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diff --git a/src/boost/libs/math/test/test_binomial.cpp b/src/boost/libs/math/test/test_binomial.cpp
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+++ b/src/boost/libs/math/test/test_binomial.cpp
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+// 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/tools/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 formula 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 percent, or
+ // 100eps of type double expressed as a percent, 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 percent
+
+ 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 ==========
+
+
+*/
generated by cgit v1.2.3 (git 2.39.1) at 2024-09-19 07:42:21 +0000