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 #include <boost/math/tools/test.hpp>
  38
  39 #include <boost/math/distributions/beta.hpp> // for beta_distribution
  40 using boost::math::beta_distribution;
  41 using boost::math::beta;
  42
  43 #define BOOST_TEST_MAIN
  44 #include <boost/test/unit_test.hpp> // for test_main
  45 #include <boost/test/tools/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION
  46
  47 #include "test_out_of_range.hpp"
  48
  49 #include <iostream>
  50 using std::cout;
  51 using std::endl;
  52 #include <limits>
  53 using std::numeric_limits;
  54
  55 template <class RealType>
  56 void test_spot(
  57      RealType a,    // alpha a
  58      RealType b,    // beta b
  59      RealType x,    // Probability
  60      RealType P,    // CDF of beta(a, b)
  61      RealType Q,    // Complement of CDF
  62      RealType tol)  // Test tolerance.
  63 {
  64    boost::math::beta_distribution<RealType> abeta(a, b);
  65    BOOST_CHECK_CLOSE_FRACTION(cdf(abeta, x), P, tol);
  66    if((P < 0.99) && (Q < 0.99))
  67    {  // We can only check this if P is not too close to 1,
  68       // so that we can guarantee that Q is free of error,
  69       // (and similarly for Q)
  70       BOOST_CHECK_CLOSE_FRACTION(
  71          cdf(complement(abeta, x)), Q, tol);
  72       if(x != 0)
  73       {
  74          BOOST_CHECK_CLOSE_FRACTION(
  75             quantile(abeta, P), x, tol);
  76       }
  77       else
  78       {
  79          // Just check quantile is very small:
  80          if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent)
  81            && (boost::is_floating_point<RealType>::value))
  82          {
  83             // Limit where this is checked: if exponent range is very large we may
  84             // run out of iterations in our root finding algorithm.
  85             BOOST_CHECK(quantile(abeta, P) < boost::math::tools::epsilon<RealType>() * 10);
  86          }
  87       } // if k
  88       if(x != 0)
  89       {
  90          BOOST_CHECK_CLOSE_FRACTION(quantile(complement(abeta, Q)), x, tol);
  91       }
  92       else
  93       {  // Just check quantile is very small:
  94          if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
  95          {  // Limit where this is checked: if exponent range is very large we may
  96             // run out of iterations in our root finding algorithm.
  97             BOOST_CHECK(quantile(complement(abeta, Q)) < boost::math::tools::epsilon<RealType>() * 10);
  98          }
  99       } // if x
 100       // Estimate alpha & beta from mean and variance:
 101
 102       BOOST_CHECK_CLOSE_FRACTION(
 103          beta_distribution<RealType>::find_alpha(mean(abeta), variance(abeta)),
 104          abeta.alpha(), tol);
 105       BOOST_CHECK_CLOSE_FRACTION(
 106          beta_distribution<RealType>::find_beta(mean(abeta), variance(abeta)),
 107          abeta.beta(), tol);
 108
 109       // Estimate sample alpha and beta from others:
 110       BOOST_CHECK_CLOSE_FRACTION(
 111          beta_distribution<RealType>::find_alpha(abeta.beta(), x, P),
 112          abeta.alpha(), tol);
 113       BOOST_CHECK_CLOSE_FRACTION(
 114          beta_distribution<RealType>::find_beta(abeta.alpha(), x, P),
 115          abeta.beta(), tol);
 116    } // if((P < 0.99) && (Q < 0.99)
 117
 118 } // template <class RealType> void test_spot
 119
 120 template <class RealType> // Any floating-point type RealType.
 121 void test_spots(RealType)
 122 {
 123   // Basic sanity checks with 'known good' values.
 124   // MathCAD test data is to double precision only,
 125   // so set tolerance to 100 eps expressed as a fraction, or
 126   // 100 eps of type double expressed as a fraction,
 127   // whichever is the larger.
 128
 129   RealType tolerance = (std::max)
 130       (boost::math::tools::epsilon<RealType>(),
 131       static_cast<RealType>(std::numeric_limits<double>::epsilon())); // 0 if real_concept.
 132
 133    cout << "Boost::math::tools::epsilon = " << boost::math::tools::epsilon<RealType>() <<endl;
 134    cout << "std::numeric_limits::epsilon = " << std::numeric_limits<RealType>::epsilon() <<endl;
 135    cout << "epsilon = " << tolerance;
 136
 137    tolerance *= 100000; // Note: NO * 100 because is fraction, NOT %.
 138    cout  << ", Tolerance = " << tolerance * 100 << "%." << endl;
 139
 140   // RealType teneps = boost::math::tools::epsilon<RealType>() * 10;
 141
 142   // Sources of spot test values:
 143
 144   // MathCAD defines dbeta(x, s1, s2) pdf, s1 == alpha, s2 = beta, x = x in Wolfram
 145   // pbeta(x, s1, s2) cdf and qbeta(x, s1, s2) inverse of cdf
 146   // returns pr(X ,= x) when random variable X
 147   // has the beta distribution with parameters s1)alpha) and s2(beta).
 148   // s1 > 0 and s2 >0 and 0 < x < 1 (but allows x == 0! and x == 1!)
 149   // dbeta(0,1,1) = 0
 150   // dbeta(0.5,1,1) = 1
 151
 152   using boost::math::beta_distribution;
 153   using  ::boost::math::cdf;
 154   using  ::boost::math::pdf;
 155
 156   // Tests that should throw:
 157   BOOST_MATH_CHECK_THROW(mode(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))), std::domain_error);
 158   // mode is undefined, and throws domain_error!
 159
 160  // BOOST_MATH_CHECK_THROW(median(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))), std::domain_error);
 161   // median is undefined, and throws domain_error!
 162   // But now median IS provided via derived accessor as quantile(half).
 163
 164
 165   BOOST_MATH_CHECK_THROW( // For various bad arguments.
 166        pdf(
 167           beta_distribution<RealType>(static_cast<RealType>(-1), static_cast<RealType>(1)), // bad alpha < 0.
 168           static_cast<RealType>(1)), std::domain_error);
 169
 170   BOOST_MATH_CHECK_THROW(
 171        pdf(
 172           beta_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(1)), // bad alpha == 0.
 173           static_cast<RealType>(1)), std::domain_error);
 174
 175   BOOST_MATH_CHECK_THROW(
 176        pdf(
 177           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(0)), // bad beta == 0.
 178           static_cast<RealType>(1)), std::domain_error);
 179
 180   BOOST_MATH_CHECK_THROW(
 181        pdf(
 182           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(-1)), // bad beta < 0.
 183           static_cast<RealType>(1)), std::domain_error);
 184
 185   BOOST_MATH_CHECK_THROW(
 186        pdf(
 187           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // bad x < 0.
 188           static_cast<RealType>(-1)), std::domain_error);
 189
 190   BOOST_MATH_CHECK_THROW(
 191        pdf(
 192           beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)), // bad x > 1.
 193           static_cast<RealType>(999)), std::domain_error);
 194
 195   // Some exact pdf values.
 196
 197   BOOST_CHECK_EQUAL( // a = b = 1 is uniform distribution.
 198      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 199      static_cast<RealType>(1)),  // x
 200      static_cast<RealType>(1));
 201   BOOST_CHECK_EQUAL(
 202      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 203      static_cast<RealType>(0)),  // x
 204      static_cast<RealType>(1));
 205   BOOST_CHECK_CLOSE_FRACTION(
 206      pdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 207      static_cast<RealType>(0.5)),  // x
 208      static_cast<RealType>(1),
 209      tolerance);
 210
 211   BOOST_CHECK_EQUAL(
 212      beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)).alpha(),
 213      static_cast<RealType>(1) ); //
 214
 215   BOOST_CHECK_EQUAL(
 216      mean(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1))),
 217      static_cast<RealType>(0.5) ); // Exact one half.
 218
 219   BOOST_CHECK_CLOSE_FRACTION(
 220      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 221      static_cast<RealType>(0.5)),  // x
 222      static_cast<RealType>(1.5), // Exactly 3/2
 223       tolerance);
 224
 225   BOOST_CHECK_CLOSE_FRACTION(
 226      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 227      static_cast<RealType>(0.5)),  // x
 228      static_cast<RealType>(1.5), // Exactly 3/2
 229       tolerance);
 230
 231   // CDF
 232   BOOST_CHECK_CLOSE_FRACTION(
 233      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 234      static_cast<RealType>(0.1)),  // x
 235      static_cast<RealType>(0.02800000000000000000000000000000000000000L), // Seems exact.
 236      // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.1&a=2&b=2&digits=40
 237       tolerance);
 238
 239   BOOST_CHECK_CLOSE_FRACTION(
 240      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 241      static_cast<RealType>(0.0001)),  // x
 242      static_cast<RealType>(2.999800000000000000000000000000000000000e-8L),
 243      // http://members.aol.com/iandjmsmith/BETAEX.HTM 2.9998000000004
 244      // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.0001&a=2&b=2&digits=40
 245       tolerance);
 246
 247
 248   BOOST_CHECK_CLOSE_FRACTION(
 249      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 250      static_cast<RealType>(0.0001)),  // x
 251      static_cast<RealType>(0.0005999400000000004L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
 252      // Slightly higher tolerance for real concept:
 253      (std::numeric_limits<RealType>::is_specialized ? 1 : 10) * tolerance);
 254
 255
 256   BOOST_CHECK_CLOSE_FRACTION(
 257      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 258      static_cast<RealType>(0.9999)),  // x
 259      static_cast<RealType>(0.999999970002L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
 260      // Wolfram 0.9999999700020000000000000000000000000000
 261       tolerance);
 262
 263   BOOST_CHECK_CLOSE_FRACTION(
 264      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(2)),
 265      static_cast<RealType>(0.9)),  // x
 266      static_cast<RealType>(0.9961174629530394895796514664963063381217L),
 267      // Wolfram
 268       tolerance);
 269
 270   BOOST_CHECK_CLOSE_FRACTION(
 271      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 272      static_cast<RealType>(0.1)),  // x
 273      static_cast<RealType>(0.2048327646991334516491978475505189480977L),
 274      // Wolfram
 275       tolerance);
 276
 277   BOOST_CHECK_CLOSE_FRACTION(
 278      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 279      static_cast<RealType>(0.9)),  // x
 280      static_cast<RealType>(0.7951672353008665483508021524494810519023L),
 281      // Wolfram
 282       tolerance);
 283
 284   BOOST_CHECK_CLOSE_FRACTION(
 285      quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 286      static_cast<RealType>(0.7951672353008665483508021524494810519023L)),  // x
 287      static_cast<RealType>(0.9),
 288      // Wolfram
 289      tolerance);
 290
 291   BOOST_CHECK_CLOSE_FRACTION(
 292      cdf(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 293      static_cast<RealType>(0.6)),  // x
 294      static_cast<RealType>(0.5640942168489749316118742861695149357858L),
 295      // Wolfram
 296       tolerance);
 297
 298   BOOST_CHECK_CLOSE_FRACTION(
 299      quantile(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 300      static_cast<RealType>(0.5640942168489749316118742861695149357858L)),  // x
 301      static_cast<RealType>(0.6),
 302      // Wolfram
 303       tolerance);
 304
 305
 306   BOOST_CHECK_CLOSE_FRACTION(
 307      cdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
 308      static_cast<RealType>(0.6)),  // x
 309      static_cast<RealType>(0.1778078083562213736802876784474931812329L),
 310      // Wolfram
 311       tolerance);
 312
 313   BOOST_CHECK_CLOSE_FRACTION(
 314      quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
 315      static_cast<RealType>(0.1778078083562213736802876784474931812329L)),  // x
 316      static_cast<RealType>(0.6),
 317      // Wolfram
 318       tolerance); // gives
 319
 320   BOOST_CHECK_CLOSE_FRACTION(
 321      cdf(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 322      static_cast<RealType>(0.1)),  // x
 323      static_cast<RealType>(0.1),  // 0.1000000000000000000000000000000000000000
 324      // Wolfram
 325       tolerance);
 326
 327   BOOST_CHECK_CLOSE_FRACTION(
 328      quantile(beta_distribution<RealType>(static_cast<RealType>(1), static_cast<RealType>(1)),
 329      static_cast<RealType>(0.1)),  // x
 330      static_cast<RealType>(0.1),  // 0.1000000000000000000000000000000000000000
 331      // Wolfram
 332       tolerance);
 333
 334   BOOST_CHECK_CLOSE_FRACTION(
 335      cdf(complement(beta_distribution<RealType>(static_cast<RealType>(0.5), static_cast<RealType>(0.5)),
 336      static_cast<RealType>(0.1))),  // complement of x
 337      static_cast<RealType>(0.7951672353008665483508021524494810519023L),
 338      // Wolfram
 339       tolerance);
 340
 341     BOOST_CHECK_CLOSE_FRACTION(
 342      quantile(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 343      static_cast<RealType>(0.0280000000000000000000000000000000000L)),  // x
 344      static_cast<RealType>(0.1),
 345      // Wolfram
 346       tolerance);
 347
 348
 349   BOOST_CHECK_CLOSE_FRACTION(
 350      cdf(complement(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 351      static_cast<RealType>(0.1))),  // x
 352      static_cast<RealType>(0.9720000000000000000000000000000000000000L), // Exact.
 353      // Wolfram
 354       tolerance);
 355
 356   BOOST_CHECK_CLOSE_FRACTION(
 357      pdf(beta_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(2)),
 358      static_cast<RealType>(0.9999)),  // x
 359      static_cast<RealType>(0.0005999399999999344L), // http://members.aol.com/iandjmsmith/BETAEX.HTM
 360       tolerance*10); // Note loss of precision calculating 1-p test value.
 361
 362   //void test_spot(
 363   //   RealType a,    // alpha a
 364   //   RealType b,    // beta b
 365   //   RealType x,    // Probability
 366   //   RealType P,    // CDF of beta(a, b)
 367   //   RealType Q,    // Complement of CDF
 368   //   RealType tol)  // Test tolerance.
 369
 370    // These test quantiles and complements, and parameter estimates as well.
 371   // Spot values using, for example:
 372   // http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=BetaRegularized&ptype=0&z=0.1&a=0.5&b=3&digits=40
 373
 374   test_spot(
 375      static_cast<RealType>(1),   // alpha a
 376      static_cast<RealType>(1),   // beta b
 377      static_cast<RealType>(0.1), // Probability  p
 378      static_cast<RealType>(0.1), // Probability of result (CDF of beta), P
 379      static_cast<RealType>(0.9),  // Complement of CDF Q = 1 - P
 380      tolerance); // Test tolerance.
 381   test_spot(
 382      static_cast<RealType>(2),   // alpha a
 383      static_cast<RealType>(2),   // beta b
 384      static_cast<RealType>(0.1), // Probability  p
 385      static_cast<RealType>(0.0280000000000000000000000000000000000L), // Probability of result (CDF of beta), P
 386      static_cast<RealType>(1 - 0.0280000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
 387      tolerance); // Test tolerance.
 388
 389
 390   test_spot(
 391      static_cast<RealType>(2),   // alpha a
 392      static_cast<RealType>(2),   // beta b
 393      static_cast<RealType>(0.5), // Probability  p
 394      static_cast<RealType>(0.5), // Probability of result (CDF of beta), P
 395      static_cast<RealType>(0.5),  // Complement of CDF Q = 1 - P
 396      tolerance); // Test tolerance.
 397
 398   test_spot(
 399      static_cast<RealType>(2),   // alpha a
 400      static_cast<RealType>(2),   // beta b
 401      static_cast<RealType>(0.9), // Probability  p
 402      static_cast<RealType>(0.972000000000000), // Probability of result (CDF of beta), P
 403      static_cast<RealType>(1-0.972000000000000),  // Complement of CDF Q = 1 - P
 404      tolerance); // Test tolerance.
 405
 406   test_spot(
 407      static_cast<RealType>(2),   // alpha a
 408      static_cast<RealType>(2),   // beta b
 409      static_cast<RealType>(0.01), // Probability  p
 410      static_cast<RealType>(0.0002980000000000000000000000000000000000000L), // Probability of result (CDF of beta), P
 411      static_cast<RealType>(1-0.0002980000000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
 412      tolerance); // Test tolerance.
 413
 414   test_spot(
 415      static_cast<RealType>(2),   // alpha a
 416      static_cast<RealType>(2),   // beta b
 417      static_cast<RealType>(0.001), // Probability  p
 418      static_cast<RealType>(2.998000000000000000000000000000000000000E-6L), // Probability of result (CDF of beta), P
 419      static_cast<RealType>(1-2.998000000000000000000000000000000000000E-6L),  // Complement of CDF Q = 1 - P
 420      tolerance); // Test tolerance.
 421
 422   test_spot(
 423      static_cast<RealType>(2),   // alpha a
 424      static_cast<RealType>(2),   // beta b
 425      static_cast<RealType>(0.0001), // Probability  p
 426      static_cast<RealType>(2.999800000000000000000000000000000000000E-8L), // Probability of result (CDF of beta), P
 427      static_cast<RealType>(1-2.999800000000000000000000000000000000000E-8L),  // Complement of CDF Q = 1 - P
 428      tolerance); // Test tolerance.
 429
 430   test_spot(
 431      static_cast<RealType>(2),   // alpha a
 432      static_cast<RealType>(2),   // beta b
 433      static_cast<RealType>(0.99), // Probability  p
 434      static_cast<RealType>(0.9997020000000000000000000000000000000000L), // Probability of result (CDF of beta), P
 435      static_cast<RealType>(1-0.9997020000000000000000000000000000000000L),  // Complement of CDF Q = 1 - P
 436      tolerance); // Test tolerance.
 437
 438   test_spot(
 439      static_cast<RealType>(0.5),   // alpha a
 440      static_cast<RealType>(2),   // beta b
 441      static_cast<RealType>(0.5), // Probability  p
 442      static_cast<RealType>(0.8838834764831844055010554526310612991060L), // Probability of result (CDF of beta), P
 443      static_cast<RealType>(1-0.8838834764831844055010554526310612991060L),  // Complement of CDF Q = 1 - P
 444      tolerance); // Test tolerance.
 445
 446   test_spot(
 447      static_cast<RealType>(0.5),   // alpha a
 448      static_cast<RealType>(3.),   // beta b
 449      static_cast<RealType>(0.7), // Probability  p
 450      static_cast<RealType>(0.9903963064097119299191611355232156905687L), // Probability of result (CDF of beta), P
 451      static_cast<RealType>(1-0.9903963064097119299191611355232156905687L),  // Complement of CDF Q = 1 - P
 452      tolerance); // Test tolerance.
 453
 454   test_spot(
 455      static_cast<RealType>(0.5),   // alpha a
 456      static_cast<RealType>(3.),   // beta b
 457      static_cast<RealType>(0.1), // Probability  p
 458      static_cast<RealType>(0.5545844446520295253493059553548880128511L), // Probability of result (CDF of beta), P
 459      static_cast<RealType>(1-0.5545844446520295253493059553548880128511L),  // Complement of CDF Q = 1 - P
 460      tolerance); // Test tolerance.
 461
 462     //
 463    // Error checks:
 464    // Construction with 'bad' parameters.
 465    BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, -1), std::domain_error);
 466    BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(-1, 1), std::domain_error);
 467    BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, 0), std::domain_error);
 468    BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(0, 1), std::domain_error);
 469
 470    beta_distribution<> dist;
 471    BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error);
 472    BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error);
 473    BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
 474    BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
 475    BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
 476    BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
 477    BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
 478
 479  // No longer allow any parameter to be NaN or inf, so all these tests should throw.
 480    if (std::numeric_limits<RealType>::has_quiet_NaN)
 481    {
 482     // Attempt to construct from non-finite should throw.
 483      RealType nan = std::numeric_limits<RealType>::quiet_NaN();
 484 #ifndef BOOST_NO_EXCEPTIONS
 485      BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(nan), std::domain_error);
 486      BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(1, nan), std::domain_error);
 487 #else
 488      BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(nan), std::domain_error);
 489      BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, nan), std::domain_error);
 490 #endif
 491
 492     // Non-finite parameters should throw.
 493      beta_distribution<RealType> w(RealType(1));
 494      BOOST_MATH_CHECK_THROW(pdf(w, +nan), std::domain_error); // x = NaN
 495      BOOST_MATH_CHECK_THROW(cdf(w, +nan), std::domain_error); // x = NaN
 496      BOOST_MATH_CHECK_THROW(cdf(complement(w, +nan)), std::domain_error); // x = + nan
 497      BOOST_MATH_CHECK_THROW(quantile(w, +nan), std::domain_error); // p = + nan
 498      BOOST_MATH_CHECK_THROW(quantile(complement(w, +nan)), std::domain_error); // p = + nan
 499   } // has_quiet_NaN
 500
 501   if (std::numeric_limits<RealType>::has_infinity)
 502   {
 503      // Attempt to construct from non-finite should throw.
 504      RealType inf = std::numeric_limits<RealType>::infinity();
 505 #ifndef BOOST_NO_EXCEPTIONS
 506      BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(inf), std::domain_error);
 507      BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(1, inf), std::domain_error);
 508 #else
 509      BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(inf), std::domain_error);
 510      BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, inf), std::domain_error);
 511 #endif
 512
 513     // Non-finite parameters should throw.
 514      beta_distribution<RealType> w(RealType(1));
 515 #ifndef BOOST_NO_EXCEPTIONS
 516      BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(inf), std::domain_error);
 517      BOOST_MATH_CHECK_THROW(beta_distribution<RealType> w(1, inf), std::domain_error);
 518 #else
 519      BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(inf), std::domain_error);
 520      BOOST_MATH_CHECK_THROW(beta_distribution<RealType>(1, inf), std::domain_error);
 521 #endif
 522      BOOST_MATH_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf
 523      BOOST_MATH_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf
 524      BOOST_MATH_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf
 525      BOOST_MATH_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf
 526      BOOST_MATH_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf
 527    } // has_infinity
 528
 529    // Error handling checks:
 530    check_out_of_range<boost::math::beta_distribution<RealType> >(1, 1); // (All) valid constructor parameter values.
 531    // and range and non-finite.
 532
 533    // Not needed??????
 534    BOOST_MATH_CHECK_THROW(pdf(boost::math::beta_distribution<RealType>(0, 1), 0), std::domain_error);
 535    BOOST_MATH_CHECK_THROW(pdf(boost::math::beta_distribution<RealType>(-1, 1), 0), std::domain_error);
 536    BOOST_MATH_CHECK_THROW(quantile(boost::math::beta_distribution<RealType>(1, 1), -1), std::domain_error);
 537    BOOST_MATH_CHECK_THROW(quantile(boost::math::beta_distribution<RealType>(1, 1), 2), std::domain_error);
 538
 539
 540 } // template <class RealType>void test_spots(RealType)
 541
 542 BOOST_AUTO_TEST_CASE( test_main )
 543 {
 544    BOOST_MATH_CONTROL_FP;
 545    // Check that can generate beta distribution using one convenience methods:
 546    beta_distribution<> mybeta11(1., 1.); // Using default RealType double.
 547    // but that
 548    // boost::math::beta mybeta1(1., 1.); // Using typedef fails.
 549    // error C2039: 'beta' : is not a member of 'boost::math'
 550
 551    // Basic sanity-check spot values.
 552
 553    // Some simple checks using double only.
 554    BOOST_CHECK_EQUAL(mybeta11.alpha(), 1); //
 555    BOOST_CHECK_EQUAL(mybeta11.beta(), 1);
 556    BOOST_CHECK_EQUAL(mean(mybeta11), 0.5); // 1 / (1 + 1) = 1/2 exactly
 557    BOOST_MATH_CHECK_THROW(mode(mybeta11), std::domain_error);
 558    beta_distribution<> mybeta22(2., 2.); // pdf is dome shape.
 559    BOOST_CHECK_EQUAL(mode(mybeta22), 0.5); // 2-1 / (2+2-2) = 1/2 exactly.
 560    beta_distribution<> mybetaH2(0.5, 2.); //
 561    beta_distribution<> mybetaH3(0.5, 3.); //
 562
 563    // Check a few values using double.
 564    BOOST_CHECK_EQUAL(pdf(mybeta11, 1), 1); // is uniform unity over 0 to 1,
 565    BOOST_CHECK_EQUAL(pdf(mybeta11, 0), 1); // including zero and unity.
 566    // Although these next three have an exact result, internally they're
 567    // *not* treated as special cases, and may be out by a couple of eps:
 568    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.5), 1.0, 5*std::numeric_limits<double>::epsilon());
 569    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.0001), 1.0, 5*std::numeric_limits<double>::epsilon());
 570    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta11, 0.9999), 1.0, 5*std::numeric_limits<double>::epsilon());
 571    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.1), 0.1, 2 * std::numeric_limits<double>::epsilon());
 572    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.5), 0.5, 2 * std::numeric_limits<double>::epsilon());
 573    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta11, 0.9), 0.9, 2 * std::numeric_limits<double>::epsilon());
 574    BOOST_CHECK_EQUAL(cdf(mybeta11, 1), 1.); // Exact unity expected.
 575
 576    double tol = std::numeric_limits<double>::epsilon() * 10;
 577    BOOST_CHECK_EQUAL(pdf(mybeta22, 1), 0); // is dome shape.
 578    BOOST_CHECK_EQUAL(pdf(mybeta22, 0), 0);
 579    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.5), 1.5, tol); // top of dome, expect exactly 3/2.
 580    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.0001), 5.9994000000000E-4, tol);
 581    BOOST_CHECK_CLOSE_FRACTION(pdf(mybeta22, 0.9999), 5.9994000000000E-4, tol*50);
 582
 583    BOOST_CHECK_EQUAL(cdf(mybeta22, 0.), 0); // cdf is a curved line from 0 to 1.
 584    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.028000000000000, tol);
 585    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.5), 0.5, tol);
 586    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.9), 0.972000000000000, tol);
 587    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.0001), 2.999800000000000000000000000000000000000E-8, tol);
 588    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.001), 2.998000000000000000000000000000000000000E-6, tol);
 589    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.01), 0.0002980000000000000000000000000000000000000, tol);
 590    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.1), 0.02800000000000000000000000000000000000000, tol); // exact
 591    BOOST_CHECK_CLOSE_FRACTION(cdf(mybeta22, 0.99), 0.9997020000000000000000000000000000000000, tol);
 592
 593    BOOST_CHECK_EQUAL(cdf(mybeta22, 1), 1.); // Exact unity expected.
 594
 595    // Complement
 596
 597    BOOST_CHECK_CLOSE_FRACTION(cdf(complement(mybeta22, 0.9)), 0.028000000000000, tol);
 598
 599    // quantile.
 600    BOOST_CHECK_CLOSE_FRACTION(quantile(mybeta22, 0.028), 0.1, tol);
 601    BOOST_CHECK_CLOSE_FRACTION(quantile(complement(mybeta22, 1 - 0.028)), 0.1, tol);
 602    BOOST_CHECK_EQUAL(kurtosis(mybeta11), 3+ kurtosis_excess(mybeta11)); // Check kurtosis_excess = kurtosis - 3;
 603    BOOST_CHECK_CLOSE_FRACTION(variance(mybeta22), 0.05, tol);
 604    BOOST_CHECK_CLOSE_FRACTION(mean(mybeta22), 0.5, tol);
 605    BOOST_CHECK_CLOSE_FRACTION(mode(mybeta22), 0.5, tol);
 606    BOOST_CHECK_CLOSE_FRACTION(median(mybeta22), 0.5, sqrt(tol)); // Theoretical maximum accuracy using Brent is sqrt(epsilon).
 607
 608    BOOST_CHECK_CLOSE_FRACTION(skewness(mybeta22), 0.0, tol);
 609    BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(mybeta22), -144.0 / 168, tol);
 610    BOOST_CHECK_CLOSE_FRACTION(skewness(beta_distribution<>(3, 5)), 0.30983866769659335081434123198259, tol);
 611
 612    BOOST_CHECK_CLOSE_FRACTION(beta_distribution<double>::find_alpha(mean(mybeta22), variance(mybeta22)), mybeta22.alpha(), tol); // mean, variance, probability.
 613    BOOST_CHECK_CLOSE_FRACTION(beta_distribution<double>::find_beta(mean(mybeta22), variance(mybeta22)), mybeta22.beta(), tol);// mean, variance, probability.
 614
 615    BOOST_CHECK_CLOSE_FRACTION(mybeta22.find_alpha(mybeta22.beta(), 0.8, cdf(mybeta22, 0.8)), mybeta22.alpha(), tol);
 616    BOOST_CHECK_CLOSE_FRACTION(mybeta22.find_beta(mybeta22.alpha(), 0.8, cdf(mybeta22, 0.8)), mybeta22.beta(), tol);
 617
 618
 619    beta_distribution<real_concept> rcbeta22(2, 2); // Using RealType real_concept.
 620    cout << "numeric_limits<real_concept>::is_specialized " << numeric_limits<real_concept>::is_specialized << endl;
 621    cout << "numeric_limits<real_concept>::digits " << numeric_limits<real_concept>::digits << endl;
 622    cout << "numeric_limits<real_concept>::digits10 " << numeric_limits<real_concept>::digits10 << endl;
 623    cout << "numeric_limits<real_concept>::epsilon " << numeric_limits<real_concept>::epsilon() << endl;
 624
 625    // (Parameter value, arbitrarily zero, only communicates the floating point type).
 626    test_spots(0.0F); // Test float.
 627    test_spots(0.0); // Test double.
 628 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 629    test_spots(0.0L); // Test long double.
 630 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
 631    test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
 632 #endif
 633 #endif
 634 } // BOOST_AUTO_TEST_CASE( test_main )
 635
 636 /*
 637
 638 Output is:
 639
 640 -Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_beta_dist.exe"
 641 Running 1 test case...
 642 numeric_limits<real_concept>::is_specialized 0
 643 numeric_limits<real_concept>::digits 0
 644 numeric_limits<real_concept>::digits10 0
 645 numeric_limits<real_concept>::epsilon 0
 646 Boost::math::tools::epsilon = 1.19209e-007
 647 std::numeric_limits::epsilon = 1.19209e-007
 648 epsilon = 1.19209e-007, Tolerance = 0.0119209%.
 649 Boost::math::tools::epsilon = 2.22045e-016
 650 std::numeric_limits::epsilon = 2.22045e-016
 651 epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
 652 Boost::math::tools::epsilon = 2.22045e-016
 653 std::numeric_limits::epsilon = 2.22045e-016
 654 epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
 655 Boost::math::tools::epsilon = 2.22045e-016
 656 std::numeric_limits::epsilon = 0
 657 epsilon = 2.22045e-016, Tolerance = 2.22045e-011%.
 658 *** No errors detected
 659
 660
 661 */
 662
 663
 664