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WSJT-X/boost/libs/math/test/test_negative_binomial.cpp

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// 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/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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