text: // test_bernoulli.cpp
  
  // Copyright John Maddock 2006.
  // Copyright  Paul A. Bristow 2007, 2012.
  
  // Use, modification and distribution are subject to the
  // Boost Software License, Version 1.0.
  // (See accompanying file LICENSE_1_0.txt
  // or copy at http://www.boost.org/LICENSE_1_0.txt)
  
  // Basic sanity test for Bernoulli Cumulative Distribution Function.
  
  #ifdef _MSC_VER
  #  pragma warning (disable : 4535) // calling _set_se_translator() requires /EHa.
  #  pragma warning (disable : 4244) // conversion possible loss of data.
  #  pragma warning (disable : 4996) // 'putenv': The POSIX name for this item is deprecated.
  #  pragma warning (disable : 4127) // conditional expression is constant.
  #endif
  
  // Default domain error policy is
  // #define BOOST_MATH_DOMAIN_ERROR_POLICY throw_on_error
  
  #include <boost/math/concepts/real_concept.hpp> // for real_concept
  using ::boost::math::concepts::real_concept;
  #include <boost/math/tools/test.hpp>
  
  #include <boost/math/distributions/bernoulli.hpp> // for bernoulli_distribution
  using boost::math::bernoulli_distribution;
  
  #define BOOST_TEST_MAIN
  #include <boost/test/unit_test.hpp> // for test_main
  #include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE_FRACTION, BOOST_CHECK_EQUAL...
  
  #include <iostream>
  using std::cout;
  using std::endl;
  using std::fixed;
  using std::right;
  using std::left;
  using std::showpoint;
  using std::showpos;
  using std::setw;
  using std::setprecision;
  
  #include <limits>
  using std::numeric_limits;
  
  template <class RealType> // Any floating-point type RealType.
  void test_spots(RealType)
  { // Parameter only provides the type, float, double... value ignored.
  
    // Basic sanity checks, test data may be to double precision only
    // so set tolerance to 100 eps expressed as a fraction,
    // or 100 eps of type double expressed as a fraction,
    // whichever is the larger.
  
    RealType tolerance = (std::max)
        (boost::math::tools::epsilon<RealType>(),
        static_cast<RealType>(std::numeric_limits<double>::epsilon()));
     tolerance *= 100;
  
    cout << "Tolerance for type " << typeid(RealType).name()  << " is "
      << setprecision(3) << tolerance  << " (or " << tolerance * 100 << "%)." << endl;
  
    // Sources of spot test values - calculator,
    // or Steve Moshier's command interpreter V1.3 100 decimal digit calculator,
    // Wolfram function evaluator.
  
    using boost::math::bernoulli_distribution; // of type RealType.
    using  ::boost::math::cdf;
    using  ::boost::math::pdf;
  
    BOOST_CHECK_EQUAL(bernoulli_distribution<RealType>(static_cast<RealType>(0.5)).success_fraction(), static_cast<RealType>(0.5));
    BOOST_CHECK_EQUAL(bernoulli_distribution<RealType>(static_cast<RealType>(0.1L)).success_fraction(), static_cast<RealType>(0.1L));
    BOOST_CHECK_EQUAL(bernoulli_distribution<RealType>(static_cast<RealType>(0.9L)).success_fraction(), static_cast<RealType>(0.9L));
  
    BOOST_MATH_CHECK_THROW( // Constructor success_fraction outside 0 to 1.
         bernoulli_distribution<RealType>(static_cast<RealType>(2)), std::domain_error);
    BOOST_MATH_CHECK_THROW(
         bernoulli_distribution<RealType>(static_cast<RealType>(-2)), std::domain_error);
  
    BOOST_MATH_CHECK_THROW(
         pdf( // pdf k neither 0 nor 1.
            bernoulli_distribution<RealType>(static_cast<RealType>(0.25L)), static_cast<RealType>(-1)), std::domain_error);
  
    BOOST_MATH_CHECK_THROW(
         pdf( // pdf k neither 0 nor 1.
            bernoulli_distribution<RealType>(static_cast<RealType>(0.25L)), static_cast<RealType>(2)), std::domain_error);
  
    BOOST_CHECK_EQUAL(
      pdf( // OK k (or n)
      bernoulli_distribution<RealType>(static_cast<RealType>(0.5L)), static_cast<RealType>(0)),
        static_cast<RealType>(0.5)); // Expect 1 - p.
  
    BOOST_CHECK_CLOSE_FRACTION(
      pdf( // OK k (or n)
      bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)), static_cast<RealType>(0)),
        static_cast<RealType>(0.4L), tolerance); // Expect  1 - p.
  
    BOOST_CHECK_CLOSE_FRACTION(
      pdf( // OK k (or n)
      bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)), static_cast<RealType>(0)),
        static_cast<RealType>(0.4L), tolerance); // Expect  1- p.
  
    BOOST_CHECK_CLOSE_FRACTION(
      pdf( // OK k (or n)
      bernoulli_distribution<RealType>(static_cast<RealType>(0.4L)), static_cast<RealType>(0)),
        static_cast<RealType>(0.6L), tolerance); // Expect  1- p.
  
    BOOST_CHECK_EQUAL(
         mean(bernoulli_distribution<RealType>(static_cast<RealType>(0.5L))), static_cast<RealType>(0.5L));
  
    BOOST_CHECK_EQUAL(
         mean(bernoulli_distribution<RealType>(static_cast<RealType>(0.1L))),
         static_cast<RealType>(0.1L));
  
    BOOST_CHECK_CLOSE_FRACTION(
         variance(bernoulli_distribution<RealType>(static_cast<RealType>(0.1L))),
         static_cast<RealType>(0.09L),
         tolerance);
  
    BOOST_CHECK_CLOSE_FRACTION(
         skewness(bernoulli_distribution<RealType>(static_cast<RealType>(0.1L))),
         static_cast<RealType>(2.666666666666666666666666666666666666666666L),
         tolerance);
  
    BOOST_CHECK_CLOSE_FRACTION(
         kurtosis(bernoulli_distribution<RealType>(static_cast<RealType>(0.1L))),
         static_cast<RealType>(8.11111111111111111111111111111111111111111111L),
         tolerance);
  
    BOOST_CHECK_CLOSE_FRACTION(
         kurtosis_excess(bernoulli_distribution<RealType>(static_cast<RealType>(0.1L))),
         static_cast<RealType>(5.11111111111111111111111111111111111111111111L),
         tolerance);
  
    BOOST_MATH_CHECK_THROW(
       quantile(
          bernoulli_distribution<RealType>(static_cast<RealType>(2)), // prob >1
          static_cast<RealType>(0)), std::domain_error
       );
    BOOST_MATH_CHECK_THROW(
       quantile(
          bernoulli_distribution<RealType>(static_cast<RealType>(-1)), // prob < 0
          static_cast<RealType>(0)), std::domain_error
       );
    BOOST_MATH_CHECK_THROW(
       quantile(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.5L)), // k >1
          static_cast<RealType>(-1)), std::domain_error
       );
    BOOST_MATH_CHECK_THROW(
       quantile(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.5L)), // k < 0
          static_cast<RealType>(2)), std::domain_error
       );
  
    BOOST_CHECK_CLOSE_FRACTION(
       cdf(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(0)),
          static_cast<RealType>(0.4L), // 1 - p
          tolerance
       );
  
    BOOST_CHECK_CLOSE_FRACTION(
       cdf(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(1)),
          static_cast<RealType>(1), // p
          tolerance
       );
  
    BOOST_CHECK_CLOSE_FRACTION(
       cdf(complement(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(1))),
          static_cast<RealType>(0),
          tolerance
       );
  
    BOOST_CHECK_CLOSE_FRACTION(
       cdf(complement(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(0))),
          static_cast<RealType>(0.6L),
          tolerance
       );
  
    BOOST_CHECK_EQUAL(
       quantile(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(0.1L)),  // < p
          static_cast<RealType>(0)
       );
  
    BOOST_CHECK_EQUAL(
       quantile(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(0.9L)),  // > p
          static_cast<RealType>(1)
       );
  
     BOOST_CHECK_EQUAL(
       quantile(complement(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(0.1L))),  // < p
          static_cast<RealType>(1)
       );
  
     BOOST_CHECK_EQUAL(
       quantile(complement(
          bernoulli_distribution<RealType>(static_cast<RealType>(0.6L)),
          static_cast<RealType>(0.9L))),  // > p
          static_cast<RealType>(0)
       );
  
     // Checks for 'bad' parameters.
     // Construction.
     BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType>(-1), std::domain_error); // p outside 0 to 1.
     BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType>(+2), std::domain_error); // p outside 0 to 1.
  
     // Parameters.
     bernoulli_distribution<RealType> dist(RealType(1));
     BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error);
     BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error);
     BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
     BOOST_MATH_CHECK_THROW(quantile(dist, 2), std::domain_error);
     BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
     BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
     BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
  
     // No longer allow any parameter to be NaN or inf, so all these tests should throw.
     if (std::numeric_limits<RealType>::has_quiet_NaN)
     {
      // Attempt to construct from non-finite should throw.
       RealType nan = std::numeric_limits<RealType>::quiet_NaN();
  #ifndef BOOST_NO_EXCEPTIONS
       BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType> b(nan), std::domain_error);
  #else
       BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType>(nan), std::domain_error);
  #endif
      // Non-finite parameters should throw.
       bernoulli_distribution<RealType> b(RealType(1));
       BOOST_MATH_CHECK_THROW(pdf(b, +nan), std::domain_error); // x = NaN
       BOOST_MATH_CHECK_THROW(cdf(b, +nan), std::domain_error); // x = NaN
       BOOST_MATH_CHECK_THROW(cdf(complement(b, +nan)), std::domain_error); // x = + nan
       BOOST_MATH_CHECK_THROW(quantile(b, +nan), std::domain_error); // p = + nan
       BOOST_MATH_CHECK_THROW(quantile(complement(b, +nan)), std::domain_error); // p = + nan
    } // has_quiet_NaN
  
    if (std::numeric_limits<RealType>::has_infinity)
    {
       RealType inf = std::numeric_limits<RealType>::infinity();
  #ifndef BOOST_NO_EXCEPTIONS
       BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType> w(inf), std::domain_error);
  #else
       BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType>(inf), std::domain_error);
  #endif
       bernoulli_distribution<RealType> w(RealType(1));
  #ifndef BOOST_NO_EXCEPTIONS
       BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType> w(inf), std::domain_error);
  #else
       BOOST_MATH_CHECK_THROW(bernoulli_distribution<RealType>(inf), std::domain_error);
  #endif
       BOOST_MATH_CHECK_THROW(pdf(w, +inf), std::domain_error); // x = inf
       BOOST_MATH_CHECK_THROW(cdf(w, +inf), std::domain_error); // x = inf
       BOOST_MATH_CHECK_THROW(cdf(complement(w, +inf)), std::domain_error); // x = + inf
       BOOST_MATH_CHECK_THROW(quantile(w, +inf), std::domain_error); // p = + inf
       BOOST_MATH_CHECK_THROW(quantile(complement(w, +inf)), std::domain_error); // p = + inf
     } // has_infinity
  
  } // template <class RealType>void test_spots(RealType)
  
  BOOST_AUTO_TEST_CASE( test_main )
  {
     BOOST_MATH_CONTROL_FP;
     // Check that can generate bernoulli distribution using both convenience methods:
     bernoulli_distribution<double> bn1(0.5); // Using default RealType double.
     boost::math::bernoulli bn2(0.5); // Using typedef.
  
    BOOST_CHECK_EQUAL(bn1.success_fraction(), 0.5);
    BOOST_CHECK_EQUAL(bn2.success_fraction(), 0.5);
  
    BOOST_CHECK_EQUAL(kurtosis(bn2) -3, kurtosis_excess(bn2));
    BOOST_CHECK_EQUAL(kurtosis_excess(bn2), -2);
  
    //using namespace boost::math; or
    using boost::math::bernoulli;
  
    double tol5eps = std::numeric_limits<double>::epsilon() * 5; // 5 eps as a fraction.
    // Default bernoulli is type double, so these test values should also be type double.
    BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(bernoulli(0.1)), 5.11111111111111111111111111111111111111111111111111, tol5eps);
    BOOST_CHECK_CLOSE_FRACTION(kurtosis_excess(bernoulli(0.9)), 5.11111111111111111111111111111111111111111111111111, tol5eps);
    BOOST_CHECK_CLOSE_FRACTION(kurtosis(bernoulli(0.6)), 1./0.4 + 1./0.6 -3., tol5eps);
    BOOST_CHECK_EQUAL(kurtosis(bernoulli(0)), +std::numeric_limits<double>::infinity());
    BOOST_CHECK_EQUAL(kurtosis(bernoulli(1)), +std::numeric_limits<double>::infinity());
   //
  
    // Basic sanity-check spot values.
  
    // (Parameter value, arbitrarily zero, only communicates the floating point type).
    test_spots(0.0F); // Test float.
    test_spots(0.0); // Test double.
    test_spots(0.0L); // Test long double.
  #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
    test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
  #endif
  
  } // BOOST_AUTO_TEST_CASE( test_main )
  
  /*
  
  Output is:
  
    Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_bernouilli.exe"
    Running 1 test case...
    Tolerance for type float is 1.19e-005 (or 0.00119%).
    Tolerance for type double is 2.22e-014 (or 2.22e-012%).
    Tolerance for type long double is 2.22e-014 (or 2.22e-012%).
    Tolerance for type class boost::math::concepts::real_concept is 2.22e-014 (or 2.22e-012%).
  
    *** No errors detected
  
  
  */
  