// test_binomial.cpp
// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
// Basic sanity test for Binomial Cumulative Distribution Function.
#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
# define TEST_FLOAT
# define TEST_DOUBLE
# define TEST_LDOUBLE
# define TEST_REAL_CONCEPT
#endif
#ifdef _MSC_VER
# pragma warning(disable: 4127) // conditional expression is constant.
# pragma warning(disable: 4100) // unreferenced formal parameter.
// Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */
//# pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test)
// Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535.
#endif
#include <boost/math/tools/test.hpp>
#include <boost/math/concepts/real_concept.hpp> // for real_concept
using ::boost::math::concepts::real_concept;
#include <boost/math/distributions/binomial.hpp> // for binomial_distribution
using boost::math::binomial_distribution;
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp> // for test_main
#include <boost/test/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE
#include "table_type.hpp"
#include "test_out_of_range.hpp"
#include <iostream>
using std::cout;
using std::endl;
#include <limits>
using std::numeric_limits;
template <class RealType>
void test_spot(
RealType N, // Number of trials
RealType k, // Number of successes
RealType p, // Probability of success
RealType P, // CDF
RealType Q, // Complement of CDF
RealType tol) // Test tolerance
{
boost::math::binomial_distribution<RealType> bn(N, p);
BOOST_CHECK_CLOSE(
cdf(bn, k), P, tol);
if((P < 0.99) && (Q < 0.99))
{
//
// We can only check this if P is not too close to 1,
// so that we can guarantee Q is free of error:
//
BOOST_CHECK_CLOSE(
cdf(complement(bn, k)), Q, tol);
if(k != 0)
{
BOOST_CHECK_CLOSE(
quantile(bn, P), k, tol);
}
else
{
// Just check quantile is very small:
if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
{
// Limit where this is checked: if exponent range is very large we may
// run out of iterations in our root finding algorithm.
BOOST_CHECK(quantile(bn, P) < boost::math::tools::epsilon<RealType>() * 10);
}
}
if(k != 0)
{
BOOST_CHECK_CLOSE(
quantile(complement(bn, Q)), k, tol);
}
else
{
// Just check quantile is very small:
if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
{
// Limit where this is checked: if exponent range is very large we may
// run out of iterations in our root finding algorithm.
BOOST_CHECK(quantile(complement(bn, Q)) < boost::math::tools::epsilon<RealType>() * 10);
}
}
if(k > 0)
{
// estimate success ratio:
// Note lower bound uses a different formual internally
// from upper bound, have to adjust things to prevent
// fencepost errors:
BOOST_CHECK_CLOSE(
binomial_distribution<RealType>::find_lower_bound_on_p(
N, k+1, Q),
p, tol);
BOOST_CHECK_CLOSE(
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, P),
p, tol);
if(Q < P)
{
// Default method (Clopper Pearson)
BOOST_CHECK(
binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, Q)
<=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, Q)
);
BOOST_CHECK((
binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, Q)
<= k/N) && (k/N <=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, Q))
);
// Bayes Method (Jeffreys Prior)
BOOST_CHECK(
binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
<=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
);
BOOST_CHECK((
binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
<= k/N) && (k/N <=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval))
);
}
else
{
// Default method (Clopper Pearson)
BOOST_CHECK(
binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, P)
<=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, P)
);
BOOST_CHECK(
(binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, P)
<= k / N) && (k/N <=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, P))
);
// Bayes Method (Jeffreys Prior)
BOOST_CHECK(
binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
<=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
);
BOOST_CHECK(
(binomial_distribution<RealType>::find_lower_bound_on_p(
N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
<= k / N) && (k/N <=
binomial_distribution<RealType>::find_upper_bound_on_p(
N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval))
);
}
}
//
// estimate sample size:
//
BOOST_CHECK_CLOSE(
binomial_distribution<RealType>::find_minimum_number_of_trials(
k, p, P),
N, tol);
BOOST_CHECK_CLOSE(
binomial_distribution<RealType>::find_maximum_number_of_trials(
k, p, Q),
N, tol);
}
// Double check consistency of CDF and PDF by computing
// the finite sum:
RealType sum = 0;
for(unsigned i = 0; i <= k; ++i)
sum += pdf(bn, RealType(i));
BOOST_CHECK_CLOSE(
sum, P, tol);
// And complement as well:
sum = 0;
for(RealType i = N; i > k; i -= 1)
sum += pdf(bn, i);
if(P < 0.99)
{
BOOST_CHECK_CLOSE(
sum, Q, tol);
}
else
{
// Not enough information content in P for Q to be meaningful
RealType tol = (std::max)(2 * Q, boost::math::tools::epsilon<RealType>());
BOOST_CHECK(sum < tol);
}
}
template <class RealType> // Any floating-point type RealType.
void test_spots(RealType T)
{
// Basic sanity checks, test data is to double precision only
// so set tolerance to 100eps expressed as a persent, or
// 100eps of type double expressed as a persent, whichever
// is the larger.
RealType tolerance = (std::max)
(boost::math::tools::epsilon<RealType>(),
static_cast<RealType>(std::numeric_limits<double>::epsilon()));
tolerance *= 100 * 1000;
RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a persent
cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl;
// Sources of spot test values:
// MathCAD defines pbinom(k, n, p)
// returns pr(X ,=k) when random variable X has the binomial distribution with parameters n and p.
// 0 <= k ,= n
// 0 <= p <= 1
// P = pbinom(30, 500, 0.05) = 0.869147702104609
using boost::math::binomial_distribution;
using ::boost::math::cdf;
using ::boost::math::pdf;
#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 0)
// Test binomial using cdf spot values from MathCAD.
// These test quantiles and complements as well.
test_spot(
static_cast<RealType>(500), // Sample size, N
static_cast<RealType>(30), // Number of successes, k
static_cast<RealType>(0.05), // Probability of success, p
static_cast<RealType>(0.869147702104609), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.869147702104609), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(500), // Sample size, N
static_cast<RealType>(250), // Number of successes, k
static_cast<RealType>(0.05), // Probability of success, p
static_cast<RealType>(1), // Probability of result (CDF), P
static_cast<RealType>(0), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(500), // Sample size, N
static_cast<RealType>(470), // Number of successes, k
static_cast<RealType>(0.95), // Probability of success, p
static_cast<RealType>(0.176470742656766), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.176470742656766), // Q = 1 - P
tolerance * 10); // Note higher tolerance on this test!
test_spot(
static_cast<RealType>(500), // Sample size, N
static_cast<RealType>(400), // Number of successes, k
static_cast<RealType>(0.05), // Probability of success, p
static_cast<RealType>(1), // Probability of result (CDF), P
static_cast<RealType>(0), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(500), // Sample size, N
static_cast<RealType>(400), // Number of successes, k
static_cast<RealType>(0.9), // Probability of success, p
static_cast<RealType>(1.80180425681923E-11), // Probability of result (CDF), P
static_cast<RealType>(1 - 1.80180425681923E-11), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(500), // Sample size, N
static_cast<RealType>(5), // Number of successes, k
static_cast<RealType>(0.05), // Probability of success, p
static_cast<RealType>(9.181808267643E-7), // Probability of result (CDF), P
static_cast<RealType>(1 - 9.181808267643E-7), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(2), // Sample size, N
static_cast<RealType>(1), // Number of successes, k
static_cast<RealType>(0.5), // Probability of success, p
static_cast<RealType>(0.75), // Probability of result (CDF), P
static_cast<RealType>(0.25), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(8), // Sample size, N
static_cast<RealType>(3), // Number of successes, k
static_cast<RealType>(0.25), // Probability of success, p
static_cast<RealType>(0.8861846923828125), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.8861846923828125), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(8), // Sample size, N
static_cast<RealType>(0), // Number of successes, k
static_cast<RealType>(0.25), // Probability of success, p
static_cast<RealType>(0.1001129150390625), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.1001129150390625), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(8), // Sample size, N
static_cast<RealType>(1), // Number of successes, k
static_cast<RealType>(0.25), // Probability of success, p
static_cast<RealType>(0.36708068847656244), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.36708068847656244), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(8), // Sample size, N
static_cast<RealType>(4), // Number of successes, k
static_cast<RealType>(0.25), // Probability of success, p
static_cast<RealType>(0.9727020263671875), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.9727020263671875), // Q = 1 - P
tolerance);
test_spot(
static_cast<RealType>(8), // Sample size, N
static_cast<RealType>(7), // Number of successes, k
static_cast<RealType>(0.25), // Probability of success, p
static_cast<RealType>(0.9999847412109375), // Probability of result (CDF), P
static_cast<RealType>(1 - 0.9999847412109375), // Q = 1 - P
tolerance);
// Tests on PDF follow:
BOOST_CHECK_CLOSE(
pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.75)),
static_cast<RealType>(10)), // k.
static_cast<RealType>(0.00992227527967770583927631378173), // 0.00992227527967770583927631378173
tolerance);
BOOST_CHECK_CLOSE(
pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.5)),
static_cast<RealType>(10)), // k.
static_cast<RealType>(0.17619705200195312500000000000000000000), // get k=10 0.049611376398388612 p = 0.25
tolerance);
// Binomial pdf Test values from
// http://www.adsciengineering.com/bpdcalc/index.php for example
// http://www.adsciengineering.com/bpdcalc/index.php?n=20&p=0.25&start=0&stop=20&Submit=Generate
// Appears to use at least 80-bit long double for 32 decimal digits accuracy,
// but loses accuracy of display if leading zeros?
// (if trailings zero then are exact values?)
// so useful for testing 64-bit double accuracy.
// P = 0.25, n = 20, k = 0 to 20
//0 C(20,0) * 0.25^0 * 0.75^20 0.00317121193893399322405457496643
//1 C(20,1) * 0.25^1 * 0.75^19 0.02114141292622662149369716644287
//2 C(20,2) * 0.25^2 * 0.75^18 0.06694780759971763473004102706909
//3 C(20,3) * 0.25^3 * 0.75^17 0.13389561519943526946008205413818
//4 C(20,4) * 0.25^4 * 0.75^16 0.18968545486586663173511624336242
//5 C(20,5) * 0.25^5 * 0.75^15 0.20233115185692440718412399291992
//6 C(20,6) * 0.25^6 * 0.75^14 0.16860929321410367265343666076660
//7 C(20,7) * 0.25^7 * 0.75^13 0.11240619547606911510229110717773
//8 C(20,8) * 0.25^8 * 0.75^12 0.06088668921620410401374101638793
//9 C(20,9) * 0.25^9 * 0.75^11 0.02706075076275737956166267395019
//10 C(20,10) * 0.25^10 * 0.75^10 0.00992227527967770583927631378173
//11 C(20,11) * 0.25^11 * 0.75^9 0.00300675008475081995129585266113
//12 C(20,12) * 0.25^12 * 0.75^8 0.00075168752118770498782396316528
//13 C(20,13) * 0.25^13 * 0.75^7 0.00015419231203850358724594116210
//14 C(20,14) * 0.25^14 * 0.75^6 0.00002569871867308393120765686035
//15 C(20,15) * 0.25^15 * 0.75^5 0.00000342649582307785749435424804
//16 C(20,16) * 0.25^16 * 0.75^4 0.00000035692664823727682232856750
//17 C(20,17) * 0.25^17 * 0.75^3 0.00000002799424692057073116302490
//18 C(20,18) * 0.25^18 * 0.75^2 0.00000000155523594003170728683471
//19 C(20,19) * 0.25^19 * 0.75^1 0.00000000005456968210637569427490
//20 C(20,20) * 0.25^20 * 0.75^0 0.00000000000090949470177292823791
BOOST_CHECK_CLOSE(
pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
static_cast<RealType>(10)), // k.
static_cast<RealType>(0.00992227527967770583927631378173), // k=10 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 0 use different formula - only exp so more accurate.
pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
static_cast<RealType>(0)), // k.
static_cast<RealType>(0.00317121193893399322405457496643), // k=0 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 20 use different formula - only exp so more accurate.
pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
static_cast<RealType>(20)), // k == n.
static_cast<RealType>(0.00000000000090949470177292823791), // k=20 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 1.
pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
static_cast<RealType>(1)), // k.
static_cast<RealType>(0.02114141292622662149369716644287), // k=1 p = 0.25
tolerance);
// Some exact (probably) values.
BOOST_CHECK_CLOSE(
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(0)), // k.
static_cast<RealType>(0.10011291503906250000000000000000), // k=0 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 1.
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(1)), // k.
static_cast<RealType>(0.26696777343750000000000000000000), // k=1 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 2.
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(2)), // k.
static_cast<RealType>(0.31146240234375000000000000000000), // k=2 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 3.
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(3)), // k.
static_cast<RealType>(0.20764160156250000000000000000000), // k=3 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 7.
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(7)), // k.
static_cast<RealType>(0.00036621093750000000000000000000), // k=7 p = 0.25
tolerance);
BOOST_CHECK_CLOSE( // k = 8.
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(8)), // k = n.
static_cast<RealType>(0.00001525878906250000000000000000), // k=8 p = 0.25
tolerance);
binomial_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(0.25));
RealType x = static_cast<RealType>(0.125);
using namespace std; // ADL of std names.
// mean:
BOOST_CHECK_CLOSE(
mean(dist)
, static_cast<RealType>(8 * 0.25), tol2);
// variance:
BOOST_CHECK_CLOSE(
variance(dist)
, static_cast<RealType>(8 * 0.25 * 0.75), tol2);
// std deviation:
BOOST_CHECK_CLOSE(
standard_deviation(dist)
, static_cast<RealType>(sqrt(8 * 0.25L * 0.75L)), tol2);
// hazard:
BOOST_CHECK_CLOSE(
hazard(dist, x)
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
// cumulative hazard:
BOOST_CHECK_CLOSE(
chf(dist, x)
, -log(cdf(complement(dist, x))), tol2);
// coefficient_of_variation:
BOOST_CHECK_CLOSE(
coefficient_of_variation(dist)
, standard_deviation(dist) / mean(dist), tol2);
// mode:
BOOST_CHECK_CLOSE(
mode(dist)
, static_cast<RealType>(std::floor(9 * 0.25)), tol2);
// skewness:
BOOST_CHECK_CLOSE(
skewness(dist)
, static_cast<RealType>(0.40824829046386301636621401245098L), (std::max)(tol2, static_cast<RealType>(5e-29))); // test data has 32 digits only.
// kurtosis:
BOOST_CHECK_CLOSE(
kurtosis(dist)
, static_cast<RealType>(2.916666666666666666666666666666666666L), tol2);
// kurtosis excess:
BOOST_CHECK_CLOSE(
kurtosis_excess(dist)
, static_cast<RealType>(-0.08333333333333333333333333333333333333L), tol2);
// Check kurtosis_excess == kurtosis -3;
BOOST_CHECK_EQUAL(kurtosis(dist), static_cast<RealType>(3) + kurtosis_excess(dist));
// special cases for PDF:
BOOST_CHECK_EQUAL(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
static_cast<RealType>(0)), static_cast<RealType>(1)
);
BOOST_CHECK_EQUAL(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
static_cast<RealType>(0.0001)), static_cast<RealType>(0)
);
BOOST_CHECK_EQUAL(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
static_cast<RealType>(0.001)), static_cast<RealType>(0)
);
BOOST_CHECK_EQUAL(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
static_cast<RealType>(8)), static_cast<RealType>(1)
);
BOOST_CHECK_EQUAL(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(0.25)),
static_cast<RealType>(0)), static_cast<RealType>(1)
);
BOOST_MATH_CHECK_THROW(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(-1), static_cast<RealType>(0.25)),
static_cast<RealType>(0)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
static_cast<RealType>(0)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
static_cast<RealType>(0)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(-1)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
pdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(9)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
cdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(-1)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
cdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(9)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
cdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
static_cast<RealType>(0)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
cdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
static_cast<RealType>(0)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
quantile(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
static_cast<RealType>(0)), std::domain_error
);
BOOST_MATH_CHECK_THROW(
quantile(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
static_cast<RealType>(0)), std::domain_error
);
BOOST_CHECK_EQUAL(
quantile(
binomial_distribution<RealType>(static_cast<RealType>(16), static_cast<RealType>(0.25)),
static_cast<RealType>(0.01)), // Less than cdf == pdf(binomial_distribution<RealType>(16, 0.25), 0)
static_cast<RealType>(0) // so expect zero as best approximation.
);
BOOST_CHECK_EQUAL(
cdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
static_cast<RealType>(8)), static_cast<RealType>(1)
);
BOOST_CHECK_EQUAL(
cdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
static_cast<RealType>(7)), static_cast<RealType>(1)
);
BOOST_CHECK_EQUAL(
cdf(
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
static_cast<RealType>(7)), static_cast<RealType>(0)
);
#endif
{
// This is a visual sanity check that everything is OK:
binomial_distribution<RealType> my8dist(8., 0.25); // Note: double values (matching the distribution definition) avoid the need for any casting.
//cout << "mean(my8dist) = " << boost::math::mean(my8dist) << endl; // mean(my8dist) = 2
//cout << "my8dist.trials() = " << my8dist.trials() << endl; // my8dist.trials() = 8
//cout << "my8dist.success_fraction() = " << my8dist.success_fraction() << endl; // my8dist.success_fraction() = 0.25
BOOST_CHECK_CLOSE(my8dist.trials(), static_cast<RealType>(8), tol2);
BOOST_CHECK_CLOSE(my8dist.success_fraction(), static_cast<RealType>(0.25), tol2);
//{
// int n = static_cast<int>(boost::math::tools::real_cast<double>(my8dist.trials()));
// RealType sumcdf = 0.;
// for (int k = 0; k <= n; k++)
// {
// cout << k << ' ' << pdf(my8dist, static_cast<RealType>(k));
// sumcdf += pdf(my8dist, static_cast<RealType>(k));
// cout << ' ' << sumcdf;
// cout << ' ' << cdf(my8dist, static_cast<RealType>(k));
// cout << ' ' << sumcdf - cdf(my8dist, static_cast<RealType>(k)) << endl;
// } // for k
// }
// n = 8, p =0.25
//k pdf cdf
//0 0.1001129150390625 0.1001129150390625
//1 0.26696777343749994 0.36708068847656244
//2 0.31146240234375017 0.67854309082031261
//3 0.20764160156249989 0.8861846923828125
//4 0.086517333984375 0.9727020263671875
//5 0.023071289062499997 0.9957733154296875
//6 0.0038452148437500009 0.9996185302734375
//7 0.00036621093749999984 0.9999847412109375
//8 1.52587890625e-005 1 1 0
}
#define T RealType
#include "binomial_quantile.ipp"
for(unsigned i = 0; i < binomial_quantile_data.size(); ++i)
{
using namespace boost::math::policies;
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>() * 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:
//
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:
//
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:
//
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":
//
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":
//
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:
//
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 ==========
*/