text: // test_binomial.cpp
  
  // Copyright John Maddock 2006.
  // Copyright  Paul A. Bristow 2007.
  
  // 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 Binomial Cumulative Distribution Function.
  
  #define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
  
  #if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
  #  define TEST_FLOAT
  #  define TEST_DOUBLE
  #  define TEST_LDOUBLE
  #  define TEST_REAL_CONCEPT
  #endif
  
  #ifdef _MSC_VER
  #  pragma warning(disable: 4127) // conditional expression is constant.
  #  pragma warning(disable: 4100) // unreferenced formal parameter.
  // Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */
  //#  pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test)
  // Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535.
  #endif
  
  #include <boost/math/tools/test.hpp>
  #include <boost/math/concepts/real_concept.hpp> // for real_concept
  using ::boost::math::concepts::real_concept;
  
  #include <boost/math/distributions/binomial.hpp> // for binomial_distribution
  using boost::math::binomial_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
  #include "table_type.hpp"
  
  #include "test_out_of_range.hpp"
  
  #include <iostream>
  using std::cout;
  using std::endl;
  #include <limits>
  using std::numeric_limits;
  
  template <class RealType>
  void test_spot(
       RealType N,    // Number of trials
       RealType k,    // Number of successes
       RealType p,    // Probability of success
       RealType P,    // CDF
       RealType Q,    // Complement of CDF
       RealType tol)  // Test tolerance
  {
     boost::math::binomial_distribution<RealType> bn(N, p);
     BOOST_CHECK_CLOSE(
        cdf(bn, k), P, tol);
     if((P < 0.99) && (Q < 0.99))
     {
        //
        // We can only check this if P is not too close to 1,
        // so that we can guarantee Q is free of error:
        //
        BOOST_CHECK_CLOSE(
           cdf(complement(bn, k)), Q, tol);
        if(k != 0)
        {
           BOOST_CHECK_CLOSE(
              quantile(bn, P), k, tol);
        }
        else
        {
           // Just check quantile is very small:
           if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
           {
              // Limit where this is checked: if exponent range is very large we may
              // run out of iterations in our root finding algorithm.
              BOOST_CHECK(quantile(bn, P) < boost::math::tools::epsilon<RealType>() * 10);
           }
        }
        if(k != 0)
        {
           BOOST_CHECK_CLOSE(
              quantile(complement(bn, Q)), k, tol);
        }
        else
        {
           // Just check quantile is very small:
           if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
           {
              // Limit where this is checked: if exponent range is very large we may
              // run out of iterations in our root finding algorithm.
              BOOST_CHECK(quantile(complement(bn, Q)) < boost::math::tools::epsilon<RealType>() * 10);
           }
        }
        if(k > 0)
        {
           // estimate success ratio:
           // Note lower bound uses a different formual internally
           // from upper bound, have to adjust things to prevent
           // fencepost errors:
           BOOST_CHECK_CLOSE(
              binomial_distribution<RealType>::find_lower_bound_on_p(
                 N, k+1, Q),
              p, tol);
           BOOST_CHECK_CLOSE(
              binomial_distribution<RealType>::find_upper_bound_on_p(
                 N, k, P),
              p, tol);
  
           if(Q < P)
           {
              // Default method (Clopper Pearson)
              BOOST_CHECK(
                 binomial_distribution<RealType>::find_lower_bound_on_p(
                    N, k, Q)
                    <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, Q)
                    );
              BOOST_CHECK((
                 binomial_distribution<RealType>::find_lower_bound_on_p(
                    N, k, Q)
                    <= k/N) && (k/N <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, Q))
                    );
              // Bayes Method (Jeffreys Prior)
              BOOST_CHECK(
                 binomial_distribution<RealType>::find_lower_bound_on_p(
                 N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
                    <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
                    );
              BOOST_CHECK((
                 binomial_distribution<RealType>::find_lower_bound_on_p(
                    N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
                    <= k/N) && (k/N <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval))
                    );
           }
           else
           {
              // Default method (Clopper Pearson)
              BOOST_CHECK(
                 binomial_distribution<RealType>::find_lower_bound_on_p(
                    N, k, P)
                    <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, P)
                    );
              BOOST_CHECK(
                 (binomial_distribution<RealType>::find_lower_bound_on_p(
                    N, k, P)
                    <= k / N) && (k/N <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, P))
                    );
              // Bayes Method (Jeffreys Prior)
              BOOST_CHECK(
                 binomial_distribution<RealType>::find_lower_bound_on_p(
                    N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
                    <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
                    );
              BOOST_CHECK(
                 (binomial_distribution<RealType>::find_lower_bound_on_p(
                    N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
                    <= k / N) && (k/N <=
                 binomial_distribution<RealType>::find_upper_bound_on_p(
                    N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval))
                    );
           }
        }
        //
        // estimate sample size:
        //
        BOOST_CHECK_CLOSE(
           binomial_distribution<RealType>::find_minimum_number_of_trials(
              k, p, P),
           N, tol);
        BOOST_CHECK_CLOSE(
           binomial_distribution<RealType>::find_maximum_number_of_trials(
              k, p, Q),
           N, tol);
     }
  
     // Double check consistency of CDF and PDF by computing
     // the finite sum:
     RealType sum = 0;
     for(unsigned i = 0; i <= k; ++i)
        sum += pdf(bn, RealType(i));
     BOOST_CHECK_CLOSE(
        sum, P, tol);
     // And complement as well:
     sum = 0;
     for(RealType i = N; i > k; i -= 1)
        sum += pdf(bn, i);
     if(P < 0.99)
     {
        BOOST_CHECK_CLOSE(
           sum, Q, tol);
     }
     else
     {
        // Not enough information content in P for Q to be meaningful
        RealType tol = (std::max)(2 * Q, boost::math::tools::epsilon<RealType>());
        BOOST_CHECK(sum < tol);
     }
  }
  
  template <class RealType> // Any floating-point type RealType.
  void test_spots(RealType T)
  {
    // Basic sanity checks, test data is to double precision only
    // so set tolerance to 100eps expressed as a persent, or
    // 100eps of type double expressed as a persent, whichever
    // is the larger.
  
    RealType tolerance = (std::max)
        (boost::math::tools::epsilon<RealType>(),
        static_cast<RealType>(std::numeric_limits<double>::epsilon()));
    tolerance *= 100 * 1000;
    RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100;  // 5 eps as a persent
  
    cout << "Tolerance for type " << typeid(T).name()  << " is " << tolerance << " %" << endl;
  
  
    // Sources of spot test values:
  
    // MathCAD defines pbinom(k, n, p)
    // returns pr(X ,=k) when random variable X has the binomial distribution with parameters n and p.
    // 0 <= k ,= n
    // 0 <= p <= 1
    // P = pbinom(30, 500, 0.05) = 0.869147702104609
  
    using boost::math::binomial_distribution;
    using  ::boost::math::cdf;
    using  ::boost::math::pdf;
  
  #if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 0)
    // Test binomial using cdf spot values from MathCAD.
    // These test quantiles and complements as well.
    test_spot(
       static_cast<RealType>(500),                     // Sample size, N
       static_cast<RealType>(30),                      // Number of successes, k
       static_cast<RealType>(0.05),                    // Probability of success, p
       static_cast<RealType>(0.869147702104609),       // Probability of result (CDF), P
       static_cast<RealType>(1 - 0.869147702104609),   // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(500),                     // Sample size, N
       static_cast<RealType>(250),                     // Number of successes, k
       static_cast<RealType>(0.05),                    // Probability of success, p
       static_cast<RealType>(1),                       // Probability of result (CDF), P
       static_cast<RealType>(0),   // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(500),                     // Sample size, N
       static_cast<RealType>(470),                     // Number of successes, k
       static_cast<RealType>(0.95),                    // Probability of success, p
       static_cast<RealType>(0.176470742656766),       // Probability of result (CDF), P
       static_cast<RealType>(1 - 0.176470742656766),   // Q = 1 - P
       tolerance * 10);                                // Note higher tolerance on this test!
  
    test_spot(
       static_cast<RealType>(500),                       // Sample size, N
       static_cast<RealType>(400),                       // Number of successes, k
       static_cast<RealType>(0.05),                      // Probability of success, p
       static_cast<RealType>(1),                         // Probability of result (CDF), P
       static_cast<RealType>(0),                         // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(500),                       // Sample size, N
       static_cast<RealType>(400),                       // Number of successes, k
       static_cast<RealType>(0.9),                       // Probability of success, p
       static_cast<RealType>(1.80180425681923E-11),      // Probability of result (CDF), P
       static_cast<RealType>(1 - 1.80180425681923E-11),  // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(500),                       // Sample size, N
       static_cast<RealType>(5),                         // Number of successes, k
       static_cast<RealType>(0.05),                      // Probability of success, p
       static_cast<RealType>(9.181808267643E-7),         // Probability of result (CDF), P
       static_cast<RealType>(1 - 9.181808267643E-7),     // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(2),                       // Sample size, N
       static_cast<RealType>(1),                       // Number of successes, k
       static_cast<RealType>(0.5),                     // Probability of success, p
       static_cast<RealType>(0.75),                    // Probability of result (CDF), P
       static_cast<RealType>(0.25),                    // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(8),                       // Sample size, N
       static_cast<RealType>(3),                       // Number of successes, k
       static_cast<RealType>(0.25),                    // Probability of success, p
       static_cast<RealType>(0.8861846923828125),      // Probability of result (CDF), P
       static_cast<RealType>(1 - 0.8861846923828125),  // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(8),                       // Sample size, N
       static_cast<RealType>(0),                       // Number of successes, k
       static_cast<RealType>(0.25),                    // Probability of success, p
       static_cast<RealType>(0.1001129150390625),      // Probability of result (CDF), P
       static_cast<RealType>(1 - 0.1001129150390625),  // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(8),                       // Sample size, N
       static_cast<RealType>(1),                       // Number of successes, k
       static_cast<RealType>(0.25),                    // Probability of success, p
       static_cast<RealType>(0.36708068847656244),     // Probability of result (CDF), P
       static_cast<RealType>(1 - 0.36708068847656244), // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(8),                       // Sample size, N
       static_cast<RealType>(4),                       // Number of successes, k
       static_cast<RealType>(0.25),                    // Probability of success, p
       static_cast<RealType>(0.9727020263671875),      // Probability of result (CDF), P
       static_cast<RealType>(1 - 0.9727020263671875),  // Q = 1 - P
       tolerance);
  
    test_spot(
       static_cast<RealType>(8),                       // Sample size, N
       static_cast<RealType>(7),                       // Number of successes, k
       static_cast<RealType>(0.25),                    // Probability of success, p
       static_cast<RealType>(0.9999847412109375),      // Probability of result (CDF), P
       static_cast<RealType>(1 - 0.9999847412109375),  // Q = 1 - P
       tolerance);
  
    // Tests on PDF follow:
    BOOST_CHECK_CLOSE(
       pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.75)),
       static_cast<RealType>(10)),  // k.
       static_cast<RealType>(0.00992227527967770583927631378173), // 0.00992227527967770583927631378173
       tolerance);
  
    BOOST_CHECK_CLOSE(
      pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.5)),
      static_cast<RealType>(10)),  // k.
      static_cast<RealType>(0.17619705200195312500000000000000000000), // get k=10 0.049611376398388612 p = 0.25
      tolerance);
  
    // Binomial pdf Test values from
    // http://www.adsciengineering.com/bpdcalc/index.php  for example
    // http://www.adsciengineering.com/bpdcalc/index.php?n=20&p=0.25&start=0&stop=20&Submit=Generate
    // Appears to use at least 80-bit long double for 32 decimal digits accuracy,
    // but loses accuracy of display if leading zeros?
    // (if trailings zero then are exact values?)
    // so useful for testing 64-bit double accuracy.
    // P = 0.25, n = 20, k = 0 to 20
  
    //0   C(20,0) * 0.25^0 * 0.75^20   0.00317121193893399322405457496643
    //1   C(20,1) * 0.25^1 * 0.75^19   0.02114141292622662149369716644287
    //2   C(20,2) * 0.25^2 * 0.75^18   0.06694780759971763473004102706909
    //3   C(20,3) * 0.25^3 * 0.75^17   0.13389561519943526946008205413818
    //4   C(20,4) * 0.25^4 * 0.75^16   0.18968545486586663173511624336242
    //5   C(20,5) * 0.25^5 * 0.75^15   0.20233115185692440718412399291992
    //6   C(20,6) * 0.25^6 * 0.75^14   0.16860929321410367265343666076660
    //7   C(20,7) * 0.25^7 * 0.75^13   0.11240619547606911510229110717773
    //8   C(20,8) * 0.25^8 * 0.75^12   0.06088668921620410401374101638793
    //9   C(20,9) * 0.25^9 * 0.75^11   0.02706075076275737956166267395019
    //10   C(20,10) * 0.25^10 * 0.75^10   0.00992227527967770583927631378173
    //11   C(20,11) * 0.25^11 * 0.75^9   0.00300675008475081995129585266113
    //12   C(20,12) * 0.25^12 * 0.75^8   0.00075168752118770498782396316528
    //13   C(20,13) * 0.25^13 * 0.75^7   0.00015419231203850358724594116210
    //14   C(20,14) * 0.25^14 * 0.75^6   0.00002569871867308393120765686035
    //15   C(20,15) * 0.25^15 * 0.75^5   0.00000342649582307785749435424804
    //16   C(20,16) * 0.25^16 * 0.75^4   0.00000035692664823727682232856750
    //17   C(20,17) * 0.25^17 * 0.75^3   0.00000002799424692057073116302490
    //18   C(20,18) * 0.25^18 * 0.75^2   0.00000000155523594003170728683471
    //19   C(20,19) * 0.25^19 * 0.75^1   0.00000000005456968210637569427490
    //20   C(20,20) * 0.25^20 * 0.75^0   0.00000000000090949470177292823791
  
  
      BOOST_CHECK_CLOSE(
      pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
      static_cast<RealType>(10)),  // k.
      static_cast<RealType>(0.00992227527967770583927631378173), // k=10  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 0 use different formula - only exp so more accurate.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
      static_cast<RealType>(0)),  // k.
      static_cast<RealType>(0.00317121193893399322405457496643), // k=0  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 20 use different formula - only exp so more accurate.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
      static_cast<RealType>(20)),  // k == n.
      static_cast<RealType>(0.00000000000090949470177292823791), // k=20  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 1.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
      static_cast<RealType>(1)),  // k.
      static_cast<RealType>(0.02114141292622662149369716644287), // k=1  p = 0.25
      tolerance);
  
      // Some exact (probably) values.
      BOOST_CHECK_CLOSE(
      pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
      static_cast<RealType>(0)),  // k.
      static_cast<RealType>(0.10011291503906250000000000000000), // k=0  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 1.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
      static_cast<RealType>(1)),  // k.
      static_cast<RealType>(0.26696777343750000000000000000000), // k=1  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 2.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
      static_cast<RealType>(2)),  // k.
      static_cast<RealType>(0.31146240234375000000000000000000), // k=2  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 3.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
      static_cast<RealType>(3)),  // k.
      static_cast<RealType>(0.20764160156250000000000000000000), // k=3  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 7.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
      static_cast<RealType>(7)),  // k.
      static_cast<RealType>(0.00036621093750000000000000000000), // k=7  p = 0.25
      tolerance);
  
      BOOST_CHECK_CLOSE( // k = 8.
      pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
      static_cast<RealType>(8)),  // k = n.
      static_cast<RealType>(0.00001525878906250000000000000000), // k=8  p = 0.25
      tolerance);
  
      binomial_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(0.25));
      RealType x = static_cast<RealType>(0.125);
      using namespace std; // ADL of std names.
      // mean:
      BOOST_CHECK_CLOSE(
         mean(dist)
         , static_cast<RealType>(8 * 0.25), tol2);
      // variance:
      BOOST_CHECK_CLOSE(
         variance(dist)
         , static_cast<RealType>(8 * 0.25 * 0.75), tol2);
      // std deviation:
      BOOST_CHECK_CLOSE(
         standard_deviation(dist)
         , static_cast<RealType>(sqrt(8 * 0.25L * 0.75L)), tol2);
      // hazard:
      BOOST_CHECK_CLOSE(
         hazard(dist, x)
         , pdf(dist, x) / cdf(complement(dist, x)), tol2);
      // cumulative hazard:
      BOOST_CHECK_CLOSE(
         chf(dist, x)
         , -log(cdf(complement(dist, x))), tol2);
      // coefficient_of_variation:
      BOOST_CHECK_CLOSE(
         coefficient_of_variation(dist)
         , standard_deviation(dist) / mean(dist), tol2);
      // mode:
      BOOST_CHECK_CLOSE(
         mode(dist)
         , static_cast<RealType>(std::floor(9 * 0.25)), tol2);
      // skewness:
      BOOST_CHECK_CLOSE(
         skewness(dist)
         , static_cast<RealType>(0.40824829046386301636621401245098L), (std::max)(tol2, static_cast<RealType>(5e-29))); // test data has 32 digits only.
      // kurtosis:
      BOOST_CHECK_CLOSE(
         kurtosis(dist)
         , static_cast<RealType>(2.916666666666666666666666666666666666L), tol2);
      // kurtosis excess:
      BOOST_CHECK_CLOSE(
         kurtosis_excess(dist)
         , static_cast<RealType>(-0.08333333333333333333333333333333333333L), tol2);
      // Check kurtosis_excess == kurtosis -3;
        BOOST_CHECK_EQUAL(kurtosis(dist), static_cast<RealType>(3) + kurtosis_excess(dist));
  
      // special cases for PDF:
      BOOST_CHECK_EQUAL(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
            static_cast<RealType>(0)), static_cast<RealType>(1)
         );
      BOOST_CHECK_EQUAL(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
            static_cast<RealType>(0.0001)), static_cast<RealType>(0)
         );
      BOOST_CHECK_EQUAL(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
            static_cast<RealType>(0.001)), static_cast<RealType>(0)
         );
      BOOST_CHECK_EQUAL(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
            static_cast<RealType>(8)), static_cast<RealType>(1)
         );
      BOOST_CHECK_EQUAL(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(0.25)),
            static_cast<RealType>(0)), static_cast<RealType>(1)
         );
      BOOST_MATH_CHECK_THROW(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(-1), static_cast<RealType>(0.25)),
            static_cast<RealType>(0)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
            static_cast<RealType>(0)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
            static_cast<RealType>(0)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
            static_cast<RealType>(-1)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         pdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
            static_cast<RealType>(9)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         cdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
            static_cast<RealType>(-1)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         cdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
            static_cast<RealType>(9)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         cdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
            static_cast<RealType>(0)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         cdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
            static_cast<RealType>(0)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         quantile(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
            static_cast<RealType>(0)), std::domain_error
         );
      BOOST_MATH_CHECK_THROW(
         quantile(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
            static_cast<RealType>(0)), std::domain_error
         );
  
      BOOST_CHECK_EQUAL(
         quantile(
            binomial_distribution<RealType>(static_cast<RealType>(16), static_cast<RealType>(0.25)),
            static_cast<RealType>(0.01)), // Less than cdf == pdf(binomial_distribution<RealType>(16, 0.25), 0)
            static_cast<RealType>(0) // so expect zero as best approximation.
         );
  
      BOOST_CHECK_EQUAL(
         cdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
            static_cast<RealType>(8)), static_cast<RealType>(1)
         );
      BOOST_CHECK_EQUAL(
         cdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
            static_cast<RealType>(7)), static_cast<RealType>(1)
         );
      BOOST_CHECK_EQUAL(
         cdf(
            binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
            static_cast<RealType>(7)), static_cast<RealType>(0)
         );
  
  #endif
  
    {
      // This is a visual sanity check that everything is OK:
      binomial_distribution<RealType> my8dist(8., 0.25); // Note: double values (matching the distribution definition) avoid the need for any casting.
      //cout << "mean(my8dist) = " << boost::math::mean(my8dist) << endl; // mean(my8dist) = 2
      //cout << "my8dist.trials() = " << my8dist.trials()  << endl; // my8dist.trials() = 8
      //cout << "my8dist.success_fraction() = " << my8dist.success_fraction()  << endl; // my8dist.success_fraction() = 0.25
      BOOST_CHECK_CLOSE(my8dist.trials(), static_cast<RealType>(8), tol2);
      BOOST_CHECK_CLOSE(my8dist.success_fraction(), static_cast<RealType>(0.25), tol2);
  
     //{
     //   int n = static_cast<int>(boost::math::tools::real_cast<double>(my8dist.trials()));
     //   RealType sumcdf = 0.;
     //   for (int k = 0; k <= n; k++)
     //   {
     //     cout << k << ' ' << pdf(my8dist, static_cast<RealType>(k));
     //     sumcdf += pdf(my8dist, static_cast<RealType>(k));
     //     cout  << ' '  << sumcdf;
     //     cout << ' ' << cdf(my8dist, static_cast<RealType>(k));
     //     cout << ' ' << sumcdf - cdf(my8dist, static_cast<RealType>(k)) << endl;
     //   } // for k
     // }
      // n = 8, p =0.25
      //k         pdf              cdf
      //0 0.1001129150390625 0.1001129150390625
      //1 0.26696777343749994 0.36708068847656244
      //2 0.31146240234375017 0.67854309082031261
      //3 0.20764160156249989 0.8861846923828125
      //4 0.086517333984375 0.9727020263671875
      //5 0.023071289062499997 0.9957733154296875
      //6 0.0038452148437500009 0.9996185302734375
      //7 0.00036621093749999984 0.9999847412109375
      //8 1.52587890625e-005 1 1 0
    }
  #define T RealType
  #include "binomial_quantile.ipp"
  
    for(unsigned i = 0; i < binomial_quantile_data.size(); ++i)
    {
       using namespace boost::math::policies;
       RealType tol = boost::math::tools::epsilon<RealType>() * 500;
       if(!boost::is_floating_point<RealType>::value)
          tol *= 10;  // no lanczos approximation implies less accuracy
       RealType x;
  #if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 1)
       //
       // Check full real value first:
       //
       typedef policy<discrete_quantile<boost::math::policies::real> > P1;
       binomial_distribution<RealType, P1> p1(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
       x = quantile(p1, binomial_quantile_data[i][2]);
       BOOST_CHECK_CLOSE_FRACTION(x, (RealType)binomial_quantile_data[i][3], tol);
       x = quantile(complement(p1, (RealType)binomial_quantile_data[i][2]));
       BOOST_CHECK_CLOSE_FRACTION(x, (RealType)binomial_quantile_data[i][4], tol);
  #endif
  #if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 2)
       //
       // Now with round down to integer:
       //
       typedef policy<discrete_quantile<integer_round_down> > P2;
       binomial_distribution<RealType, P2> p2(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
       x = quantile(p2, binomial_quantile_data[i][2]);
       BOOST_CHECK_EQUAL(x, (RealType)floor(binomial_quantile_data[i][3]));
       x = quantile(complement(p2, binomial_quantile_data[i][2]));
       BOOST_CHECK_EQUAL(x, (RealType)floor(binomial_quantile_data[i][4]));
  #endif
  #if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 3)
       //
       // Now with round up to integer:
       //
       typedef policy<discrete_quantile<integer_round_up> > P3;
       binomial_distribution<RealType, P3> p3(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
       x = quantile(p3, binomial_quantile_data[i][2]);
       BOOST_CHECK_EQUAL(x, (RealType)ceil(binomial_quantile_data[i][3]));
       x = quantile(complement(p3, binomial_quantile_data[i][2]));
       BOOST_CHECK_EQUAL(x, (RealType)ceil(binomial_quantile_data[i][4]));
  #endif
  #if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 4)
       //
       // Now with round to integer "outside":
       //
       typedef policy<discrete_quantile<integer_round_outwards> > P4;
       binomial_distribution<RealType, P4> p4(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
       x = quantile(p4, binomial_quantile_data[i][2]);
       BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? floor(binomial_quantile_data[i][3]) : ceil(binomial_quantile_data[i][3])));
       x = quantile(complement(p4, binomial_quantile_data[i][2]));
       BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? ceil(binomial_quantile_data[i][4]) : floor(binomial_quantile_data[i][4])));
  #endif
  #if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 5)
       //
       // Now with round to integer "inside":
       //
       typedef policy<discrete_quantile<integer_round_inwards> > P5;
       binomial_distribution<RealType, P5> p5(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
       x = quantile(p5, binomial_quantile_data[i][2]);
       BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? ceil(binomial_quantile_data[i][3]) : floor(binomial_quantile_data[i][3])));
       x = quantile(complement(p5, binomial_quantile_data[i][2]));
       BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? floor(binomial_quantile_data[i][4]) : ceil(binomial_quantile_data[i][4])));
  #endif
  #if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 6)
       //
       // Now with round to nearest integer:
       //
       typedef policy<discrete_quantile<integer_round_nearest> > P6;
       binomial_distribution<RealType, P6> p6(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
       x = quantile(p6, binomial_quantile_data[i][2]);
       BOOST_CHECK_EQUAL(x, (RealType)(floor(binomial_quantile_data[i][3] + 0.5f)));
       x = quantile(complement(p6, binomial_quantile_data[i][2]));
       BOOST_CHECK_EQUAL(x, (RealType)(floor(binomial_quantile_data[i][4] + 0.5f)));
  #endif
    }
  
     check_out_of_range<boost::math::binomial_distribution<RealType> >(1, 1); // (All) valid constructor parameter values.
  
  
  } // template <class RealType>void test_spots(RealType)
  
  BOOST_AUTO_TEST_CASE( test_main )
  {
     BOOST_MATH_CONTROL_FP;
     // Check that can generate binomial distribution using one convenience methods:
     binomial_distribution<> mybn2(1., 0.5); // Using default RealType double.
    // but that
     // boost::math::binomial mybn1(1., 0.5); // Using typedef fails
    // error C2039: 'binomial' : is not a member of 'boost::math'
  
    // Basic sanity-check spot values.
  
    // (Parameter value, arbitrarily zero, only communicates the floating point type).
  #ifdef TEST_FLOAT
    test_spots(0.0F); // Test float.
  #endif
  #ifdef TEST_DOUBLE
    test_spots(0.0); // Test double.
  #endif
  #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
  #ifdef TEST_LDOUBLE
    test_spots(0.0L); // Test long double.
  #endif
  #if !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
  #ifdef TEST_REAL_CONCEPT
    test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
  #endif
  #endif
  #else
     std::cout << "<note>The long double tests have been disabled on this platform "
        "either because the long double overloads of the usual math functions are "
        "not available at all, or because they are too inaccurate for these tests "
        "to pass.</note>" << std::endl;
  #endif
  
  } // BOOST_AUTO_TEST_CASE( test_main )
  
  /*
  
  Output is:
  
    Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_binomial.exe"
    Running 1 test case...
    Tolerance for type float is 0.0119209 %
    Tolerance for type double is 2.22045e-011 %
    Tolerance for type long double is 2.22045e-011 %
    Tolerance for type class boost::math::concepts::real_concept is 2.22045e-011 %
  
    *** No errors detected
  
  ========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
  
  
  */
  