libs/math/test/test_beta_dist.cpp

   1 // test_beta_dist.cpp
   2
   3 // Copyright John Maddock 2006.
   4 // Copyright  Paul A. Bristow 2007, 2009, 2010, 2012.
   5
   6 // Use, modification and distribution are subject to the
   7 // Boost Software License, Version 1.0.
   8 // (See accompanying file LICENSE_1_0.txt
   9 // or copy at http://www.boost.org/LICENSE_1_0.txt)
  10
  11 // Basic sanity tests for the beta Distribution.
  12
  13 // http://members.aol.com/iandjmsmith/BETAEX.HTM  beta distribution calculator
  14 // Appreas to be a 64-bit calculator showing 17 decimal digit (last is noisy).
  15 // Similar to mathCAD?
  16
  17 // http://www.nuhertz.com/statmat/distributions.html#Beta
  18 // Pretty graphs and explanations for most distributions.
  19
  20 // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp
  21 // provided 40 decimal digits accuracy incomplete beta aka beta regularized == cdf
  22
  23 // http://www.ausvet.com.au/pprev/content.php?page=PPscript
  24 // mode 0.75    5/95% 0.9    alpha 7.39    beta 3.13
  25 // http://www.epi.ucdavis.edu/diagnostictests/betabuster.html
  26 // Beta Buster also calculates alpha and beta from mode & percentile estimates.
  27 // This is NOT (yet) implemented.
  28
  29 #ifdef _MSC_VER
  30 #  pragma warning(disable: 4127) // conditional expression is constant.
  31 # pragma warning (disable : 4996) // POSIX name for this item is deprecated.
  32 # pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'arg' was previously defined as a type.
  33 #endif
  34
  35 #include <boost/math/concepts/real_concept.hpp> // for real_concept
  36 using ::boost::math::concepts::real_concept;
  37
  38 #include <boost/math/distributions/beta.hpp> // for beta_distribution
  39 using boost::math::beta_distribution;
  40 using boost::math::beta;
  41
  42 #define BOOST_TEST_MAIN
  43 #include <boost/test/unit_test.hpp> // for test_main
  44 #include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION
  45
  46 #include "test_out_of_range.hpp"
  47
  48 #include <iostream>
  49 using std::cout;
  50 using std::endl;
  51 #include <limits>
  52 using std::numeric_limits;
  53
  54 template <class RealType>
  55 void test_spot(
  56      RealType a,    // alpha a
  57      RealType b,    // beta b
  58      RealType x,    // Probability
  59      RealType P,    // CDF of beta(a, b)
  60      RealType Q,    // Complement of CDF
  61      RealType tol)  // Test tolerance.
  62 {
  63    boost::math::beta_distribution<RealType> abeta(a, b);
  64    BOOST_CHECK_CLOSE_FRACTION(cdf(abeta, x), P, tol);
  65    if((P < 0.99) && (Q < 0.99))
  66    {  // We can only check this if P is not too close to 1,
  67       // so that we can guarantee that Q is free of error,
  68       // (and similarly for Q)
  69       BOOST_CHECK_CLOSE_FRACTION(
  70          cdf(complement(abeta, x)), Q, tol);
  71       if(x != 0)
  72       {
  73          BOOST_CHECK_CLOSE_FRACTION(
  74             quantile(abeta, P), x, tol);
  75       }
  76       else
  77       {
  78          // Just check quantile is very small:
  79          if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent)
  80            && (boost::is_floating_point<RealType>::value))
  81          {
  82             // Limit where this is checked: if exponent range is very large we may
  83             // run out of iterations in our root finding algorithm.
  84             BOOST_CHECK(quantile(abeta, P) < boost::math::tools::epsilon<RealType>() * 10);
  85          }
  86       } // if k
  87       if(x != 0)
  88       {
  89          BOOST_CHECK_CLOSE_FRACTION(quantile(complement(abeta, Q)), x, tol);
  90       }
  91       else
  92       {  // Just check quantile is very small:
  93          if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
  94          {  // Limit where this is checked: if exponent range is very large we may
  95             // run out of iterations in our root finding algorithm.
  96             BOOST_CHECK(quantile(complement(abeta, Q)) < boost::math::tools::epsilon<RealType>() * 10);
  97          }
  98       } // if x
  99       // Estimate alpha & beta from mean and variance:
 100
 101       BOOST_CHECK_CLOSE_FRACTION(
 102          beta_distribution<RealType>::find_alpha(mean(abeta), variance(abeta)),
 103          abeta.alpha(), tol);
 104       BOOST_CHECK_CLOSE_FRACTION(
 105          beta_distribution<RealType>::find_beta(mean(abeta), variance(abeta)),
 106          abeta.beta(), tol);
 107
 108       // Estimate sample alpha and beta from others:
 109       BOOST_CHECK_CLOSE_FRACTION(
 110          beta_distribution<RealType>::find_alpha(abeta.beta(), x, P),
 111          abeta.alpha(), tol);
 112       BOOST_CHECK_CLOSE_FRACTION(
 113          beta_distribution<RealType>::find_beta(abeta.alpha(), x, P),
 114          abeta.beta(), tol);
 115    } // if((P < 0.99) && (Q < 0.99)
 116
 117 } // template <class RealType> void test_spot
 118
 119 template <class RealType> // Any floating-point type RealType.
 120 void test_spots(RealType)
 121 {
 122   // Basic sanity checks with 'known good' values.
 123   // MathCAD test data is to double precision only,
 124   // so set tolerance to 100 eps expressed as a fraction, or
 125   // 100 eps of type double expressed as a fraction,
 126   // whichever is the larger.
 127
 128   RealType tolerance = (std::max)
 129       (boost::math::tools::epsilon<RealType>(),
 130       static_cast<RealType>(std::numeric_limits<double>::epsilon())); // 0 if real_concept.
 131
 132    cout << "Boost::math::tools::epsilon = " << boost::math::tools::epsilon<RealType>() <<endl;
 133    cout << "std::numeric_limits::epsilon = " << std::numeric_limits<RealType>::epsilon() <<endl;
 134    cout << "epsilon = " << tolerance;
 135
 136    tolerance *= 100000; // Note: NO * 100 because is fraction, NOT %.
 137    cout  << ", Tolerance = " << tolerance * 100 << "%." << endl;
 138
 139   // RealType teneps = boost::math::tools::epsilon<RealType>() * 10;
 140
 141   // Sources of spot test values:
 142
 143   // MathCAD defines dbeta(x, s1, s2) pdf, s1 == alpha, s2 = beta, x = x in Wolfram
 144   // pbeta(x, s1, s2) cdf and qbeta(x, s1, s2) inverse of cdf
 145   // returns pr(X ,= x) when random variable X
 146   // has the beta distribution with parameters s1)alpha) and s2(beta).
 147   // s1 > 0 and s2 >0 and 0 < x < 1 (but allows x == 0! and x == 1!)
 148   // dbeta(0,1,1) = 0
 149   // dbeta(0.5,1,1) = 1
 150
 151   using boost::math::beta_distribution;
 152   using  ::boost::math::cdf;
 153   using  ::boost::math::pdf;
 154
 155   // Tests that should throw:
 156   BOOST_CHECK_THROW(mode(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))), std::domain_error);
 157   // mode is undefined, and throws domain_error!
 158
 159  // BOOST_CHECK_THROW(median(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))), std::domain_error);
 160   // median is undefined, and throws domain_error!
 161   // But now median IS provided via derived accessor as quantile(half).
 162
 163
 164   BOOST_CHECK_THROW( // For various bad arguments.
 165        pdf(
 166           beta_distribution<RealType>(static_cast<RealType>(-1), static_cast<RealType>(1)), // bad alpha < 0.
 167           static_cast<RealType>(1)), std::domain_error);
 168
 169   BOOST_CHECK_THROW(
 170        pdf(
 171           beta_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1)), // bad alpha == 0.
 172           static_cast<RealType>(1)), std::domain_error);
 173
 174   BOOST_CHECK_THROW(
 175        pdf(
 176           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(0)), // bad beta == 0.
 177           static_cast<RealType>(1)), std::domain_error);
 178
 179   BOOST_CHECK_THROW(
 180        pdf(
 181           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(-1)), // bad beta < 0.
 182           static_cast<RealType>(1)), std::domain_error);
 183
 184   BOOST_CHECK_THROW(
 185        pdf(
 186           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // bad x < 0.
 187           static_cast<RealType>(-1)), std::domain_error);
 188
 189   BOOST_CHECK_THROW(
 190        pdf(
 191           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // bad x > 1.
 192           static_cast<RealType>(999)), std::domain_error);
 193
 194   // Some exact pdf values.
 195
 196   BOOST_CHECK_EQUAL( // a = b = 1 is uniform distribution.
 197      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 198      static_cast<RealType>(1)),  // x
 199      static_cast<RealType>(1));
 200   BOOST_CHECK_EQUAL(
 201      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 202      static_cast<RealType>(0)),  // x
 203      static_cast<RealType>(1));
 204   BOOST_CHECK_CLOSE_FRACTION(
 205      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 206      static_cast<RealType>(0.5)),  // x
 207      static_cast<RealType>(1),
 208      tolerance);
 209
 210   BOOST_CHECK_EQUAL(
 211      beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)).alpha(),
 212      static_cast<RealType>(1) ); //
 213
 214   BOOST_CHECK_EQUAL(
 215      mean(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))),
 216      static_cast<RealType>(0.5) ); // Exact one half.
 217
 218   BOOST_CHECK_CLOSE_FRACTION(
 219      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 220      static_cast<RealType>(0.5)),  // x
 221      static_cast<RealType>(1.5), // Exactly 3/2
 222       tolerance);
 223
 224   BOOST_CHECK_CLOSE_FRACTION(
 225      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 226      static_cast<RealType>(0.5)),  // x
 227      static_cast<RealType>(1.5), // Exactly 3/2
 228       tolerance);
 229
 230   // CDF
 231   BOOST_CHECK_CLOSE_FRACTION(
 232      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 233      static_cast<RealType>(0.1)),  // x
 234      static_cast<RealType>(0.02800000000000000000000000000000000000000L), // Seems exact.
 235      // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.1&a=2&b=2&digits=40
 236       tolerance);
 237
 238   BOOST_CHECK_CLOSE_FRACTION(
 239      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 240      static_cast<RealType>(0.0001)),  // x
 241      static_cast<RealType>(2.999800000000000000000000000000000000000e-8L),
 242      // http://members.aol.com/iandjmsmith/BETAEX.HTM 2.9998000000004
 243      // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.0001&a=2&b=2&digits=40
 244       tolerance);
 245
 246
 247   BOOST_CHECK_CLOSE_FRACTION(
 248      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 249      static_cast<RealType>(0.0001)),  // x
 250      static_cast<RealType>(0.0005999400000000004L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
 251      // Slightly higher tolerance for real concept:
 252      (std::numeric_limits<RealType>::is_specialized ? 1 : 10) * tolerance);
 253
 254
 255   BOOST_CHECK_CLOSE_FRACTION(
 256      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 257      static_cast<RealType>(0.9999)),  // x
 258      static_cast<RealType>(0.999999970002L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
 259      // Wolfram 0.9999999700020000000000000000000000000000
 260       tolerance);
 261
 262   BOOST_CHECK_CLOSE_FRACTION(
 263      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(2)),
 264      static_cast<RealType>(0.9)),  // x
 265      static_cast<RealType>(0.9961174629530394895796514664963063381217L),
 266      // Wolfram
 267       tolerance);
 268
 269   BOOST_CHECK_CLOSE_FRACTION(
 270      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 271      static_cast<RealType>(0.1)),  // x
 272      static_cast<RealType>(0.2048327646991334516491978475505189480977L),
 273      // Wolfram
 274       tolerance);
 275
 276   BOOST_CHECK_CLOSE_FRACTION(
 277      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 278      static_cast<RealType>(0.9)),  // x
 279      static_cast<RealType>(0.7951672353008665483508021524494810519023L),
 280      // Wolfram
 281       tolerance);
 282
 283   BOOST_CHECK_CLOSE_FRACTION(
 284      quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 285      static_cast<RealType>(0.7951672353008665483508021524494810519023L)),  // x
 286      static_cast<RealType>(0.9),
 287      // Wolfram
 288      tolerance);
 289
 290   BOOST_CHECK_CLOSE_FRACTION(
 291      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 292      static_cast<RealType>(0.6)),  // x
 293      static_cast<RealType>(0.5640942168489749316118742861695149357858L),
 294      // Wolfram
 295       tolerance);
 296
 297   BOOST_CHECK_CLOSE_FRACTION(
 298      quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 299      static_cast<RealType>(0.5640942168489749316118742861695149357858L)),  // x
 300      static_cast<RealType>(0.6),
 301      // Wolfram
 302       tolerance);
 303
 304
 305   BOOST_CHECK_CLOSE_FRACTION(
 306      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
 307      static_cast<RealType>(0.6)),  // x
 308      static_cast<RealType>(0.1778078083562213736802876784474931812329L),
 309      // Wolfram
 310       tolerance);
 311
 312   BOOST_CHECK_CLOSE_FRACTION(
 313      quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
 314      static_cast<RealType>(0.1778078083562213736802876784474931812329L)),  // x
 315      static_cast<RealType>(0.6),
 316      // Wolfram
 317       tolerance); // gives
 318
 319   BOOST_CHECK_CLOSE_FRACTION(
 320      cdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 321      static_cast<RealType>(0.1)),  // x
 322      static_cast<RealType>(0.1),  // 0.1000000000000000000000000000000000000000
 323      // Wolfram
 324       tolerance);
 325
 326   BOOST_CHECK_CLOSE_FRACTION(
 327      quantile(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 328      static_cast<RealType>(0.1)),  // x
 329      static_cast<RealType>(0.1),  // 0.1000000000000000000000000000000000000000
 330      // Wolfram
 331       tolerance);
 332
 333   BOOST_CHECK_CLOSE_FRACTION(
 334      cdf(complement(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 335      static_cast<RealType>(0.1))),  // complement of x
 336      static_cast<RealType>(0.7951672353008665483508021524494810519023L),
 337      // Wolfram
 338       tolerance);
 339
 340     BOOST_CHECK_CLOSE_FRACTION(
 341      quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 342      static_cast<RealType>(0.0280000000000000000000000000000000000L)),  // x
 343      static_cast<RealType>(0.1),
 344      // Wolfram
 345       tolerance);
 346
 347
 348   BOOST_CHECK_CLOSE_FRACTION(
 349      cdf(complement(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 350      static_cast<RealType>(0.1))),  // x
 351      static_cast<RealType>(0.9720000000000000000000000000000000000000L), // Exact.
 352      // Wolfram
 353       tolerance);
 354
 355   BOOST_CHECK_CLOSE_FRACTION(
 356      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 357      static_cast<RealType>(0.9999)),  // x
 358      static_cast<RealType>(0.0005999399999999344L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
 359       tolerance*10); // Note loss of precision calculating 1-p test value.
 360
 361   //void test_spot(
 362   //   RealType a,    // alpha a
 363   //   RealType b,    // beta b
 364   //   RealType x,    // Probability
 365   //   RealType P,    // CDF of beta(a, b)
 366   //   RealType Q,    // Complement of CDF
 367   //   RealType tol)  // Test tolerance.
 368
 369    // These test quantiles and complements, and parameter estimates as well.
 370   // Spot values using, for example:
 371   // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.1&a=0.5&b=3&digits=40
 372
 373   test_spot(
 374      static_cast<RealType>(1),   // alpha a
 375      static_cast<RealType>(1),   // beta b
 376      static_cast<RealType>(0.1), // Probability  p
 377      static_cast<RealType>(0.1), // Probability of result (CDF of beta), P
 378      static_cast<RealType>(0.9),  // Complement of CDF Q = 1 - P
 379      tolerance); // Test tolerance.
 380   test_spot(
 381      static_cast<RealType>(2),   // alpha a
 382      static_cast<RealType>(2),   // beta b
 383      static_cast<RealType>(0.1), // Probability  p
 384      static_cast<RealType>(0.0280000000000000000000000000000000000L), // Probability of result (CDF of beta), P
 385      static_cast<RealType>(1 - 0.0280000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
 386      tolerance); // Test tolerance.
 387
 388
 389   test_spot(
 390      static_cast<RealType>(2),   // alpha a
 391      static_cast<RealType>(2),   // beta b
 392      static_cast<RealType>(0.5), // Probability  p
 393      static_cast<RealType>(0.5), // Probability of result (CDF of beta), P
 394      static_cast<RealType>(0.5),  // Complement of CDF Q = 1 - P
 395      tolerance); // Test tolerance.
 396
 397   test_spot(
 398      static_cast<RealType>(2),   // alpha a
 399      static_cast<RealType>(2),   // beta b
 400      static_cast<RealType>(0.9), // Probability  p
 401      static_cast<RealType>(0.972000000000000), // Probability of result (CDF of beta), P
 402      static_cast<RealType>(1-0.972000000000000),  // Complement of CDF Q = 1 - P
 403      tolerance); // Test tolerance.
 404
 405   test_spot(
 406      static_cast<RealType>(2),   // alpha a
 407      static_cast<RealType>(2),   // beta b
 408      static_cast<RealType>(0.01), // Probability  p
 409      static_cast<RealType>(0.0002980000000000000000000000000000000000000L), // Probability of result (CDF of beta), P
 410      static_cast<RealType>(1-0.0002980000000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
 411      tolerance); // Test tolerance.
 412
 413   test_spot(
 414      static_cast<RealType>(2),   // alpha a
 415      static_cast<RealType>(2),   // beta b
 416      static_cast<RealType>(0.001), // Probability  p
 417      static_cast<RealType>(2.998000000000000000000000000000000000000E-6L), // Probability of result (CDF of beta), P
 418      static_cast<RealType>(1-2.998000000000000000000000000000000000000E-6L),  // Complement of CDF Q = 1 - P
 419      tolerance); // Test tolerance.
 420
 421   test_spot(
 422      static_cast<RealType>(2),   // alpha a
 423      static_cast<RealType>(2),   // beta b
 424      static_cast<RealType>(0.0001), // Probability  p
 425      static_cast<RealType>(2.999800000000000000000000000000000000000E-8L), // Probability of result (CDF of beta), P
 426      static_cast<RealType>(1-2.999800000000000000000000000000000000000E-8L),  // Complement of CDF Q = 1 - P
 427      tolerance); // Test tolerance.
 428
 429   test_spot(
 430      static_cast<RealType>(2),   // alpha a
 431      static_cast<RealType>(2),   // beta b
 432      static_cast<RealType>(0.99), // Probability  p
 433      static_cast<RealType>(0.9997020000000000000000000000000000000000L), // Probability of result (CDF of beta), P
 434      static_cast<RealType>(1-0.9997020000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
 435      tolerance); // Test tolerance.
 436
 437   test_spot(
 438      static_cast<RealType>(0.5),   // alpha a
 439      static_cast<RealType>(2),   // beta b
 440      static_cast<RealType>(0.5), // Probability  p
 441      static_cast<RealType>(0.8838834764831844055010554526310612991060L), // Probability of result (CDF of beta), P
 442      static_cast<RealType>(1-0.8838834764831844055010554526310612991060L),  // Complement of CDF Q = 1 - P
 443      tolerance); // Test tolerance.
 444
 445   test_spot(
 446      static_cast<RealType>(0.5),   // alpha a
 447      static_cast<RealType>(3.),   // beta b
 448      static_cast<RealType>(0.7), // Probability  p
 449      static_cast<RealType>(0.9903963064097119299191611355232156905687L), // Probability of result (CDF of beta), P
 450      static_cast<RealType>(1-0.9903963064097119299191611355232156905687L),  // Complement of CDF Q = 1 - P
 451      tolerance); // Test tolerance.
 452
 453   test_spot(
 454      static_cast<RealType>(0.5),   // alpha a
 455      static_cast<RealType>(3.),   // beta b
 456      static_cast<RealType>(0.1), // Probability  p
 457      static_cast<RealType>(0.5545844446520295253493059553548880128511L), // Probability of result (CDF of beta), P
 458      static_cast<RealType>(1-0.5545844446520295253493059553548880128511L),  // Complement of CDF Q = 1 - P
 459      tolerance); // Test tolerance.
 460
 461     //
 462    // Error checks:
 463    // Construction with 'bad' parameters.
 464    BOOST_CHECK_THROW(beta_distribution<RealType>(1, -1), std::domain_error);
 465    BOOST_CHECK_THROW(beta_distribution<RealType>(-1, 1), std::domain_error);
 466    BOOST_CHECK_THROW(beta_distribution<RealType>(1, 0), std::domain_error);
 467    BOOST_CHECK_THROW(beta_distribution<RealType>(0, 1), std::domain_error);
 468
 469    beta_distribution<> dist;
 470    BOOST_CHECK_THROW(pdf(dist, -1), std::domain_error);
 471    BOOST_CHECK_THROW(cdf(dist, -1), std::domain_error);
 472    BOOST_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
 473    BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error);
 474    BOOST_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
 475    BOOST_CHECK_THROW(quantile(dist, -1), std::domain_error);
 476    BOOST_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
 477
 478  // No longer allow any parameter to be NaN or inf, so all these tests should throw.
 479    if (std::numeric_limits<RealType>::has_quiet_NaN)
 480    {
 481     // Attempt to construct from non-finite should throw.
 482      RealType nan = std::numeric_limits<RealType>::quiet_NaN();
 483      BOOST_CHECK_THROW(beta_distribution<RealType> w(nan), std::domain_error);
 484      BOOST_CHECK_THROW(beta_distribution<RealType> w(1, nan), std::domain_error);
 485
 486     // Non-finite parameters should throw.
 487      beta_distribution<RealType> w(RealType(1));
 488      BOOST_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN
 489      BOOST_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN
 490      BOOST_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan
 491      BOOST_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan
 492      BOOST_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan
 493   } // has_quiet_NaN
 494
 495   if (std::numeric_limits<RealType>::has_infinity)
 496   {
 497      // Attempt to construct from non-finite should throw.
 498      RealType inf = std::numeric_limits<RealType>::infinity();
 499
 500      BOOST_CHECK_THROW(beta_distribution<RealType> w(inf), std::domain_error);
 501      BOOST_CHECK_THROW(beta_distribution<RealType> w(1, inf), std::domain_error);
 502
 503     // Non-finite parameters should throw.
 504      beta_distribution<RealType> w(RealType(1));
 505      BOOST_CHECK_THROW(beta_distribution<RealType> w(inf), std::domain_error);
 506      BOOST_CHECK_THROW(beta_distribution<RealType> w(1, inf), std::domain_error);
 507      BOOST_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf
 508      BOOST_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf
 509      BOOST_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf
 510      BOOST_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf
 511      BOOST_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf
 512    } // has_infinity
 513
 514    // Error handling checks:
 515    check_out_of_range<boost::math::beta_distribution<RealType> >(1, 1); // (All) valid constructor parameter values.
 516    // and range and non-finite.
 517
 518    // Not needed??????
 519    BOOST_CHECK_THROW(pdf(boost::math::beta_distribution<RealType>(0, 1), 0), std::domain_error);
 520    BOOST_CHECK_THROW(pdf(boost::math::beta_distribution<RealType>(-1, 1), 0), std::domain_error);
 521    BOOST_CHECK_THROW(quantile(boost::math::beta_distribution<RealType>(1, 1), -1), std::domain_error);
 522    BOOST_CHECK_THROW(quantile(boost::math::beta_distribution<RealType>(1, 1), 2), std::domain_error);
 523
 524
 525 } // template <class RealType>void test_spots(RealType)
 526
 527 BOOST_AUTO_TEST_CASE( test_main )
 528 {
 529    BOOST_MATH_CONTROL_FP;
 530    // Check that can generate beta distribution using one convenience methods:
 531    beta_distribution<> mybeta11(1., 1.); // Using default RealType double.
 532    // but that
 533    // boost::math::beta mybeta1(1., 1.); // Using typedef fails.
 534    // error C2039: 'beta' : is not a member of 'boost::math'
 535
 536    // Basic sanity-check spot values.
 537
 538    // Some simple checks using double only.
 539    BOOST_CHECK_EQUAL(mybeta11.alpha(), 1); //
 540    BOOST_CHECK_EQUAL(mybeta11.beta(), 1);
 541    BOOST_CHECK_EQUAL(mean(mybeta11), 0.5); // 1 / (1 + 1) = 1/2 exactly
 542    BOOST_CHECK_THROW(mode(mybeta11), std::domain_error);
 543    beta_distribution<> mybeta22(2., 2.); // pdf is dome shape.
 544    BOOST_CHECK_EQUAL(mode(mybeta22), 0.5); // 2-1 / (2+2-2) = 1/2 exactly.
 545    beta_distribution<> mybetaH2(0.5, 2.); //
 546    beta_distribution<> mybetaH3(0.5, 3.); //
 547
 548    // Check a few values using double.
 549    BOOST_CHECK_EQUAL(pdf(mybeta11, 1), 1); // is uniform unity over 0 to 1,
 550    BOOST_CHECK_EQUAL(pdf(mybeta11, 0), 1); // including zero and unity.
 551    // Although these next three have an exact result, internally they're
 552    // *not* treated as special cases, and may be out by a couple of eps:
 553    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.5), 1.0, 5*std::numeric_limits<double>::epsilon());
 554    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.0001), 1.0, 5*std::numeric_limits<double>::epsilon());
 555    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.9999), 1.0, 5*std::numeric_limits<double>::epsilon());
 556    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.1), 0.1, 2 * std::numeric_limits<double>::epsilon());
 557    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.5), 0.5, 2 * std::numeric_limits<double>::epsilon());
 558    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.9), 0.9, 2 * std::numeric_limits<double>::epsilon());
 559    BOOST_CHECK_EQUAL(cdf(mybeta11, 1), 1.); // Exact unity expected.
 560
 561    double tol = std::numeric_limits<double>::epsilon() * 10;
 562    BOOST_CHECK_EQUAL(pdf(mybeta22, 1), 0); // is dome shape.
 563    BOOST_CHECK_EQUAL(pdf(mybeta22, 0), 0);
 564    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.5), 1.5, tol); // top of dome, expect exactly 3/2.
 565    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.0001), 5.9994000000000E-4, tol);
 566    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.9999), 5.9994000000000E-4, tol*50);
 567
 568    BOOST_CHECK_EQUAL(cdf(mybeta22, 0.), 0); // cdf is a curved line from 0 to 1.
 569    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.028000000000000, tol);
 570    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.5), 0.5, tol);
 571    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.9), 0.972000000000000, tol);
 572    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.0001), 2.999800000000000000000000000000000000000E-8, tol);
 573    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.001), 2.998000000000000000000000000000000000000E-6, tol);
 574    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.01), 0.0002980000000000000000000000000000000000000, tol);
 575    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.02800000000000000000000000000000000000000, tol); // exact
 576    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.99), 0.9997020000000000000000000000000000000000, tol);
 577
 578    BOOST_CHECK_EQUAL(cdf(mybeta22, 1), 1.); // Exact unity expected.
 579
 580    // Complement
 581
 582    BOOST_CHECK_CLOSE_FRACTION(cdf(complement(mybeta22, 0.9)), 0.028000000000000, tol);
 583
 584    // quantile.
 585    BOOST_CHECK_CLOSE_FRACTION(quantile(mybeta22, 0.028), 0.1, tol);
 586    BOOST_CHECK_CLOSE_FRACTION(quantile(complement(mybeta22, 1 - 0.028)), 0.1, tol);
 587    BOOST_CHECK_EQUAL(kurtosis(mybeta11), 3+ kurtosis_excess(mybeta11)); // Check kurtosis_excess = kurtosis - 3;
 588    BOOST_CHECK_CLOSE_FRACTION(variance(mybeta22), 0.05, tol);
 589    BOOST_CHECK_CLOSE_FRACTION(mean(mybeta22), 0.5, tol);
 590    BOOST_CHECK_CLOSE_FRACTION(mode(mybeta22), 0.5, tol);
 591    BOOST_CHECK_CLOSE_FRACTION(median(mybeta22), 0.5, sqrt(tol)); // Theoretical maximum accuracy using Brent is sqrt(epsilon).
 592
 593    BOOST_CHECK_CLOSE_FRACTION(skewness(mybeta22), 0.0, tol);
 594    BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(mybeta22), -144.0 / 168, tol);
 595    BOOST_CHECK_CLOSE_FRACTION(skewness(beta_distribution<>(3, 5)), 0.30983866769659335081434123198259, tol);
 596
 597    BOOST_CHECK_CLOSE_FRACTION(beta_distribution<double>::find_alpha(mean(mybeta22), variance(mybeta22)), mybeta22.alpha(), tol); // mean, variance, probability.
 598    BOOST_CHECK_CLOSE_FRACTION(beta_distribution<double>::find_beta(mean(mybeta22), variance(mybeta22)), mybeta22.beta(), tol);// mean, variance, probability.
 599
 600    BOOST_CHECK_CLOSE_FRACTION(mybeta22.find_alpha(mybeta22.beta(), 0.8, cdf(mybeta22, 0.8)), mybeta22.alpha(), tol);
 601    BOOST_CHECK_CLOSE_FRACTION(mybeta22.find_beta(mybeta22.alpha(), 0.8, cdf(mybeta22, 0.8)), mybeta22.beta(), tol);
 602
 603
 604    beta_distribution<real_concept> rcbeta22(2, 2); // Using RealType real_concept.
 605    cout << "numeric_limits<real_concept>::is_specialized " << numeric_limits<real_concept>::is_specialized << endl;
 606    cout << "numeric_limits<real_concept>::digits " << numeric_limits<real_concept>::digits << endl;
 607    cout << "numeric_limits<real_concept>::digits10 " << numeric_limits<real_concept>::digits10 << endl;
 608    cout << "numeric_limits<real_concept>::epsilon " << numeric_limits<real_concept>::epsilon() << endl;
 609
 610    // (Parameter value, arbitrarily zero, only communicates the floating point type).
 611    test_spots(0.0F); // Test float.
 612    test_spots(0.0); // Test double.
 613 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 614    test_spots(0.0L); // Test long double.
 615 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
 616    test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 617 #endif
 618 #endif
 619 } // BOOST_AUTO_TEST_CASE( test_main )
 620
 621 /*
 622
 623 Output is:
 624
 625 -Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_beta_dist.exe"
 626 Running 1 test case...
 627 numeric_limits<real_concept>::is_specialized 0
 628 numeric_limits<real_concept>::digits 0
 629 numeric_limits<real_concept>::digits10 0
 630 numeric_limits<real_concept>::epsilon 0
 631 Boost::math::tools::epsilon = 1.19209e-007
 632 std::numeric_limits::epsilon = 1.19209e-007
 633 epsilon = 1.19209e-007, Tolerance = 0.0119209%.
 634 Boost::math::tools::epsilon = 2.22045e-016
 635 std::numeric_limits::epsilon = 2.22045e-016
 636 epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
 637 Boost::math::tools::epsilon = 2.22045e-016
 638 std::numeric_limits::epsilon = 2.22045e-016
 639 epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
 640 Boost::math::tools::epsilon = 2.22045e-016
 641 std::numeric_limits::epsilon = 0
 642 epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
 643 *** No errors detected
 644
 645
 646 */
 647
 648
 649