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-rw-r--r--src/boost/libs/math/test/test_negative_binomial.cpp861
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diff --git a/src/boost/libs/math/test/test_negative_binomial.cpp b/src/boost/libs/math/test/test_negative_binomial.cpp
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+++ b/src/boost/libs/math/test/test_negative_binomial.cpp
@@ -0,0 +1,861 @@
+// test_negative_binomial.cpp
+
+// Copyright Paul A. Bristow 2007.
+// Copyright John Maddock 2006.
+
+// 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)
+
+// Tests for Negative Binomial Distribution.
+
+// Note that these defines must be placed BEFORE #includes.
+#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
+// because several tests overflow & underflow by design.
+#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
+
+#ifdef _MSC_VER
+# pragma warning(disable: 4127) // conditional expression is constant.
+#endif
+
+#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
+
+#include <boost/math/tools/test.hpp> // for real_concept
+#include <boost/math/concepts/real_concept.hpp> // for real_concept
+using ::boost::math::concepts::real_concept;
+
+#include <boost/math/distributions/negative_binomial.hpp> // for negative_binomial_distribution
+using boost::math::negative_binomial_distribution;
+
+#include <boost/math/special_functions/gamma.hpp>
+ using boost::math::lgamma; // log gamma
+
+#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;
+using std::setprecision;
+using std::showpoint;
+#include <limits>
+using std::numeric_limits;
+
+template <class RealType>
+void test_spot( // Test a single spot value against 'known good' values.
+ RealType N, // Number of successes.
+ RealType k, // Number of failures.
+ RealType p, // Probability of success_fraction.
+ RealType P, // CDF probability.
+ RealType Q, // Complement of CDF.
+ RealType tol) // Test tolerance.
+{
+ boost::math::negative_binomial_distribution<RealType> bn(N, p);
+ BOOST_CHECK_EQUAL(N, bn.successes());
+ BOOST_CHECK_EQUAL(p, bn.success_fraction());
+ 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 that 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);
+ }
+ }
+ // estimate success ratio:
+ BOOST_CHECK_CLOSE(
+ negative_binomial_distribution<RealType>::find_lower_bound_on_p(
+ N+k, N, P),
+ p, tol);
+ // Note we bump up the sample size here, purely for the sake of the test,
+ // internally the function has to adjust the sample size so that we get
+ // the right upper bound, our test undoes this, so we can verify the result.
+ BOOST_CHECK_CLOSE(
+ negative_binomial_distribution<RealType>::find_upper_bound_on_p(
+ N+k+1, N, Q),
+ p, tol);
+
+ if(Q < P)
+ {
+ //
+ // We check two things here, that the upper and lower bounds
+ // are the right way around, and that they do actually bracket
+ // the naive estimate of p = successes / (sample size)
+ //
+ BOOST_CHECK(
+ negative_binomial_distribution<RealType>::find_lower_bound_on_p(
+ N+k, N, Q)
+ <=
+ negative_binomial_distribution<RealType>::find_upper_bound_on_p(
+ N+k, N, Q)
+ );
+ BOOST_CHECK(
+ negative_binomial_distribution<RealType>::find_lower_bound_on_p(
+ N+k, N, Q)
+ <=
+ N / (N+k)
+ );
+ BOOST_CHECK(
+ N / (N+k)
+ <=
+ negative_binomial_distribution<RealType>::find_upper_bound_on_p(
+ N+k, N, Q)
+ );
+ }
+ else
+ {
+ // As above but when P is small.
+ BOOST_CHECK(
+ negative_binomial_distribution<RealType>::find_lower_bound_on_p(
+ N+k, N, P)
+ <=
+ negative_binomial_distribution<RealType>::find_upper_bound_on_p(
+ N+k, N, P)
+ );
+ BOOST_CHECK(
+ negative_binomial_distribution<RealType>::find_lower_bound_on_p(
+ N+k, N, P)
+ <=
+ N / (N+k)
+ );
+ BOOST_CHECK(
+ N / (N+k)
+ <=
+ negative_binomial_distribution<RealType>::find_upper_bound_on_p(
+ N+k, N, P)
+ );
+ }
+
+ // Estimate sample size:
+ BOOST_CHECK_CLOSE(
+ negative_binomial_distribution<RealType>::find_minimum_number_of_trials(
+ k, p, P),
+ N+k, tol);
+ BOOST_CHECK_CLOSE(
+ negative_binomial_distribution<RealType>::find_maximum_number_of_trials(
+ k, p, Q),
+ N+k, 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);
+
+ // Complement is not possible since sum is to infinity.
+ } //
+} // test_spot
+
+template <class RealType> // Any floating-point type RealType.
+void test_spots(RealType)
+{
+ // Basic sanity checks, test data is to double precision only
+ // so set tolerance to 1000 eps expressed as a percent, or
+ // 1000 eps 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 * 100000.0f;
+
+ cout << "Tolerance = " << tolerance << "%." << endl;
+
+ RealType tol1eps = boost::math::tools::epsilon<RealType>() * 2; // Very tight, suit exact values.
+ //RealType tol2eps = boost::math::tools::epsilon<RealType>() * 2; // Tight, suit exact values.
+ RealType tol5eps = boost::math::tools::epsilon<RealType>() * 5; // Wider 5 epsilon.
+ cout << "Tolerance 5 eps = " << tol5eps << "%." << endl;
+
+ // Sources of spot test values:
+
+ // MathCAD defines pbinom(k, r, p) (at about 64-bit double precision, about 16 decimal digits)
+ // returns pr(X , k) when random variable X has the binomial distribution with parameters r and p.
+ // 0 <= k
+ // r > 0
+ // 0 <= p <= 1
+ // P = pbinom(30, 500, 0.05) = 0.869147702104609
+
+ // And functions.wolfram.com
+
+ using boost::math::negative_binomial_distribution;
+ using ::boost::math::negative_binomial;
+ using ::boost::math::cdf;
+ using ::boost::math::pdf;
+
+ // Test negative binomial using cdf spot values from MathCAD cdf = pnbinom(k, r, p).
+ // These test quantiles and complements as well.
+
+ test_spot( // pnbinom(1,2,0.5) = 0.5
+ static_cast<RealType>(2), // successes r
+ static_cast<RealType>(1), // Number of failures, k
+ static_cast<RealType>(0.5), // Probability of success as fraction, p
+ static_cast<RealType>(0.5), // Probability of result (CDF), P
+ static_cast<RealType>(0.5), // complement CCDF Q = 1 - P
+ tolerance);
+
+ test_spot( // pbinom(0, 2, 0.25)
+ static_cast<RealType>(2), // successes r
+ static_cast<RealType>(0), // Number of failures, k
+ static_cast<RealType>(0.25),
+ static_cast<RealType>(0.0625), // Probability of result (CDF), P
+ static_cast<RealType>(0.9375), // Q = 1 - P
+ tolerance);
+
+ test_spot( // pbinom(48,8,0.25)
+ static_cast<RealType>(8), // successes r
+ static_cast<RealType>(48), // Number of failures, k
+ static_cast<RealType>(0.25), // Probability of success, p
+ static_cast<RealType>(9.826582228110670E-1), // Probability of result (CDF), P
+ static_cast<RealType>(1 - 9.826582228110670E-1), // Q = 1 - P
+ tolerance);
+
+ test_spot( // pbinom(2,5,0.4)
+ static_cast<RealType>(5), // successes r
+ static_cast<RealType>(2), // Number of failures, k
+ static_cast<RealType>(0.4), // Probability of success, p
+ static_cast<RealType>(9.625600000000020E-2), // Probability of result (CDF), P
+ static_cast<RealType>(1 - 9.625600000000020E-2), // Q = 1 - P
+ tolerance);
+
+ test_spot( // pbinom(10,100,0.9)
+ static_cast<RealType>(100), // successes r
+ static_cast<RealType>(10), // Number of failures, k
+ static_cast<RealType>(0.9), // Probability of success, p
+ static_cast<RealType>(4.535522887695670E-1), // Probability of result (CDF), P
+ static_cast<RealType>(1 - 4.535522887695670E-1), // Q = 1 - P
+ tolerance);
+
+ test_spot( // pbinom(1,100,0.991)
+ static_cast<RealType>(100), // successes r
+ static_cast<RealType>(1), // Number of failures, k
+ static_cast<RealType>(0.991), // Probability of success, p
+ static_cast<RealType>(7.693413044217000E-1), // Probability of result (CDF), P
+ static_cast<RealType>(1 - 7.693413044217000E-1), // Q = 1 - P
+ tolerance);
+
+ test_spot( // pbinom(10,100,0.991)
+ static_cast<RealType>(100), // successes r
+ static_cast<RealType>(10), // Number of failures, k
+ static_cast<RealType>(0.991), // Probability of success, p
+ static_cast<RealType>(9.999999940939000E-1), // Probability of result (CDF), P
+ static_cast<RealType>(1 - 9.999999940939000E-1), // Q = 1 - P
+ tolerance);
+
+if(std::numeric_limits<RealType>::is_specialized)
+{ // An extreme value test that takes 3 minutes using the real concept type
+ // for which numeric_limits<RealType>::is_specialized == false, deliberately
+ // and for which there is no Lanczos approximation defined (also deliberately)
+ // giving a very slow computation, but with acceptable accuracy.
+ // A possible enhancement might be to use a normal approximation for
+ // extreme values, but this is not implemented.
+ test_spot( // pbinom(100000,100,0.001)
+ static_cast<RealType>(100), // successes r
+ static_cast<RealType>(100000), // Number of failures, k
+ static_cast<RealType>(0.001), // Probability of success, p
+ static_cast<RealType>(5.173047534260320E-1), // Probability of result (CDF), P
+ static_cast<RealType>(1 - 5.173047534260320E-1), // Q = 1 - P
+ tolerance*1000); // *1000 is OK 0.51730475350664229 versus
+
+ // functions.wolfram.com
+ // for I[0.001](100, 100000+1) gives:
+ // Wolfram 0.517304753506834882009032744488738352004003696396461766326713
+ // JM nonLanczos 0.51730475350664229 differs at the 13th decimal digit.
+ // MathCAD 0.51730475342603199 differs at 10th decimal digit.
+
+ // Error tests:
+ check_out_of_range<negative_binomial_distribution<RealType> >(20, 0.5);
+ BOOST_MATH_CHECK_THROW(negative_binomial_distribution<RealType>(0, 0.5), std::domain_error);
+ BOOST_MATH_CHECK_THROW(negative_binomial_distribution<RealType>(-2, 0.5), std::domain_error);
+ BOOST_MATH_CHECK_THROW(negative_binomial_distribution<RealType>(20, -0.5), std::domain_error);
+ BOOST_MATH_CHECK_THROW(negative_binomial_distribution<RealType>(20, 1.5), std::domain_error);
+}
+ // End of single spot tests using RealType
+
+
+ // Tests on PDF:
+ BOOST_CHECK_CLOSE(
+ pdf(negative_binomial_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)),
+ static_cast<RealType>(0) ), // k = 0.
+ static_cast<RealType>(0.25), // 0
+ tolerance);
+
+ BOOST_CHECK_CLOSE(
+ pdf(negative_binomial_distribution<RealType>(static_cast<RealType>(4), static_cast<RealType>(0.5)),
+ static_cast<RealType>(0)), // k = 0.
+ static_cast<RealType>(0.0625), // exact 1/16
+ tolerance);
+
+ BOOST_CHECK_CLOSE(
+ pdf(negative_binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0)), // k = 0
+ static_cast<RealType>(9.094947017729270E-13), // pbinom(0,20,0.25) = 9.094947017729270E-13
+ tolerance);
+
+ BOOST_CHECK_CLOSE(
+ pdf(negative_binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.2)),
+ static_cast<RealType>(0)), // k = 0
+ static_cast<RealType>(1.0485760000000003e-014), // MathCAD 1.048576000000000E-14
+ tolerance);
+
+ BOOST_CHECK_CLOSE(
+ pdf(negative_binomial_distribution<RealType>(static_cast<RealType>(10), static_cast<RealType>(0.1)),
+ static_cast<RealType>(0)), // k = 0.
+ static_cast<RealType>(1e-10), // MathCAD says zero, but suffers cancellation error?
+ tolerance);
+
+ BOOST_CHECK_CLOSE(
+ pdf(negative_binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.1)),
+ static_cast<RealType>(0)), // k = 0.
+ static_cast<RealType>(1e-20), // MathCAD says zero, but suffers cancellation error?
+ tolerance);
+
+
+ BOOST_CHECK_CLOSE( // .
+ pdf(negative_binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.9)),
+ static_cast<RealType>(0)), // k.
+ static_cast<RealType>(1.215766545905690E-1), // k=20 p = 0.9
+ tolerance);
+
+ // Tests on cdf:
+ // MathCAD pbinom k, r, p) == failures, successes, probability.
+
+ BOOST_CHECK_CLOSE(cdf(
+ negative_binomial_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)), // successes = 2,prob 0.25
+ static_cast<RealType>(0) ), // k = 0
+ static_cast<RealType>(0.25), // probability 1/4
+ tolerance);
+
+ BOOST_CHECK_CLOSE(cdf(complement(
+ negative_binomial_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.5)), // successes = 2,prob 0.25
+ static_cast<RealType>(0) )), // k = 0
+ static_cast<RealType>(0.75), // probability 3/4
+ tolerance);
+ BOOST_CHECK_CLOSE( // k = 1.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1)), // k =1.
+ static_cast<RealType>(1.455191522836700E-11),
+ tolerance);
+
+ BOOST_CHECK_SMALL( // Check within an epsilon with CHECK_SMALL
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1)) -
+ static_cast<RealType>(1.455191522836700E-11),
+ tolerance );
+
+ // Some exact (probably - judging by trailing zeros) values.
+ BOOST_CHECK_CLOSE(
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0)), // k.
+ static_cast<RealType>(1.525878906250000E-5),
+ tolerance);
+
+ BOOST_CHECK_CLOSE(
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0)), // k.
+ static_cast<RealType>(1.525878906250000E-5),
+ tolerance);
+
+ BOOST_CHECK_SMALL(
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0)) -
+ static_cast<RealType>(1.525878906250000E-5),
+ tolerance );
+
+ BOOST_CHECK_CLOSE( // k = 1.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1)), // k.
+ static_cast<RealType>(1.068115234375010E-4),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( // k = 2.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(2)), // k.
+ static_cast<RealType>(4.158020019531300E-4),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( // k = 3.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(3)), // k.bristow
+ static_cast<RealType>(1.188278198242200E-3),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( // k = 4.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(4)), // k.
+ static_cast<RealType>(2.781510353088410E-3),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( // k = 5.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(5)), // k.
+ static_cast<RealType>(5.649328231811500E-3),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( // k = 6.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(6)), // k.
+ static_cast<RealType>(1.030953228473680E-2),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( // k = 7.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(7)), // k.
+ static_cast<RealType>(1.729983836412430E-2),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( // k = 8.
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(8)), // k = n.
+ static_cast<RealType>(2.712995628826370E-2),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( //
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(48)), // k
+ static_cast<RealType>(9.826582228110670E-1),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( //
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(64)), // k
+ static_cast<RealType>(9.990295004935590E-1),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( //
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(5), static_cast<RealType>(0.4)),
+ static_cast<RealType>(26)), // k
+ static_cast<RealType>(9.989686246611190E-1),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( //
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(5), static_cast<RealType>(0.4)),
+ static_cast<RealType>(2)), // k failures
+ static_cast<RealType>(9.625600000000020E-2),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( //
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(50), static_cast<RealType>(0.9)),
+ static_cast<RealType>(20)), // k
+ static_cast<RealType>(9.999970854144170E-1),
+ tolerance);
+
+ BOOST_CHECK_CLOSE( //
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(500), static_cast<RealType>(0.7)),
+ static_cast<RealType>(200)), // k
+ static_cast<RealType>(2.172846379930550E-1),
+ tolerance* 2);
+
+ BOOST_CHECK_CLOSE( //
+ cdf(negative_binomial_distribution<RealType>(static_cast<RealType>(50), static_cast<RealType>(0.7)),
+ static_cast<RealType>(20)), // k
+ static_cast<RealType>(4.550203671301790E-1),
+ tolerance);
+
+ // Tests of other functions, mean and other moments ...
+
+ negative_binomial_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(0.25));
+ using namespace std; // ADL of std names.
+ // mean:
+ BOOST_CHECK_CLOSE(
+ mean(dist), static_cast<RealType>(8 * (1 - 0.25) /0.25), tol5eps);
+ BOOST_CHECK_CLOSE(
+ mode(dist), static_cast<RealType>(21), tol1eps);
+ // variance:
+ BOOST_CHECK_CLOSE(
+ variance(dist), static_cast<RealType>(8 * (1 - 0.25) / (0.25 * 0.25)), tol5eps);
+ // std deviation:
+ BOOST_CHECK_CLOSE(
+ standard_deviation(dist), // 9.79795897113271239270
+ static_cast<RealType>(9.797958971132712392789136298823565567864L), // using functions.wolfram.com
+ // 9.79795897113271152534 == sqrt(8 * (1 - 0.25) / (0.25 * 0.25)))
+ tol5eps * 100);
+ BOOST_CHECK_CLOSE(
+ skewness(dist), //
+ static_cast<RealType>(0.71443450831176036),
+ // using http://mathworld.wolfram.com/skewness.html
+ tolerance);
+ BOOST_CHECK_CLOSE(
+ kurtosis_excess(dist), //
+ static_cast<RealType>(0.7604166666666666666666666666666666666666L), // using Wikipedia Kurtosis(excess) formula
+ tol5eps * 100);
+ BOOST_CHECK_CLOSE(
+ kurtosis(dist), // true
+ static_cast<RealType>(3.76041666666666666666666666666666666666666L), //
+ tol5eps * 100);
+ // hazard:
+ RealType x = static_cast<RealType>(0.125);
+ BOOST_CHECK_CLOSE(
+ hazard(dist, x)
+ , pdf(dist, x) / cdf(complement(dist, x)), tol5eps);
+ // cumulative hazard:
+ BOOST_CHECK_CLOSE(
+ chf(dist, x), -log(cdf(complement(dist, x))), tol5eps);
+ // coefficient_of_variation:
+ BOOST_CHECK_CLOSE(
+ coefficient_of_variation(dist)
+ , standard_deviation(dist) / mean(dist), tol5eps);
+
+ // Special cases for PDF:
+ BOOST_CHECK_EQUAL(
+ pdf(
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)), //
+ static_cast<RealType>(0)),
+ static_cast<RealType>(0) );
+
+ BOOST_CHECK_EQUAL(
+ pdf(
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
+ static_cast<RealType>(0.0001)),
+ static_cast<RealType>(0) );
+
+ BOOST_CHECK_EQUAL(
+ pdf(
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
+ static_cast<RealType>(0.001)),
+ static_cast<RealType>(0) );
+
+ BOOST_CHECK_EQUAL(
+ pdf(
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
+ static_cast<RealType>(8)),
+ static_cast<RealType>(0) );
+
+ BOOST_CHECK_SMALL(
+ pdf(
+ negative_binomial_distribution<RealType>(static_cast<RealType>(2), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0))-
+ static_cast<RealType>(0.0625),
+ 2 * boost::math::tools::epsilon<RealType>() ); // Expect exact, but not quite.
+ // numeric_limits<RealType>::epsilon()); // Not suitable for real concept!
+
+ // Quantile boundary cases checks:
+ BOOST_CHECK_EQUAL(
+ quantile( // zero P < cdf(0) so should be exactly zero.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0)),
+ static_cast<RealType>(0));
+
+ BOOST_CHECK_EQUAL(
+ quantile( // min P < cdf(0) so should be exactly zero.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(boost::math::tools::min_value<RealType>())),
+ static_cast<RealType>(0));
+
+ BOOST_CHECK_CLOSE_FRACTION(
+ quantile( // Small P < cdf(0) so should be near zero.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(boost::math::tools::epsilon<RealType>())), //
+ static_cast<RealType>(0),
+ tol5eps);
+
+ BOOST_CHECK_CLOSE(
+ quantile( // Small P < cdf(0) so should be exactly zero.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0.0001)),
+ static_cast<RealType>(0.95854156929288470),
+ tolerance);
+
+ //BOOST_CHECK( // Fails with overflow for real_concept
+ //quantile( // Small P near 1 so k failures should be big.
+ //negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ //static_cast<RealType>(1 - boost::math::tools::epsilon<RealType>())) <=
+ //static_cast<RealType>(189.56999032670058) // 106.462769 for float
+ //);
+
+ if(std::numeric_limits<RealType>::has_infinity)
+ { // BOOST_CHECK tests for infinity using std::numeric_limits<>::infinity()
+ // Note that infinity is not implemented for real_concept, so these tests
+ // are only done for types, like built-in float, double.. that have infinity.
+ // Note that these assume that BOOST_MATH_OVERFLOW_ERROR_POLICY is NOT throw_on_error.
+ // #define BOOST_MATH_THROW_ON_OVERFLOW_POLICY == throw_on_error would throw here.
+ // #define BOOST_MAT_DOMAIN_ERROR_POLICY IS defined throw_on_error,
+ // so the throw path of error handling is tested below with BOOST_MATH_CHECK_THROW tests.
+
+ BOOST_CHECK(
+ quantile( // At P == 1 so k failures should be infinite.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1)) ==
+ //static_cast<RealType>(boost::math::tools::infinity<RealType>())
+ static_cast<RealType>(std::numeric_limits<RealType>::infinity()) );
+
+ BOOST_CHECK_EQUAL(
+ quantile( // At 1 == P so should be infinite.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1)), //
+ std::numeric_limits<RealType>::infinity() );
+
+ BOOST_CHECK_EQUAL(
+ quantile(complement( // Q zero 1 so P == 1 < cdf(0) so should be exactly infinity.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0))),
+ std::numeric_limits<RealType>::infinity() );
+ } // test for infinity using std::numeric_limits<>::infinity()
+ else
+ { // real_concept case, so check it throws rather than returning infinity.
+ BOOST_CHECK_EQUAL(
+ quantile( // At P == 1 so k failures should be infinite.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1)),
+ boost::math::tools::max_value<RealType>() );
+
+ BOOST_CHECK_EQUAL(
+ quantile(complement( // Q zero 1 so P == 1 < cdf(0) so should be exactly infinity.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0))),
+ boost::math::tools::max_value<RealType>());
+ }
+ BOOST_CHECK( // Should work for built-in and real_concept.
+ quantile(complement( // Q very near to 1 so P nearly 1 < so should be large > 384.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(boost::math::tools::min_value<RealType>())))
+ >= static_cast<RealType>(384) );
+
+ BOOST_CHECK_EQUAL(
+ quantile( // P == 0 < cdf(0) so should be zero.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0)),
+ static_cast<RealType>(0));
+
+ // Quantile Complement boundary cases:
+
+ BOOST_CHECK_EQUAL(
+ quantile(complement( // Q = 1 so P = 0 < cdf(0) so should be exactly zero.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1))),
+ static_cast<RealType>(0)
+ );
+
+ BOOST_CHECK_EQUAL(
+ quantile(complement( // Q very near 1 so P == epsilon < cdf(0) so should be exactly zero.
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(1 - boost::math::tools::epsilon<RealType>()))),
+ static_cast<RealType>(0)
+ );
+
+ // Check that duff arguments throw domain_error:
+ BOOST_MATH_CHECK_THROW(
+ pdf( // Negative successes!
+ negative_binomial_distribution<RealType>(static_cast<RealType>(-1), static_cast<RealType>(0.25)),
+ static_cast<RealType>(0)), std::domain_error
+ );
+ BOOST_MATH_CHECK_THROW(
+ pdf( // Negative success_fraction!
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
+ static_cast<RealType>(0)), std::domain_error
+ );
+ BOOST_MATH_CHECK_THROW(
+ pdf( // Success_fraction > 1!
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
+ static_cast<RealType>(0)),
+ std::domain_error
+ );
+ BOOST_MATH_CHECK_THROW(
+ pdf( // Negative k argument !
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(-1)),
+ std::domain_error
+ );
+ //BOOST_MATH_CHECK_THROW(
+ //pdf( // Unlike binomial there is NO limit on k (failures)
+ //negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ //static_cast<RealType>(9)), std::domain_error
+ //);
+ BOOST_MATH_CHECK_THROW(
+ cdf( // Negative k argument !
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
+ static_cast<RealType>(-1)),
+ std::domain_error
+ );
+ BOOST_MATH_CHECK_THROW(
+ cdf( // Negative success_fraction!
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
+ static_cast<RealType>(0)), std::domain_error
+ );
+ BOOST_MATH_CHECK_THROW(
+ cdf( // Success_fraction > 1!
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
+ static_cast<RealType>(0)), std::domain_error
+ );
+ BOOST_MATH_CHECK_THROW(
+ quantile( // Negative success_fraction!
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
+ static_cast<RealType>(0)), std::domain_error
+ );
+ BOOST_MATH_CHECK_THROW(
+ quantile( // Success_fraction > 1!
+ negative_binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
+ static_cast<RealType>(0)), std::domain_error
+ );
+ // End of check throwing 'duff' out-of-domain values.
+
+#define T RealType
+#include "negative_binomial_quantile.ipp"
+
+ for(unsigned i = 0; i < negative_binomial_quantile_data.size(); ++i)
+ {
+ using namespace boost::math::policies;
+ typedef policy<discrete_quantile<boost::math::policies::real> > P1;
+ typedef policy<discrete_quantile<integer_round_down> > P2;
+ typedef policy<discrete_quantile<integer_round_up> > P3;
+ typedef policy<discrete_quantile<integer_round_outwards> > P4;
+ typedef policy<discrete_quantile<integer_round_inwards> > P5;
+ typedef policy<discrete_quantile<integer_round_nearest> > P6;
+ RealType tol = boost::math::tools::epsilon<RealType>() * 700;
+ if(!boost::is_floating_point<RealType>::value)
+ tol *= 10; // no lanczos approximation implies less accuracy
+ //
+ // Check full real value first:
+ //
+ negative_binomial_distribution<RealType, P1> p1(negative_binomial_quantile_data[i][0], negative_binomial_quantile_data[i][1]);
+ RealType x = quantile(p1, negative_binomial_quantile_data[i][2]);
+ BOOST_CHECK_CLOSE_FRACTION(x, negative_binomial_quantile_data[i][3], tol);
+ x = quantile(complement(p1, negative_binomial_quantile_data[i][2]));
+ BOOST_CHECK_CLOSE_FRACTION(x, negative_binomial_quantile_data[i][4], tol);
+ //
+ // Now with round down to integer:
+ //
+ negative_binomial_distribution<RealType, P2> p2(negative_binomial_quantile_data[i][0], negative_binomial_quantile_data[i][1]);
+ x = quantile(p2, negative_binomial_quantile_data[i][2]);
+ BOOST_CHECK_EQUAL(x, floor(negative_binomial_quantile_data[i][3]));
+ x = quantile(complement(p2, negative_binomial_quantile_data[i][2]));
+ BOOST_CHECK_EQUAL(x, floor(negative_binomial_quantile_data[i][4]));
+ //
+ // Now with round up to integer:
+ //
+ negative_binomial_distribution<RealType, P3> p3(negative_binomial_quantile_data[i][0], negative_binomial_quantile_data[i][1]);
+ x = quantile(p3, negative_binomial_quantile_data[i][2]);
+ BOOST_CHECK_EQUAL(x, ceil(negative_binomial_quantile_data[i][3]));
+ x = quantile(complement(p3, negative_binomial_quantile_data[i][2]));
+ BOOST_CHECK_EQUAL(x, ceil(negative_binomial_quantile_data[i][4]));
+ //
+ // Now with round to integer "outside":
+ //
+ negative_binomial_distribution<RealType, P4> p4(negative_binomial_quantile_data[i][0], negative_binomial_quantile_data[i][1]);
+ x = quantile(p4, negative_binomial_quantile_data[i][2]);
+ BOOST_CHECK_EQUAL(x, negative_binomial_quantile_data[i][2] < 0.5f ? floor(negative_binomial_quantile_data[i][3]) : ceil(negative_binomial_quantile_data[i][3]));
+ x = quantile(complement(p4, negative_binomial_quantile_data[i][2]));
+ BOOST_CHECK_EQUAL(x, negative_binomial_quantile_data[i][2] < 0.5f ? ceil(negative_binomial_quantile_data[i][4]) : floor(negative_binomial_quantile_data[i][4]));
+ //
+ // Now with round to integer "inside":
+ //
+ negative_binomial_distribution<RealType, P5> p5(negative_binomial_quantile_data[i][0], negative_binomial_quantile_data[i][1]);
+ x = quantile(p5, negative_binomial_quantile_data[i][2]);
+ BOOST_CHECK_EQUAL(x, negative_binomial_quantile_data[i][2] < 0.5f ? ceil(negative_binomial_quantile_data[i][3]) : floor(negative_binomial_quantile_data[i][3]));
+ x = quantile(complement(p5, negative_binomial_quantile_data[i][2]));
+ BOOST_CHECK_EQUAL(x, negative_binomial_quantile_data[i][2] < 0.5f ? floor(negative_binomial_quantile_data[i][4]) : ceil(negative_binomial_quantile_data[i][4]));
+ //
+ // Now with round to nearest integer:
+ //
+ negative_binomial_distribution<RealType, P6> p6(negative_binomial_quantile_data[i][0], negative_binomial_quantile_data[i][1]);
+ x = quantile(p6, negative_binomial_quantile_data[i][2]);
+ BOOST_CHECK_EQUAL(x, floor(negative_binomial_quantile_data[i][3] + 0.5f));
+ x = quantile(complement(p6, negative_binomial_quantile_data[i][2]));
+ BOOST_CHECK_EQUAL(x, floor(negative_binomial_quantile_data[i][4] + 0.5f));
+ }
+
+ return;
+} // template <class RealType> void test_spots(RealType) // Any floating-point type RealType.
+
+BOOST_AUTO_TEST_CASE( test_main )
+{
+ // Check that can generate negative_binomial distribution using the two convenience methods:
+ using namespace boost::math;
+ negative_binomial mynb1(2., 0.5); // Using typedef - default type is double.
+ negative_binomial_distribution<> myf2(2., 0.5); // Using default RealType double.
+
+ // Basic sanity-check spot values.
+
+ // Test some simple double only examples.
+ negative_binomial_distribution<double> my8dist(8., 0.25);
+ // 8 successes (r), 0.25 success fraction = 35% or 1 in 4 successes.
+ // Note: double values (matching the distribution definition) avoid the need for any casting.
+
+ // Check accessor functions return exact values for double at least.
+ BOOST_CHECK_EQUAL(my8dist.successes(), static_cast<double>(8));
+ BOOST_CHECK_EQUAL(my8dist.success_fraction(), static_cast<double>(1./4.));
+
+ // (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
+#ifndef 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 )
+
+/*
+
+Autorun "i:\boost-06-05-03-1300\libs\math\test\Math_test\debug\test_negative_binomial.exe"
+Running 1 test case...
+Tolerance = 0.0119209%.
+Tolerance 5 eps = 5.96046e-007%.
+Tolerance = 2.22045e-011%.
+Tolerance 5 eps = 1.11022e-015%.
+Tolerance = 2.22045e-011%.
+Tolerance 5 eps = 1.11022e-015%.
+Tolerance = 2.22045e-011%.
+Tolerance 5 eps = 1.11022e-015%.
+*** No errors detected
+
+*/
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