775 lines
32 KiB
C++
775 lines
32 KiB
C++
// test_binomial.cpp
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// Copyright John Maddock 2006.
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// Copyright Paul A. Bristow 2007.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0.
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// (See accompanying file LICENSE_1_0.txt
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// or copy at http://www.boost.org/LICENSE_1_0.txt)
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// Basic sanity test for Binomial Cumulative Distribution Function.
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#define BOOST_MATH_DISCRETE_QUANTILE_POLICY real
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#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
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# define TEST_FLOAT
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# define TEST_DOUBLE
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# define TEST_LDOUBLE
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# define TEST_REAL_CONCEPT
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#endif
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#ifdef _MSC_VER
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# pragma warning(disable: 4127) // conditional expression is constant.
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# pragma warning(disable: 4100) // unreferenced formal parameter.
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// Seems an entirely spurious warning - formal parameter T IS used - get error if /* T */
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//# pragma warning(disable: 4535) // calling _set_se_translator() requires /EHa (in Boost.test)
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// Enable C++ Exceptions Yes With SEH Exceptions (/EHa) prevents warning 4535.
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#endif
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#include <boost/math/tools/test.hpp>
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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using ::boost::math::concepts::real_concept;
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#include <boost/math/distributions/binomial.hpp> // for binomial_distribution
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using boost::math::binomial_distribution;
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // for test_main
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#include <boost/test/tools/floating_point_comparison.hpp> // for BOOST_CHECK_CLOSE
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#include "table_type.hpp"
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#include "test_out_of_range.hpp"
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#include <iostream>
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using std::cout;
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using std::endl;
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#include <limits>
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using std::numeric_limits;
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template <class RealType>
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void test_spot(
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RealType N, // Number of trials
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RealType k, // Number of successes
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RealType p, // Probability of success
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RealType P, // CDF
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RealType Q, // Complement of CDF
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RealType tol) // Test tolerance
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{
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boost::math::binomial_distribution<RealType> bn(N, p);
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BOOST_CHECK_CLOSE(
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cdf(bn, k), P, tol);
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if((P < 0.99) && (Q < 0.99))
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{
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//
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// We can only check this if P is not too close to 1,
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// so that we can guarantee Q is free of error:
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//
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BOOST_CHECK_CLOSE(
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cdf(complement(bn, k)), Q, tol);
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if(k != 0)
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{
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BOOST_CHECK_CLOSE(
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quantile(bn, P), k, tol);
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}
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else
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{
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// Just check quantile is very small:
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if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
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{
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// Limit where this is checked: if exponent range is very large we may
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// run out of iterations in our root finding algorithm.
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BOOST_CHECK(quantile(bn, P) < boost::math::tools::epsilon<RealType>() * 10);
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}
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}
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if(k != 0)
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{
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BOOST_CHECK_CLOSE(
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quantile(complement(bn, Q)), k, tol);
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}
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else
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{
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// Just check quantile is very small:
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if((std::numeric_limits<RealType>::max_exponent <= std::numeric_limits<double>::max_exponent) && (boost::is_floating_point<RealType>::value))
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{
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// Limit where this is checked: if exponent range is very large we may
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// run out of iterations in our root finding algorithm.
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BOOST_CHECK(quantile(complement(bn, Q)) < boost::math::tools::epsilon<RealType>() * 10);
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}
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}
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if(k > 0)
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{
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// estimate success ratio:
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// Note lower bound uses a different formual internally
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// from upper bound, have to adjust things to prevent
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// fencepost errors:
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BOOST_CHECK_CLOSE(
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binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k+1, Q),
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p, tol);
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BOOST_CHECK_CLOSE(
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, P),
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p, tol);
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if(Q < P)
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{
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// Default method (Clopper Pearson)
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BOOST_CHECK(
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binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, Q)
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<=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, Q)
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);
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BOOST_CHECK((
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binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, Q)
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<= k/N) && (k/N <=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, Q))
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);
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// Bayes Method (Jeffreys Prior)
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BOOST_CHECK(
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binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
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<=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
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);
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BOOST_CHECK((
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binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval)
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<= k/N) && (k/N <=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, Q, binomial_distribution<RealType>::jeffreys_prior_interval))
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);
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}
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else
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{
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// Default method (Clopper Pearson)
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BOOST_CHECK(
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binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, P)
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<=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, P)
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);
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BOOST_CHECK(
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(binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, P)
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<= k / N) && (k/N <=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, P))
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);
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// Bayes Method (Jeffreys Prior)
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BOOST_CHECK(
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binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
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<=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
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);
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BOOST_CHECK(
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(binomial_distribution<RealType>::find_lower_bound_on_p(
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N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval)
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<= k / N) && (k/N <=
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binomial_distribution<RealType>::find_upper_bound_on_p(
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N, k, P, binomial_distribution<RealType>::jeffreys_prior_interval))
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);
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}
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}
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//
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// estimate sample size:
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//
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BOOST_CHECK_CLOSE(
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binomial_distribution<RealType>::find_minimum_number_of_trials(
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k, p, P),
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N, tol);
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BOOST_CHECK_CLOSE(
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binomial_distribution<RealType>::find_maximum_number_of_trials(
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k, p, Q),
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N, tol);
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}
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// Double check consistency of CDF and PDF by computing
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// the finite sum:
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RealType sum = 0;
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for(unsigned i = 0; i <= k; ++i)
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sum += pdf(bn, RealType(i));
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BOOST_CHECK_CLOSE(
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sum, P, tol);
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// And complement as well:
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sum = 0;
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for(RealType i = N; i > k; i -= 1)
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sum += pdf(bn, i);
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if(P < 0.99)
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{
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BOOST_CHECK_CLOSE(
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sum, Q, tol);
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}
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else
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{
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// Not enough information content in P for Q to be meaningful
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RealType tol = (std::max)(2 * Q, boost::math::tools::epsilon<RealType>());
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BOOST_CHECK(sum < tol);
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}
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}
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template <class RealType> // Any floating-point type RealType.
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void test_spots(RealType T)
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{
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// Basic sanity checks, test data is to double precision only
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// so set tolerance to 100eps expressed as a persent, or
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// 100eps of type double expressed as a persent, whichever
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// is the larger.
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RealType tolerance = (std::max)
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(boost::math::tools::epsilon<RealType>(),
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static_cast<RealType>(std::numeric_limits<double>::epsilon()));
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tolerance *= 100 * 1000;
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RealType tol2 = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a persent
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cout << "Tolerance for type " << typeid(T).name() << " is " << tolerance << " %" << endl;
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// Sources of spot test values:
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// MathCAD defines pbinom(k, n, p)
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// returns pr(X ,=k) when random variable X has the binomial distribution with parameters n and p.
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// 0 <= k ,= n
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// 0 <= p <= 1
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// P = pbinom(30, 500, 0.05) = 0.869147702104609
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using boost::math::binomial_distribution;
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using ::boost::math::cdf;
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using ::boost::math::pdf;
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#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 0)
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// Test binomial using cdf spot values from MathCAD.
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// These test quantiles and complements as well.
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test_spot(
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static_cast<RealType>(500), // Sample size, N
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static_cast<RealType>(30), // Number of successes, k
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static_cast<RealType>(0.05), // Probability of success, p
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static_cast<RealType>(0.869147702104609), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.869147702104609), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(500), // Sample size, N
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static_cast<RealType>(250), // Number of successes, k
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static_cast<RealType>(0.05), // Probability of success, p
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static_cast<RealType>(1), // Probability of result (CDF), P
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static_cast<RealType>(0), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(500), // Sample size, N
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static_cast<RealType>(470), // Number of successes, k
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static_cast<RealType>(0.95), // Probability of success, p
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static_cast<RealType>(0.176470742656766), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.176470742656766), // Q = 1 - P
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tolerance * 10); // Note higher tolerance on this test!
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test_spot(
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static_cast<RealType>(500), // Sample size, N
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static_cast<RealType>(400), // Number of successes, k
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static_cast<RealType>(0.05), // Probability of success, p
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static_cast<RealType>(1), // Probability of result (CDF), P
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static_cast<RealType>(0), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(500), // Sample size, N
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static_cast<RealType>(400), // Number of successes, k
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static_cast<RealType>(0.9), // Probability of success, p
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static_cast<RealType>(1.80180425681923E-11), // Probability of result (CDF), P
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static_cast<RealType>(1 - 1.80180425681923E-11), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(500), // Sample size, N
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static_cast<RealType>(5), // Number of successes, k
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static_cast<RealType>(0.05), // Probability of success, p
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static_cast<RealType>(9.181808267643E-7), // Probability of result (CDF), P
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static_cast<RealType>(1 - 9.181808267643E-7), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(2), // Sample size, N
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static_cast<RealType>(1), // Number of successes, k
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static_cast<RealType>(0.5), // Probability of success, p
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static_cast<RealType>(0.75), // Probability of result (CDF), P
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static_cast<RealType>(0.25), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(8), // Sample size, N
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static_cast<RealType>(3), // Number of successes, k
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static_cast<RealType>(0.25), // Probability of success, p
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static_cast<RealType>(0.8861846923828125), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.8861846923828125), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(8), // Sample size, N
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static_cast<RealType>(0), // Number of successes, k
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static_cast<RealType>(0.25), // Probability of success, p
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static_cast<RealType>(0.1001129150390625), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.1001129150390625), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(8), // Sample size, N
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static_cast<RealType>(1), // Number of successes, k
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static_cast<RealType>(0.25), // Probability of success, p
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static_cast<RealType>(0.36708068847656244), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.36708068847656244), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(8), // Sample size, N
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static_cast<RealType>(4), // Number of successes, k
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static_cast<RealType>(0.25), // Probability of success, p
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static_cast<RealType>(0.9727020263671875), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.9727020263671875), // Q = 1 - P
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tolerance);
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test_spot(
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static_cast<RealType>(8), // Sample size, N
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static_cast<RealType>(7), // Number of successes, k
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static_cast<RealType>(0.25), // Probability of success, p
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static_cast<RealType>(0.9999847412109375), // Probability of result (CDF), P
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static_cast<RealType>(1 - 0.9999847412109375), // Q = 1 - P
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tolerance);
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// Tests on PDF follow:
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BOOST_CHECK_CLOSE(
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pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.75)),
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static_cast<RealType>(10)), // k.
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static_cast<RealType>(0.00992227527967770583927631378173), // 0.00992227527967770583927631378173
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.5)),
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static_cast<RealType>(10)), // k.
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static_cast<RealType>(0.17619705200195312500000000000000000000), // get k=10 0.049611376398388612 p = 0.25
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tolerance);
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// Binomial pdf Test values from
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// http://www.adsciengineering.com/bpdcalc/index.php for example
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// http://www.adsciengineering.com/bpdcalc/index.php?n=20&p=0.25&start=0&stop=20&Submit=Generate
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// Appears to use at least 80-bit long double for 32 decimal digits accuracy,
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// but loses accuracy of display if leading zeros?
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// (if trailings zero then are exact values?)
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// so useful for testing 64-bit double accuracy.
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// P = 0.25, n = 20, k = 0 to 20
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//0 C(20,0) * 0.25^0 * 0.75^20 0.00317121193893399322405457496643
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//1 C(20,1) * 0.25^1 * 0.75^19 0.02114141292622662149369716644287
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//2 C(20,2) * 0.25^2 * 0.75^18 0.06694780759971763473004102706909
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//3 C(20,3) * 0.25^3 * 0.75^17 0.13389561519943526946008205413818
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//4 C(20,4) * 0.25^4 * 0.75^16 0.18968545486586663173511624336242
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//5 C(20,5) * 0.25^5 * 0.75^15 0.20233115185692440718412399291992
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//6 C(20,6) * 0.25^6 * 0.75^14 0.16860929321410367265343666076660
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//7 C(20,7) * 0.25^7 * 0.75^13 0.11240619547606911510229110717773
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//8 C(20,8) * 0.25^8 * 0.75^12 0.06088668921620410401374101638793
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//9 C(20,9) * 0.25^9 * 0.75^11 0.02706075076275737956166267395019
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//10 C(20,10) * 0.25^10 * 0.75^10 0.00992227527967770583927631378173
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//11 C(20,11) * 0.25^11 * 0.75^9 0.00300675008475081995129585266113
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//12 C(20,12) * 0.25^12 * 0.75^8 0.00075168752118770498782396316528
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//13 C(20,13) * 0.25^13 * 0.75^7 0.00015419231203850358724594116210
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//14 C(20,14) * 0.25^14 * 0.75^6 0.00002569871867308393120765686035
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//15 C(20,15) * 0.25^15 * 0.75^5 0.00000342649582307785749435424804
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//16 C(20,16) * 0.25^16 * 0.75^4 0.00000035692664823727682232856750
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//17 C(20,17) * 0.25^17 * 0.75^3 0.00000002799424692057073116302490
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//18 C(20,18) * 0.25^18 * 0.75^2 0.00000000155523594003170728683471
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//19 C(20,19) * 0.25^19 * 0.75^1 0.00000000005456968210637569427490
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//20 C(20,20) * 0.25^20 * 0.75^0 0.00000000000090949470177292823791
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BOOST_CHECK_CLOSE(
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pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
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static_cast<RealType>(10)), // k.
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static_cast<RealType>(0.00992227527967770583927631378173), // k=10 p = 0.25
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tolerance);
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BOOST_CHECK_CLOSE( // k = 0 use different formula - only exp so more accurate.
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pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
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static_cast<RealType>(0)), // k.
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static_cast<RealType>(0.00317121193893399322405457496643), // k=0 p = 0.25
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tolerance);
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BOOST_CHECK_CLOSE( // k = 20 use different formula - only exp so more accurate.
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pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
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static_cast<RealType>(20)), // k == n.
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static_cast<RealType>(0.00000000000090949470177292823791), // k=20 p = 0.25
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tolerance);
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BOOST_CHECK_CLOSE( // k = 1.
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pdf(binomial_distribution<RealType>(static_cast<RealType>(20), static_cast<RealType>(0.25)),
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static_cast<RealType>(1)), // k.
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static_cast<RealType>(0.02114141292622662149369716644287), // k=1 p = 0.25
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tolerance);
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// Some exact (probably) values.
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BOOST_CHECK_CLOSE(
|
|
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(0)), // k.
|
|
static_cast<RealType>(0.10011291503906250000000000000000), // k=0 p = 0.25
|
|
tolerance);
|
|
|
|
BOOST_CHECK_CLOSE( // k = 1.
|
|
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(1)), // k.
|
|
static_cast<RealType>(0.26696777343750000000000000000000), // k=1 p = 0.25
|
|
tolerance);
|
|
|
|
BOOST_CHECK_CLOSE( // k = 2.
|
|
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(2)), // k.
|
|
static_cast<RealType>(0.31146240234375000000000000000000), // k=2 p = 0.25
|
|
tolerance);
|
|
|
|
BOOST_CHECK_CLOSE( // k = 3.
|
|
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(3)), // k.
|
|
static_cast<RealType>(0.20764160156250000000000000000000), // k=3 p = 0.25
|
|
tolerance);
|
|
|
|
BOOST_CHECK_CLOSE( // k = 7.
|
|
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(7)), // k.
|
|
static_cast<RealType>(0.00036621093750000000000000000000), // k=7 p = 0.25
|
|
tolerance);
|
|
|
|
BOOST_CHECK_CLOSE( // k = 8.
|
|
pdf(binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(8)), // k = n.
|
|
static_cast<RealType>(0.00001525878906250000000000000000), // k=8 p = 0.25
|
|
tolerance);
|
|
|
|
binomial_distribution<RealType> dist(static_cast<RealType>(8), static_cast<RealType>(0.25));
|
|
RealType x = static_cast<RealType>(0.125);
|
|
using namespace std; // ADL of std names.
|
|
// mean:
|
|
BOOST_CHECK_CLOSE(
|
|
mean(dist)
|
|
, static_cast<RealType>(8 * 0.25), tol2);
|
|
// variance:
|
|
BOOST_CHECK_CLOSE(
|
|
variance(dist)
|
|
, static_cast<RealType>(8 * 0.25 * 0.75), tol2);
|
|
// std deviation:
|
|
BOOST_CHECK_CLOSE(
|
|
standard_deviation(dist)
|
|
, static_cast<RealType>(sqrt(8 * 0.25L * 0.75L)), tol2);
|
|
// hazard:
|
|
BOOST_CHECK_CLOSE(
|
|
hazard(dist, x)
|
|
, pdf(dist, x) / cdf(complement(dist, x)), tol2);
|
|
// cumulative hazard:
|
|
BOOST_CHECK_CLOSE(
|
|
chf(dist, x)
|
|
, -log(cdf(complement(dist, x))), tol2);
|
|
// coefficient_of_variation:
|
|
BOOST_CHECK_CLOSE(
|
|
coefficient_of_variation(dist)
|
|
, standard_deviation(dist) / mean(dist), tol2);
|
|
// mode:
|
|
BOOST_CHECK_CLOSE(
|
|
mode(dist)
|
|
, static_cast<RealType>(std::floor(9 * 0.25)), tol2);
|
|
// skewness:
|
|
BOOST_CHECK_CLOSE(
|
|
skewness(dist)
|
|
, static_cast<RealType>(0.40824829046386301636621401245098L), (std::max)(tol2, static_cast<RealType>(5e-29))); // test data has 32 digits only.
|
|
// kurtosis:
|
|
BOOST_CHECK_CLOSE(
|
|
kurtosis(dist)
|
|
, static_cast<RealType>(2.916666666666666666666666666666666666L), tol2);
|
|
// kurtosis excess:
|
|
BOOST_CHECK_CLOSE(
|
|
kurtosis_excess(dist)
|
|
, static_cast<RealType>(-0.08333333333333333333333333333333333333L), tol2);
|
|
// Check kurtosis_excess == kurtosis -3;
|
|
BOOST_CHECK_EQUAL(kurtosis(dist), static_cast<RealType>(3) + kurtosis_excess(dist));
|
|
|
|
// special cases for PDF:
|
|
BOOST_CHECK_EQUAL(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
|
|
static_cast<RealType>(0)), static_cast<RealType>(1)
|
|
);
|
|
BOOST_CHECK_EQUAL(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
|
|
static_cast<RealType>(0.0001)), static_cast<RealType>(0)
|
|
);
|
|
BOOST_CHECK_EQUAL(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
|
|
static_cast<RealType>(0.001)), static_cast<RealType>(0)
|
|
);
|
|
BOOST_CHECK_EQUAL(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
|
|
static_cast<RealType>(8)), static_cast<RealType>(1)
|
|
);
|
|
BOOST_CHECK_EQUAL(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(0), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(0)), static_cast<RealType>(1)
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(-1), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(0)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
|
|
static_cast<RealType>(0)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
|
|
static_cast<RealType>(0)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(-1)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
pdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(9)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
cdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(-1)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
cdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(9)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
cdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
|
|
static_cast<RealType>(0)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
cdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
|
|
static_cast<RealType>(0)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
quantile(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(-0.25)),
|
|
static_cast<RealType>(0)), std::domain_error
|
|
);
|
|
BOOST_MATH_CHECK_THROW(
|
|
quantile(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1.25)),
|
|
static_cast<RealType>(0)), std::domain_error
|
|
);
|
|
|
|
BOOST_CHECK_EQUAL(
|
|
quantile(
|
|
binomial_distribution<RealType>(static_cast<RealType>(16), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(0.01)), // Less than cdf == pdf(binomial_distribution<RealType>(16, 0.25), 0)
|
|
static_cast<RealType>(0) // so expect zero as best approximation.
|
|
);
|
|
|
|
BOOST_CHECK_EQUAL(
|
|
cdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0.25)),
|
|
static_cast<RealType>(8)), static_cast<RealType>(1)
|
|
);
|
|
BOOST_CHECK_EQUAL(
|
|
cdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(0)),
|
|
static_cast<RealType>(7)), static_cast<RealType>(1)
|
|
);
|
|
BOOST_CHECK_EQUAL(
|
|
cdf(
|
|
binomial_distribution<RealType>(static_cast<RealType>(8), static_cast<RealType>(1)),
|
|
static_cast<RealType>(7)), static_cast<RealType>(0)
|
|
);
|
|
|
|
#endif
|
|
|
|
{
|
|
// This is a visual sanity check that everything is OK:
|
|
binomial_distribution<RealType> my8dist(8., 0.25); // Note: double values (matching the distribution definition) avoid the need for any casting.
|
|
//cout << "mean(my8dist) = " << boost::math::mean(my8dist) << endl; // mean(my8dist) = 2
|
|
//cout << "my8dist.trials() = " << my8dist.trials() << endl; // my8dist.trials() = 8
|
|
//cout << "my8dist.success_fraction() = " << my8dist.success_fraction() << endl; // my8dist.success_fraction() = 0.25
|
|
BOOST_CHECK_CLOSE(my8dist.trials(), static_cast<RealType>(8), tol2);
|
|
BOOST_CHECK_CLOSE(my8dist.success_fraction(), static_cast<RealType>(0.25), tol2);
|
|
|
|
//{
|
|
// int n = static_cast<int>(boost::math::tools::real_cast<double>(my8dist.trials()));
|
|
// RealType sumcdf = 0.;
|
|
// for (int k = 0; k <= n; k++)
|
|
// {
|
|
// cout << k << ' ' << pdf(my8dist, static_cast<RealType>(k));
|
|
// sumcdf += pdf(my8dist, static_cast<RealType>(k));
|
|
// cout << ' ' << sumcdf;
|
|
// cout << ' ' << cdf(my8dist, static_cast<RealType>(k));
|
|
// cout << ' ' << sumcdf - cdf(my8dist, static_cast<RealType>(k)) << endl;
|
|
// } // for k
|
|
// }
|
|
// n = 8, p =0.25
|
|
//k pdf cdf
|
|
//0 0.1001129150390625 0.1001129150390625
|
|
//1 0.26696777343749994 0.36708068847656244
|
|
//2 0.31146240234375017 0.67854309082031261
|
|
//3 0.20764160156249989 0.8861846923828125
|
|
//4 0.086517333984375 0.9727020263671875
|
|
//5 0.023071289062499997 0.9957733154296875
|
|
//6 0.0038452148437500009 0.9996185302734375
|
|
//7 0.00036621093749999984 0.9999847412109375
|
|
//8 1.52587890625e-005 1 1 0
|
|
}
|
|
#define T RealType
|
|
#include "binomial_quantile.ipp"
|
|
|
|
for(unsigned i = 0; i < binomial_quantile_data.size(); ++i)
|
|
{
|
|
using namespace boost::math::policies;
|
|
RealType tol = boost::math::tools::epsilon<RealType>() * 500;
|
|
if(!boost::is_floating_point<RealType>::value)
|
|
tol *= 10; // no lanczos approximation implies less accuracy
|
|
RealType x;
|
|
#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 1)
|
|
//
|
|
// Check full real value first:
|
|
//
|
|
typedef policy<discrete_quantile<boost::math::policies::real> > P1;
|
|
binomial_distribution<RealType, P1> p1(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
|
|
x = quantile(p1, binomial_quantile_data[i][2]);
|
|
BOOST_CHECK_CLOSE_FRACTION(x, (RealType)binomial_quantile_data[i][3], tol);
|
|
x = quantile(complement(p1, (RealType)binomial_quantile_data[i][2]));
|
|
BOOST_CHECK_CLOSE_FRACTION(x, (RealType)binomial_quantile_data[i][4], tol);
|
|
#endif
|
|
#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 2)
|
|
//
|
|
// Now with round down to integer:
|
|
//
|
|
typedef policy<discrete_quantile<integer_round_down> > P2;
|
|
binomial_distribution<RealType, P2> p2(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
|
|
x = quantile(p2, binomial_quantile_data[i][2]);
|
|
BOOST_CHECK_EQUAL(x, (RealType)floor(binomial_quantile_data[i][3]));
|
|
x = quantile(complement(p2, binomial_quantile_data[i][2]));
|
|
BOOST_CHECK_EQUAL(x, (RealType)floor(binomial_quantile_data[i][4]));
|
|
#endif
|
|
#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 3)
|
|
//
|
|
// Now with round up to integer:
|
|
//
|
|
typedef policy<discrete_quantile<integer_round_up> > P3;
|
|
binomial_distribution<RealType, P3> p3(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
|
|
x = quantile(p3, binomial_quantile_data[i][2]);
|
|
BOOST_CHECK_EQUAL(x, (RealType)ceil(binomial_quantile_data[i][3]));
|
|
x = quantile(complement(p3, binomial_quantile_data[i][2]));
|
|
BOOST_CHECK_EQUAL(x, (RealType)ceil(binomial_quantile_data[i][4]));
|
|
#endif
|
|
#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 4)
|
|
//
|
|
// Now with round to integer "outside":
|
|
//
|
|
typedef policy<discrete_quantile<integer_round_outwards> > P4;
|
|
binomial_distribution<RealType, P4> p4(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
|
|
x = quantile(p4, binomial_quantile_data[i][2]);
|
|
BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? floor(binomial_quantile_data[i][3]) : ceil(binomial_quantile_data[i][3])));
|
|
x = quantile(complement(p4, binomial_quantile_data[i][2]));
|
|
BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? ceil(binomial_quantile_data[i][4]) : floor(binomial_quantile_data[i][4])));
|
|
#endif
|
|
#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 5)
|
|
//
|
|
// Now with round to integer "inside":
|
|
//
|
|
typedef policy<discrete_quantile<integer_round_inwards> > P5;
|
|
binomial_distribution<RealType, P5> p5(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
|
|
x = quantile(p5, binomial_quantile_data[i][2]);
|
|
BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? ceil(binomial_quantile_data[i][3]) : floor(binomial_quantile_data[i][3])));
|
|
x = quantile(complement(p5, binomial_quantile_data[i][2]));
|
|
BOOST_CHECK_EQUAL(x, (RealType)(binomial_quantile_data[i][2] < 0.5f ? floor(binomial_quantile_data[i][4]) : ceil(binomial_quantile_data[i][4])));
|
|
#endif
|
|
#if !defined(TEST_ROUNDING) || (TEST_ROUNDING == 6)
|
|
//
|
|
// Now with round to nearest integer:
|
|
//
|
|
typedef policy<discrete_quantile<integer_round_nearest> > P6;
|
|
binomial_distribution<RealType, P6> p6(binomial_quantile_data[i][0], binomial_quantile_data[i][1]);
|
|
x = quantile(p6, binomial_quantile_data[i][2]);
|
|
BOOST_CHECK_EQUAL(x, (RealType)(floor(binomial_quantile_data[i][3] + 0.5f)));
|
|
x = quantile(complement(p6, binomial_quantile_data[i][2]));
|
|
BOOST_CHECK_EQUAL(x, (RealType)(floor(binomial_quantile_data[i][4] + 0.5f)));
|
|
#endif
|
|
}
|
|
|
|
check_out_of_range<boost::math::binomial_distribution<RealType> >(1, 1); // (All) valid constructor parameter values.
|
|
|
|
|
|
} // template <class RealType>void test_spots(RealType)
|
|
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
|
{
|
|
BOOST_MATH_CONTROL_FP;
|
|
// Check that can generate binomial distribution using one convenience methods:
|
|
binomial_distribution<> mybn2(1., 0.5); // Using default RealType double.
|
|
// but that
|
|
// boost::math::binomial mybn1(1., 0.5); // Using typedef fails
|
|
// error C2039: 'binomial' : is not a member of 'boost::math'
|
|
|
|
// Basic sanity-check spot values.
|
|
|
|
// (Parameter value, arbitrarily zero, only communicates the floating point type).
|
|
#ifdef TEST_FLOAT
|
|
test_spots(0.0F); // Test float.
|
|
#endif
|
|
#ifdef TEST_DOUBLE
|
|
test_spots(0.0); // Test double.
|
|
#endif
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
#ifdef TEST_LDOUBLE
|
|
test_spots(0.0L); // Test long double.
|
|
#endif
|
|
#if !defined(BOOST_MATH_NO_REAL_CONCEPT_TESTS)
|
|
#ifdef TEST_REAL_CONCEPT
|
|
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
|
|
#endif
|
|
#endif
|
|
#else
|
|
std::cout << "<note>The long double tests have been disabled on this platform "
|
|
"either because the long double overloads of the usual math functions are "
|
|
"not available at all, or because they are too inaccurate for these tests "
|
|
"to pass.</note>" << std::endl;
|
|
#endif
|
|
|
|
} // BOOST_AUTO_TEST_CASE( test_main )
|
|
|
|
/*
|
|
|
|
Output is:
|
|
|
|
Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_binomial.exe"
|
|
Running 1 test case...
|
|
Tolerance for type float is 0.0119209 %
|
|
Tolerance for type double is 2.22045e-011 %
|
|
Tolerance for type long double is 2.22045e-011 %
|
|
Tolerance for type class boost::math::concepts::real_concept is 2.22045e-011 %
|
|
|
|
*** No errors detected
|
|
|
|
========== Build: 1 succeeded, 0 failed, 0 up-to-date, 0 skipped ==========
|
|
|
|
|
|
*/
|