libs/math/test/test_skew_normal.cpp

   1 // Copyright Paul A. Bristow 2012.
   2 // Copyright John Maddock 2012.
   3 // Copyright Benjamin Sobotta 2012
   4
   5 // Use, modification and distribution are subject to the
   6 // Boost Software License, Version 1.0.
   7 // (See accompanying file LICENSE_1_0.txt
   8 // or copy at http://www.boost.org/LICENSE_1_0.txt)
   9
  10 #ifdef _MSC_VER
  11 #  pragma warning (disable : 4127) // conditional expression is constant.
  12 #  pragma warning (disable : 4305) // 'initializing' : truncation from 'double' to 'const float'.
  13 #  pragma warning (disable : 4310) // cast truncates constant value.
  14 #  pragma warning (disable : 4512) // assignment operator could not be generated.
  15 #endif
  16
  17 //#include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
  18
  19 #include <boost/math/concepts/real_concept.hpp> // for real_concept
  20 #include <boost/test/test_exec_monitor.hpp> // Boost.Test
  21 #include <boost/test/floating_point_comparison.hpp>
  22
  23 #include <boost/math/distributions/skew_normal.hpp>
  24 using boost::math::skew_normal_distribution;
  25 using boost::math::skew_normal;
  26
  27 #include <iostream>
  28 using std::cout;
  29 using std::endl;
  30 using std::setprecision;
  31 #include <limits>
  32 using std::numeric_limits;
  33
  34 template <class RealType>
  35 void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
  36 {
  37  using boost::math::skew_normal_distribution;
  38
  39   BOOST_CHECK_CLOSE_FRACTION(
  40     ::boost::math::cdf(   // Check cdf
  41     skew_normal_distribution<RealType>(mean, scale, shape),      // distribution.
  42     x),    // random variable.
  43     p,     // probability.
  44     tol);   // tolerance.
  45   BOOST_CHECK_CLOSE_FRACTION(
  46     ::boost::math::cdf( // Check cdf complement
  47     complement(
  48     skew_normal_distribution<RealType>(mean, scale, shape),   // distribution.
  49     x)),   // random variable.
  50     q,      // probability complement.
  51     tol);    // %tolerance.
  52   BOOST_CHECK_CLOSE_FRACTION(
  53     ::boost::math::quantile( // Check quantile
  54     skew_normal_distribution<RealType>(mean, scale, shape),    // distribution.
  55     p),   // probability.
  56     x,   // random variable.
  57     tol);   // tolerance.
  58   BOOST_CHECK_CLOSE_FRACTION(
  59     ::boost::math::quantile( // Check quantile complement
  60     complement(
  61     skew_normal_distribution<RealType>(mean, scale, shape),   // distribution.
  62     q)),   // probability complement.
  63     x,     // random variable.
  64     tol);  // tolerance.
  65
  66    skew_normal_distribution<RealType> dist (mean, scale, shape);
  67
  68    if((p < 0.999) && (q < 0.999))
  69    {  // We can only check this if P is not too close to 1,
  70       // so that we can guarantee Q is accurate:
  71       BOOST_CHECK_CLOSE_FRACTION(
  72         cdf(complement(dist, x)), q, tol); // 1 - cdf
  73       BOOST_CHECK_CLOSE_FRACTION(
  74         quantile(dist, p), x, tol); // quantile(cdf) = x
  75       BOOST_CHECK_CLOSE_FRACTION(
  76         quantile(complement(dist, q)), x, tol); // quantile(complement(1 - cdf)) = x
  77    }
  78 } // template <class RealType>void check_skew_normal()
  79
  80
  81 template <class RealType>
  82 void test_spots(RealType)
  83 {
  84    // Basic sanity checks
  85    RealType tolerance = 1e-4f; // 1e-4 (as %)
  86
  87   // Check some bad parameters to the distribution,
  88
  89    BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
  90    BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
  91
  92   // Tests on extreme values of random variate x, if has numeric_limit infinity etc.
  93     skew_normal_distribution<RealType> N01;
  94   if(std::numeric_limits<RealType>::has_infinity)
  95   {
  96     BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
  97     BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
  98     BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
  99     BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
 100     BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
 101     BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
 102     BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
 103     BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(),  static_cast<RealType>(1)), std::domain_error); // -infinite mean
 104     BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
 105   }
 106
 107   if (std::numeric_limits<RealType>::has_quiet_NaN)
 108   {
 109     // No longer allow x to be NaN, then these tests should throw.
 110     BOOST_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
 111     BOOST_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
 112     BOOST_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
 113     BOOST_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
 114     BOOST_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
 115   }
 116
 117    cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;
 118
 119    // Tests where shape = 0, so same as normal tests.
 120    // (These might be removed later).
 121    check_skew_normal(
 122       static_cast<RealType>(5),
 123       static_cast<RealType>(2),
 124       static_cast<RealType>(0),
 125       static_cast<RealType>(4.8),
 126       static_cast<RealType>(0.46017),
 127       static_cast<RealType>(1 - 0.46017),
 128       tolerance);
 129
 130    check_skew_normal(
 131       static_cast<RealType>(5),
 132       static_cast<RealType>(2),
 133       static_cast<RealType>(0),
 134       static_cast<RealType>(5.2),
 135       static_cast<RealType>(1 - 0.46017),
 136       static_cast<RealType>(0.46017),
 137       tolerance);
 138
 139    check_skew_normal(
 140       static_cast<RealType>(5),
 141       static_cast<RealType>(2),
 142       static_cast<RealType>(0),
 143       static_cast<RealType>(2.2),
 144       static_cast<RealType>(0.08076),
 145       static_cast<RealType>(1 - 0.08076),
 146       tolerance);
 147
 148    check_skew_normal(
 149       static_cast<RealType>(5),
 150       static_cast<RealType>(2),
 151       static_cast<RealType>(0),
 152       static_cast<RealType>(7.8),
 153       static_cast<RealType>(1 - 0.08076),
 154       static_cast<RealType>(0.08076),
 155       tolerance);
 156
 157    check_skew_normal(
 158       static_cast<RealType>(-3),
 159       static_cast<RealType>(5),
 160       static_cast<RealType>(0),
 161       static_cast<RealType>(-4.5),
 162       static_cast<RealType>(0.38209),
 163       static_cast<RealType>(1 - 0.38209),
 164       tolerance);
 165
 166    check_skew_normal(
 167       static_cast<RealType>(-3),
 168       static_cast<RealType>(5),
 169       static_cast<RealType>(0),
 170       static_cast<RealType>(-1.5),
 171       static_cast<RealType>(1 - 0.38209),
 172       static_cast<RealType>(0.38209),
 173       tolerance);
 174
 175    check_skew_normal(
 176       static_cast<RealType>(-3),
 177       static_cast<RealType>(5),
 178       static_cast<RealType>(0),
 179       static_cast<RealType>(-8.5),
 180       static_cast<RealType>(0.13567),
 181       static_cast<RealType>(1 - 0.13567),
 182       tolerance);
 183
 184    check_skew_normal(
 185       static_cast<RealType>(-3),
 186       static_cast<RealType>(5),
 187       static_cast<RealType>(0),
 188       static_cast<RealType>(2.5),
 189       static_cast<RealType>(1 - 0.13567),
 190       static_cast<RealType>(0.13567),
 191       tolerance);
 192
 193    // Tests where shape != 0, specific to skew_normal distribution.
 194    //void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
 195       check_skew_normal( // 1st R example.
 196       static_cast<RealType>(1.1),
 197       static_cast<RealType>(2.2),
 198       static_cast<RealType>(-3.3),
 199       static_cast<RealType>(0.4), // x
 200       static_cast<RealType>(0.733918618927874), // p == psn
 201       static_cast<RealType>(1 - 0.733918618927874), // q
 202       tolerance);
 203
 204    // Not sure about these yet.
 205       //check_skew_normal( // 2nd R example.
 206       //static_cast<RealType>(1.1),
 207       //static_cast<RealType>(0.02),
 208       //static_cast<RealType>(0.03),
 209       //static_cast<RealType>(1.3), // x
 210       //static_cast<RealType>(0.01), // p
 211       //static_cast<RealType>(0.09), // q
 212       //tolerance);
 213       //check_skew_normal( // 3nd R example.
 214       //static_cast<RealType>(10.1),
 215       //static_cast<RealType>(5.),
 216       //static_cast<RealType>(-0.03),
 217       //static_cast<RealType>(-1.3), // x
 218       //static_cast<RealType>(0.01201290665838824), // p
 219       //static_cast<RealType>(1. - 0.01201290665838824), // q 0.987987101
 220       //tolerance);
 221
 222     // Tests for PDF: we know that the normal peak value is at 1/sqrt(2*pi)
 223    //
 224    tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction
 225    BOOST_CHECK_CLOSE_FRACTION(
 226       pdf(skew_normal_distribution<RealType>(), static_cast<RealType>(0)),
 227       static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
 228       tolerance);
 229    BOOST_CHECK_CLOSE_FRACTION(
 230       pdf(skew_normal_distribution<RealType>(3), static_cast<RealType>(3)),
 231       static_cast<RealType>(0.3989422804014326779399460599343818684759L),
 232       tolerance);
 233    BOOST_CHECK_CLOSE_FRACTION(
 234       pdf(skew_normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
 235       static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
 236       tolerance);
 237
 238    // Shape != 0.
 239    BOOST_CHECK_CLOSE_FRACTION(
 240       pdf(skew_normal_distribution<RealType>(3,5,1e-6), static_cast<RealType>(3)),
 241       static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
 242       tolerance);
 243
 244
 245    // Checks on mean, variance cumulants etc.
 246    // Checks on shape ==0
 247
 248     RealType tol5 = boost::math::tools::epsilon<RealType>() * 5;
 249     skew_normal_distribution<RealType> dist(8, 3);
 250     RealType x = static_cast<RealType>(0.125);
 251
 252     BOOST_MATH_STD_USING // ADL of std math lib names
 253
 254     // mean:
 255     BOOST_CHECK_CLOSE(
 256        mean(dist)
 257        , static_cast<RealType>(8), tol5);
 258     // variance:
 259     BOOST_CHECK_CLOSE(
 260        variance(dist)
 261        , static_cast<RealType>(9), tol5);
 262     // std deviation:
 263     BOOST_CHECK_CLOSE(
 264        standard_deviation(dist)
 265        , static_cast<RealType>(3), tol5);
 266     // hazard:
 267     BOOST_CHECK_CLOSE(
 268        hazard(dist, x)
 269        , pdf(dist, x) / cdf(complement(dist, x)), tol5);
 270     // cumulative hazard:
 271     BOOST_CHECK_CLOSE(
 272        chf(dist, x)
 273        , -log(cdf(complement(dist, x))), tol5);
 274     // coefficient_of_variation:
 275     BOOST_CHECK_CLOSE(
 276        coefficient_of_variation(dist)
 277        , standard_deviation(dist) / mean(dist), tol5);
 278     // mode:
 279     BOOST_CHECK_CLOSE_FRACTION(mode(dist), static_cast<RealType>(8), 0.001);
 280
 281     BOOST_CHECK_CLOSE(
 282        median(dist)
 283        , static_cast<RealType>(8), tol5);
 284
 285     // skewness:
 286     BOOST_CHECK_CLOSE(
 287        skewness(dist)
 288        , static_cast<RealType>(0), tol5);
 289     // kurtosis:
 290     BOOST_CHECK_CLOSE(
 291        kurtosis(dist)
 292        , static_cast<RealType>(3), tol5);
 293     // kurtosis excess:
 294     BOOST_CHECK_CLOSE(
 295        kurtosis_excess(dist)
 296        , static_cast<RealType>(0), tol5);
 297
 298     skew_normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
 299     BOOST_CHECK_CLOSE(
 300        mean(norm01),
 301        static_cast<RealType>(0), 0); // Mean == zero
 302
 303     skew_normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
 304     BOOST_CHECK_CLOSE(
 305        mean(defsd_norm01),
 306        static_cast<RealType>(0), 0); // Mean == zero
 307
 308     skew_normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
 309     BOOST_CHECK_CLOSE(
 310        mean(def_norm01),
 311        static_cast<RealType>(0), 0); // Mean == zero
 312
 313     BOOST_CHECK_CLOSE(
 314        standard_deviation(def_norm01),
 315        static_cast<RealType>(1), 0);  //
 316
 317     BOOST_CHECK_CLOSE(
 318        mode(def_norm01),
 319        static_cast<RealType>(0), 0); // Mode == zero
 320
 321
 322     // Skew_normal tests with shape != 0.
 323     {
 324       //RealType tol5 = boost::math::tools::epsilon<RealType>() * 5;
 325       RealType tol100 = boost::math::tools::epsilon<RealType>() * 100;
 326       RealType tol1000 = boost::math::tools::epsilon<RealType>() * 1000;
 327
 328       //skew_normal_distribution<RealType> dist(1.1, 0.02, 0.03);
 329
 330       BOOST_MATH_STD_USING // ADL of std math lib names.
 331
 332       // Test values from R = see skew_normal_drv.cpp which included the R code used.
 333       {
 334         skew_normal_distribution<RealType> dist(static_cast<RealType>(1.1l), static_cast<RealType>(2.2l), static_cast<RealType>(-3.3l));
 335
 336         BOOST_CHECK_CLOSE(      // mean:
 337            mean(dist)
 338            , static_cast<RealType>(-0.579908992539856825862549L), tol100);
 339          BOOST_CHECK_CLOSE(      // variance:
 340           variance(dist)
 341           , static_cast<RealType>(2.0179057767837232633904L), tol100);
 342
 343         BOOST_CHECK_CLOSE(      // skewness:
 344            skewness(dist)
 345            , static_cast<RealType>(-0.709854548171537509192897824663L), tol1000);
 346         BOOST_CHECK_CLOSE(      // kurtosis:
 347            kurtosis(dist)
 348            , static_cast<RealType>(3.5538752625241790601377L), tol1000);
 349         BOOST_CHECK_CLOSE(      // kurtosis excess:
 350            kurtosis_excess(dist)
 351            , static_cast<RealType>(0.5538752625241790601377L), tol1000);
 352
 353         BOOST_CHECK_CLOSE(
 354           pdf(dist, static_cast<RealType>(0.4L)),
 355           static_cast<RealType>(0.294140110156599539564571L),
 356           tol100);
 357
 358         BOOST_CHECK_CLOSE(
 359           cdf(dist, static_cast<RealType>(0.4L)),
 360           static_cast<RealType>(0.7339186189278737976326676452L),
 361           tol1000);
 362
 363         BOOST_CHECK_CLOSE(
 364           quantile(dist, static_cast<RealType>(0.3L)),
 365           static_cast<RealType>(-1.180104068086875314419247L),
 366           tol1000);
 367
 368
 369       { // mode tests
 370
 371         skew_normal_distribution<RealType> dist(static_cast<RealType>(0.l), static_cast<RealType>(1.l), static_cast<RealType>(4.l));
 372
 373         cout << "pdf(dist, 0) = " << pdf(dist, 0) <<  ", pdf(dist, 0.45) = " << pdf(dist, 0.45) << endl;
 374        // BOOST_CHECK_CLOSE(mode(dist), boost::math::constants::root_two<RealType>() / 2, tol5);
 375         BOOST_CHECK_CLOSE(mode(dist), static_cast<RealType>(0.41697299497388863932L), tol1000);
 376       }
 377
 378
 379       }
 380       {
 381         skew_normal_distribution<RealType> dist(static_cast<RealType>(1.1l), static_cast<RealType>(0.02l), static_cast<RealType>(0.03l));
 382
 383         BOOST_CHECK_CLOSE(      // mean:
 384            mean(dist)
 385            , static_cast<RealType>(1.1004785154529557886162L), tol100);
 386         BOOST_CHECK_CLOSE(      // variance:
 387           variance(dist)
 388            , static_cast<RealType>(0.00039977102296128251645L), tol100);
 389
 390         BOOST_CHECK_CLOSE(      // skewness:
 391            skewness(dist)
 392            , static_cast<RealType>(5.8834811259890359782e-006L), tol1000);
 393         BOOST_CHECK_CLOSE(      // kurtosis:
 394            kurtosis(dist)
 395            , static_cast<RealType>(3.L + 9.2903475812137800239002e-008L), tol1000);
 396         BOOST_CHECK_CLOSE(      // kurtosis excess:
 397            kurtosis_excess(dist)
 398            , static_cast<RealType>(9.2903475812137800239002e-008L), tol1000);
 399       }
 400       {
 401         skew_normal_distribution<RealType> dist(static_cast<RealType>(10.1l), static_cast<RealType>(5.l), static_cast<RealType>(-0.03l));
 402         BOOST_CHECK_CLOSE(      // mean:
 403            mean(dist)
 404            , static_cast<RealType>(9.9803711367610528459485937L), tol100);
 405         BOOST_CHECK_CLOSE(      // variance:
 406           variance(dist)
 407            , static_cast<RealType>(24.98568893508015727823L), tol100);
 408
 409         BOOST_CHECK_CLOSE(      // skewness:
 410            skewness(dist)
 411            , static_cast<RealType>(-5.8834811259890359782085e-006L), tol1000);
 412         BOOST_CHECK_CLOSE(      // kurtosis:
 413            kurtosis(dist)
 414            , static_cast<RealType>(3.L + 9.2903475812137800239002e-008L), tol1000);
 415         BOOST_CHECK_CLOSE(      // kurtosis excess:
 416            kurtosis_excess(dist)
 417            , static_cast<RealType>(9.2903475812137800239002e-008L), tol1000);
 418       }
 419       {
 420         skew_normal_distribution<RealType> dist(static_cast<RealType>(-10.1l), static_cast<RealType>(5.l), static_cast<RealType>(30.l));
 421         BOOST_CHECK_CLOSE(      // mean:
 422            mean(dist)
 423            , static_cast<RealType>(-6.11279169674138408531365L), 2 * tol100);
 424         BOOST_CHECK_CLOSE(      // variance:
 425           variance(dist)
 426           , static_cast<RealType>(9.10216994642554914628242L), tol100 * 2);
 427
 428         BOOST_CHECK_CLOSE(      // skewness:
 429            skewness(dist)
 430            , static_cast<RealType>(0.99072425443686904424L), tol1000);
 431         BOOST_CHECK_CLOSE(      // kurtosis:
 432            kurtosis(dist)
 433            , static_cast<RealType>(3.L + 0.8638862008406084244563L), tol1000);
 434         BOOST_CHECK_CLOSE(      // kurtosis excess:
 435            kurtosis_excess(dist)
 436            , static_cast<RealType>(0.8638862008406084244563L), tol1000);
 437       }
 438
 439
 440     }
 441
 442
 443 } // template <class RealType>void test_spots(RealType)
 444
 445 int test_main(int, char* [])
 446 {
 447
 448
 449   using boost::math::skew_normal;
 450   using boost::math::skew_normal_distribution;
 451
 452   //int precision = 17; // std::numeric_limits<double::max_digits10;
 453   double tolfeweps = numeric_limits<double>::epsilon() * 5;
 454   //double tol6decdigits = numeric_limits<float>::epsilon() * 2;
 455   // Check that can generate skew_normal distribution using the two convenience methods:
 456   boost::math::skew_normal w12(1., 2); // Using typedef.
 457   boost::math::skew_normal_distribution<> w01; // Use default unity values for mean and scale.
 458   // Note NOT myn01() as the compiler will interpret as a function!
 459
 460   // Checks on constructors.
 461   // Default parameters.
 462   BOOST_CHECK_EQUAL(w01.location(), 0);
 463   BOOST_CHECK_EQUAL(w01.scale(), 1);
 464   BOOST_CHECK_EQUAL(w01.shape(), 0);
 465
 466   skew_normal_distribution<> w23(2., 3); // Using default RealType double.
 467   BOOST_CHECK_EQUAL(w23.scale(), 3);
 468   BOOST_CHECK_EQUAL(w23.shape(), 0);
 469
 470   skew_normal_distribution<> w123(1., 2., 3.); // Using default RealType double.
 471   BOOST_CHECK_EQUAL(w123.location(), 1.);
 472   BOOST_CHECK_EQUAL(w123.scale(), 2.);
 473   BOOST_CHECK_EQUAL(w123.shape(), 3.);
 474
 475   BOOST_CHECK_CLOSE_FRACTION(mean(w01), static_cast<double>(0), tolfeweps); // Default mean == zero
 476   BOOST_CHECK_CLOSE_FRACTION(scale(w01), static_cast<double>(1), tolfeweps); // Default scale == unity
 477
 478   // Basic sanity-check spot values for all floating-point types..
 479   // (Parameter value, arbitrarily zero, only communicates the floating point type).
 480   test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
 481   test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
 482 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 483   test_spots(0.0L); // Test long double.
 484 #ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
 485   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 486 #endif
 487 #else
 488   std::cout << "<note>The long double tests have been disabled on this platform "
 489     "either because the long double overloads of the usual math functions are "
 490     "not available at all, or because they are too inaccurate for these tests "
 491     "to pass.</note>" << std::cout;
 492 #endif
 493   /*      */
 494   return 0;
 495 } // int test_main(int, char* [])
 496
 497 /*
 498
 499 Output:
 500
 501
 502 */
 503
 504