spot(
 156       static_cast<RealType>(1.2345L), // location
 157       static_cast<RealType>(0.12345L), // scale
 158       static_cast<RealType>(0.0012345L), // x
 159       static_cast<RealType>(0.0000458541039469413343331170952855318L), // p
 160       static_cast<RealType>(0.999954145896053058665666882904714L), //q
 161       80*tolerance);
 162
 163
 164
 165    test_spot(
 166       static_cast<RealType>(5L), // location
 167       static_cast<RealType>(2L), // scale
 168       static_cast<RealType>(0.0012345L), // x
 169       static_cast<RealType>(0.0759014628704232983512906076564256L), // p
 170       static_cast<RealType>(0.924098537129576701648709392343574L), //q
 171       80*tolerance);
 172
 173    //negative location
 174    test_spot(
 175       static_cast<RealType>(-123.123123L), // location
 176       static_cast<RealType>(2.123L), // scale
 177       static_cast<RealType>(3), // x
 178       static_cast<RealType>(0.999999999999999999999999984171276L), // p
 179       static_cast<RealType>(1.58287236765203121622150720373972e-26L), //q
 180       tolerance);
 181    //PDF Testing
 182    BOOST_CHECK_CLOSE(
 183       ::boost::math::pdf(
 184       logistic_distribution<RealType>(5,2),
 185          static_cast<RealType>(0.125L) ),//x
 186          static_cast<RealType>(0.0369500730133475464584898192104821L),              // probability
 187       tolerance); // %
 188
 189    BOOST_CHECK_CLOSE(
 190       ::boost::math::pdf(
 191          logistic_distribution<RealType>(static_cast<RealType>(1.2345L), static_cast<RealType>(0.12345L)),
 192          static_cast<RealType>(0.0012345L) ),//x
 193          static_cast<RealType>(0.000371421639109700748742498671686243L),              // probability
 194       tolerance); // %
 195    BOOST_CHECK_CLOSE(
 196       ::boost::math::pdf(
 197       logistic_distribution<RealType>(2,1),
 198          static_cast<RealType>(2L) ),//x
 199          static_cast<RealType>(0.25L),              // probability
 200       tolerance); // %
 201
 202    //Extreme value testing
 203
 204    if(std::numeric_limits<RealType>::has_infinity)
 205    {
 206       BOOST_CHECK_EQUAL(pdf(logistic_distribution<RealType>(), +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
 207       BOOST_CHECK_EQUAL(pdf(logistic_distribution<RealType>(), -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
 208       BOOST_CHECK_EQUAL(cdf(logistic_distribution<RealType>(), +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
 209       BOOST_CHECK_EQUAL(cdf(logistic_distribution<RealType>(), -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
 210       BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution<RealType>(), +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
 211       BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution<RealType>(), -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
 212    }
 213    BOOST_MATH_CHECK_THROW(quantile(logistic_distribution<RealType>(), static_cast<RealType>(1)), std::overflow_error); // x = + infinity, cdf = 1
 214    BOOST_MATH_CHECK_THROW(quantile(logistic_distribution<RealType>(), static_cast<RealType>(0)), std::overflow_error); // x = - infinity, cdf = 0
 215    BOOST_MATH_CHECK_THROW(quantile(complement(logistic_distribution<RealType>(), static_cast<RealType>(1))), std::overflow_error); // x = - infinity, cdf = 0
 216    BOOST_MATH_CHECK_THROW(quantile(complement(logistic_distribution<RealType>(), static_cast<RealType>(0))), std::overflow_error); // x = + infinity, cdf = 1
 217    BOOST_CHECK_EQUAL(cdf(logistic_distribution<RealType>(), +boost::math::tools::max_value<RealType>()), 1); // x = + infinity, cdf = 1
 218    BOOST_CHECK_EQUAL(cdf(logistic_distribution<RealType>(), -boost::math::tools::max_value<RealType>()), 0); // x = - infinity, cdf = 0
 219    BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution<RealType>(), +boost::math::tools::max_value<RealType>())), 0); // x = + infinity, c cdf = 0
 220    BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution<RealType>(), -boost::math::tools::max_value<RealType>())), 1); // x = - infinity, c cdf = 1
 221    BOOST_CHECK_EQUAL(pdf(logistic_distribution<RealType>(), +boost::math::tools::max_value<RealType>()), 0); // x = + infinity, pdf = 0
 222    BOOST_CHECK_EQUAL(pdf(logistic_distribution<RealType>(), -boost::math::tools::max_value<RealType>()), 0); // x = - infinity, pdf = 0
 223
 224    //
 225    // Things that are errors:
 226    // 1. Domain errors for scale and location.
 227    // 2. x being NAN.
 228    // 3. Probabilies being outside (0,1).
 229    check_out_of_range<logistic_distribution<RealType> >(0, 1);
 230    if(std::numeric_limits<RealType>::has_infinity)
 231    {
 232       RealType inf = std::numeric_limits<RealType>::infinity();
 233       BOOST_CHECK_EQUAL(pdf(logistic_distribution<RealType>(0, 1), inf), 0);
 234       BOOST_CHECK_EQUAL(pdf(logistic_distribution<RealType>(0, 1), -inf), 0);
 235       BOOST_CHECK_EQUAL(cdf(logistic_distribution<RealType>(0, 1), inf), 1);
 236       BOOST_CHECK_EQUAL(cdf(logistic_distribution<RealType>(0, 1), -inf), 0);
 237       BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution<RealType>(0, 1), inf)), 0);
 238       BOOST_CHECK_EQUAL(cdf(complement(logistic_distribution<RealType>(0, 1), -inf)), 1);
 239    }
 240
 241    // location/scale can't be infinity.
 242    if(std::numeric_limits<RealType>::has_infinity)
 243    {
 244 #ifndef BOOST_NO_EXCEPTIONS
 245       BOOST_MATH_CHECK_THROW(
 246          logistic_distribution<RealType> dist(std::numeric_limits<RealType>::infinity(), 0.5),
 247          std::domain_error);
 248       BOOST_MATH_CHECK_THROW(
 249          logistic_distribution<RealType> dist(0.5, std::numeric_limits<RealType>::infinity()),
 250          std::domain_error);
 251 #else
 252       BOOST_MATH_CHECK_THROW(
 253          logistic_distribution<RealType>(std::numeric_limits<RealType>::infinity(), 0.5),
 254          std::domain_error);
 255       BOOST_MATH_CHECK_THROW(
 256          logistic_distribution<RealType>(0.5, std::numeric_limits<RealType>::infinity()),
 257          std::domain_error);
 258 #endif
 259    }
 260    // scale can't be negative or 0.
 261 #ifndef BOOST_NO_EXCEPTIONS
 262    BOOST_MATH_CHECK_THROW(
 263       logistic_distribution<RealType> dist(0.5, -0.5),
 264       std::domain_error);
 265    BOOST_MATH_CHECK_THROW(
 266       logistic_distribution<RealType> dist(0.5, 0),
 267       std::domain_error);
 268 #else
 269    BOOST_MATH_CHECK_THROW(
 270       logistic_distribution<RealType>(0.5, -0.5),
 271       std::domain_error);
 272    BOOST_MATH_CHECK_THROW(
 273       logistic_distribution<RealType>(0.5, 0),
 274       std::domain_error);
 275 #endif
 276
 277    logistic_distribution<RealType> dist(0.5, 0.5);
 278    // x can't be NaN, p can't be NaN.
 279
 280    if (std::numeric_limits<RealType>::has_quiet_NaN)
 281    {
 282       // No longer allow x to be NaN, then these tests should throw.
 283       BOOST_MATH_CHECK_THROW(pdf(dist, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
 284       BOOST_MATH_CHECK_THROW(cdf(dist, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
 285       BOOST_MATH_CHECK_THROW(cdf(complement(dist, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
 286       BOOST_MATH_CHECK_THROW(quantile(dist, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
 287       BOOST_MATH_CHECK_THROW(quantile(complement(dist, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
 288    }
 289    if (std::numeric_limits<RealType>::has_infinity)
 290    {
 291   // Added test for Trac https://svn.boost.org/trac/boost/ticket/9126#comment:1
 292      logistic_distribution<RealType> dist(0., 0.5);
 293      BOOST_CHECK_EQUAL(pdf(dist, +std::numeric_limits<RealType>::infinity()), static_cast<RealType>(0) ); // x = infinity
 294
 295    }
 296
 297
 298    // p can't be outside (0,1).
 299    BOOST_MATH_CHECK_THROW(quantile(dist, static_cast<RealType>(1.1)), std::domain_error);
 300    BOOST_MATH_CHECK_THROW(quantile(dist, static_cast<RealType>(-0.1)), std::domain_error);
 301    BOOST_MATH_CHECK_THROW(quantile(dist, static_cast<RealType>(1)), std::overflow_error);
 302    BOOST_MATH_CHECK_THROW(quantile(dist, static_cast<RealType>(0)), std::overflow_error);
 303
 304    BOOST_MATH_CHECK_THROW(quantile(complement(dist, static_cast<RealType>(1.1))), std::domain_error);
 305    BOOST_MATH_CHECK_THROW(quantile(complement(dist, static_cast<RealType>(-0.1))), std::domain_error);
 306    BOOST_MATH_CHECK_THROW(quantile(complement(dist, static_cast<RealType>(1))), std::overflow_error);
 307    BOOST_MATH_CHECK_THROW(quantile(complement(dist, static_cast<RealType>(0))), std::overflow_error);
 308
 309    // Tests for mean,mode,median,variance,skewness,kurtosis.
 310    //mean
 311    BOOST_CHECK_CLOSE(
 312       ::boost::math::mean(
 313       logistic_distribution<RealType>(2,1)
 314       ),//x
 315       static_cast<RealType>(2),              // probability
 316       tolerance); // %
 317    //median
 318    BOOST_CHECK_CLOSE(
 319       ::boost::math::median(
 320       logistic_distribution<RealType>(2,1)
 321       ),//x
 322       static_cast<RealType>(2),              // probability
 323       tolerance);
 324    //mode
 325    BOOST_CHECK_CLOSE(
 326       ::boost::math::mode(
 327       logistic_distribution<RealType>(2,1)
 328       ),//x
 329       static_cast<RealType>(2),              // probability
 330       tolerance);
 331    //variance
 332    BOOST_CHECK_CLOSE(
 333       ::boost::math::variance(
 334       logistic_distribution<RealType>(2,1)
 335       ),//x
 336       static_cast<RealType>(3.28986813369645287294483033329205L),  // probability
 337       tolerance);
 338    //skewness
 339    BOOST_CHECK_CLOSE(
 340       ::boost::math::skewness(
 341       logistic_distribution<RealType>(2,1)
 342       ),//x
 343       static_cast<RealType>(0),              // probability
 344       tolerance);
 345    BOOST_CHECK_CLOSE(
 346       ::boost::math::kurtosis_excess(
 347       logistic_distribution<RealType>(2,1)
 348       ),//x
 349       static_cast<RealType>(1.2L),              // probability
 350       tolerance);
 351
 352 } // template <class RealType>void test_spots(RealType)
 353
 354
 355 BOOST_AUTO_TEST_CASE( test_main )
 356 {
 357   // Check that can generate logistic distribution using the two convenience methods:
 358    boost::math::logistic mycexp1(1.); // Using typedef
 359    logistic_distribution<> myexp2(1.); // Using default RealType double.
 360
 361    // Basic sanity-check spot values.
 362    // (Parameter value, arbitrarily zero, only communicates the floating point type).
 363   test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
 364   test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
 365 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 366   test_spots(0.0L); // Test long double.
 367 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
 368   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 369 #endif
 370 #else
 371    std::cout << "<note>The long double tests have been disabled on this platform "
 372       "either because the long double overloads of the usual math functions are "
 373       "not available at all, or because they are too inaccurate for these tests "
 374       "to pass.</note>" << std::endl;
 375 #endif
 376
 377 } // BOOST_AUTO_TEST_CASE( test_main )
 378