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524 lines
21 KiB
C++
524 lines
21 KiB
C++
// Copyright Paul A. Bristow 2012.
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// Copyright John Maddock 2012.
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// Copyright Benjamin Sobotta 2012
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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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#ifdef _MSC_VER
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# pragma warning (disable : 4127) // conditional expression is constant.
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# pragma warning (disable : 4305) // 'initializing' : truncation from 'double' to 'const float'.
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# pragma warning (disable : 4310) // cast truncates constant value.
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# pragma warning (disable : 4512) // assignment operator could not be generated.
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#endif
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//#include <pch.hpp> // include directory libs/math/src/tr1/ is needed.
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#include <boost/math/concepts/real_concept.hpp> // for real_concept
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#define BOOST_TEST_MAIN
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#include <boost/test/unit_test.hpp> // Boost.Test
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#include <boost/test/floating_point_comparison.hpp>
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#include <boost/math/distributions/skew_normal.hpp>
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using boost::math::skew_normal_distribution;
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using boost::math::skew_normal;
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#include <boost/math/tools/test.hpp>
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#include <iostream>
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#include <iomanip>
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using std::cout;
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using std::endl;
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using std::setprecision;
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#include <limits>
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using std::numeric_limits;
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#include "test_out_of_range.hpp"
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template <class RealType>
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void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
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{
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using boost::math::skew_normal_distribution;
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf( // Check cdf
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skew_normal_distribution<RealType>(mean, scale, shape), // distribution.
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x), // random variable.
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p, // probability.
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tol); // tolerance.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::cdf( // Check cdf complement
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complement(
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skew_normal_distribution<RealType>(mean, scale, shape), // distribution.
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x)), // random variable.
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q, // probability complement.
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tol); // %tolerance.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile( // Check quantile
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skew_normal_distribution<RealType>(mean, scale, shape), // distribution.
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p), // probability.
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x, // random variable.
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tol); // tolerance.
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BOOST_CHECK_CLOSE_FRACTION(
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::boost::math::quantile( // Check quantile complement
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complement(
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skew_normal_distribution<RealType>(mean, scale, shape), // distribution.
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q)), // probability complement.
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x, // random variable.
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tol); // tolerance.
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skew_normal_distribution<RealType> dist (mean, scale, shape);
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if((p < 0.999) && (q < 0.999))
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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 accurate:
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BOOST_CHECK_CLOSE_FRACTION(
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cdf(complement(dist, x)), q, tol); // 1 - cdf
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(dist, p), x, tol); // quantile(cdf) = x
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BOOST_CHECK_CLOSE_FRACTION(
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quantile(complement(dist, q)), x, tol); // quantile(complement(1 - cdf)) = x
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}
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} // template <class RealType>void check_skew_normal()
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template <class RealType>
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void test_spots(RealType)
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{
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// Basic sanity checks
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RealType tolerance = 1e-4f; // 1e-4 (as %)
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// Check some bad parameters to the distribution,
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#ifndef BOOST_NO_EXCEPTIONS
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd
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#else
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType>(0, 0), std::domain_error); // zero sd
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType>(0, -1), std::domain_error); // negative sd
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#endif
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// Tests on extreme values of random variate x, if has numeric_limit infinity etc.
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skew_normal_distribution<RealType> N01;
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if(std::numeric_limits<RealType>::has_infinity)
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{
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BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0
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BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0
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BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1
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BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0
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BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0
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BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1
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#ifndef BOOST_NO_EXCEPTIONS
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
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#else
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType>(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType>(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean
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BOOST_MATH_CHECK_THROW(boost::math::skew_normal_distribution<RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd
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#endif
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}
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if (std::numeric_limits<RealType>::has_quiet_NaN)
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{
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// No longer allow x to be NaN, then these tests should throw.
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BOOST_MATH_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
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BOOST_MATH_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN
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BOOST_MATH_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity
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BOOST_MATH_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity
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BOOST_MATH_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity
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}
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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// Tests where shape = 0, so same as normal tests.
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// (These might be removed later).
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check_skew_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(0),
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static_cast<RealType>(4.8),
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static_cast<RealType>(0.46017),
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static_cast<RealType>(1 - 0.46017),
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tolerance);
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check_skew_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(0),
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static_cast<RealType>(5.2),
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static_cast<RealType>(1 - 0.46017),
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static_cast<RealType>(0.46017),
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tolerance);
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check_skew_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(0),
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static_cast<RealType>(2.2),
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static_cast<RealType>(0.08076),
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static_cast<RealType>(1 - 0.08076),
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tolerance);
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check_skew_normal(
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static_cast<RealType>(5),
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static_cast<RealType>(2),
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static_cast<RealType>(0),
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static_cast<RealType>(7.8),
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static_cast<RealType>(1 - 0.08076),
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static_cast<RealType>(0.08076),
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tolerance);
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check_skew_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(0),
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static_cast<RealType>(-4.5),
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static_cast<RealType>(0.38209),
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static_cast<RealType>(1 - 0.38209),
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tolerance);
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check_skew_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(0),
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static_cast<RealType>(-1.5),
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static_cast<RealType>(1 - 0.38209),
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static_cast<RealType>(0.38209),
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tolerance);
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check_skew_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(0),
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static_cast<RealType>(-8.5),
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static_cast<RealType>(0.13567),
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static_cast<RealType>(1 - 0.13567),
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tolerance);
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check_skew_normal(
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static_cast<RealType>(-3),
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static_cast<RealType>(5),
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static_cast<RealType>(0),
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static_cast<RealType>(2.5),
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static_cast<RealType>(1 - 0.13567),
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static_cast<RealType>(0.13567),
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tolerance);
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// Tests where shape != 0, specific to skew_normal distribution.
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//void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol)
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check_skew_normal( // 1st R example.
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static_cast<RealType>(1.1),
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static_cast<RealType>(2.2),
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static_cast<RealType>(-3.3),
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static_cast<RealType>(0.4), // x
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static_cast<RealType>(0.733918618927874), // p == psn
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static_cast<RealType>(1 - 0.733918618927874), // q
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tolerance);
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// Not sure about these yet.
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//check_skew_normal( // 2nd R example.
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//static_cast<RealType>(1.1),
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//static_cast<RealType>(0.02),
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//static_cast<RealType>(0.03),
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//static_cast<RealType>(1.3), // x
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//static_cast<RealType>(0.01), // p
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//static_cast<RealType>(0.09), // q
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//tolerance);
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//check_skew_normal( // 3nd R example.
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//static_cast<RealType>(10.1),
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//static_cast<RealType>(5.),
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//static_cast<RealType>(-0.03),
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//static_cast<RealType>(-1.3), // x
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//static_cast<RealType>(0.01201290665838824), // p
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//static_cast<RealType>(1. - 0.01201290665838824), // q 0.987987101
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//tolerance);
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// Tests for PDF: we know that the normal peak value is at 1/sqrt(2*pi)
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//
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tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction
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BOOST_CHECK_CLOSE_FRACTION(
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pdf(skew_normal_distribution<RealType>(), static_cast<RealType>(0)),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi)
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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pdf(skew_normal_distribution<RealType>(3), static_cast<RealType>(3)),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L),
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tolerance);
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BOOST_CHECK_CLOSE_FRACTION(
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pdf(skew_normal_distribution<RealType>(3, 5), static_cast<RealType>(3)),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
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tolerance);
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// Shape != 0.
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BOOST_CHECK_CLOSE_FRACTION(
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pdf(skew_normal_distribution<RealType>(3,5,1e-6), static_cast<RealType>(3)),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5),
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tolerance);
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// Checks on mean, variance cumulants etc.
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// Checks on shape ==0
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RealType tol5 = boost::math::tools::epsilon<RealType>() * 5;
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skew_normal_distribution<RealType> dist(8, 3);
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RealType x = static_cast<RealType>(0.125);
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BOOST_MATH_STD_USING // ADL of std math lib names
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// mean:
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BOOST_CHECK_CLOSE(
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mean(dist)
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, static_cast<RealType>(8), tol5);
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// variance:
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BOOST_CHECK_CLOSE(
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variance(dist)
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, static_cast<RealType>(9), tol5);
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// std deviation:
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BOOST_CHECK_CLOSE(
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standard_deviation(dist)
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, static_cast<RealType>(3), tol5);
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// hazard:
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BOOST_CHECK_CLOSE(
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hazard(dist, x)
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, pdf(dist, x) / cdf(complement(dist, x)), tol5);
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// cumulative hazard:
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BOOST_CHECK_CLOSE(
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chf(dist, x)
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, -log(cdf(complement(dist, x))), tol5);
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// coefficient_of_variation:
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BOOST_CHECK_CLOSE(
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coefficient_of_variation(dist)
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, standard_deviation(dist) / mean(dist), tol5);
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// mode:
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BOOST_CHECK_CLOSE_FRACTION(mode(dist), static_cast<RealType>(8), 0.001f);
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BOOST_CHECK_CLOSE(
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median(dist)
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, static_cast<RealType>(8), tol5);
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// skewness:
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BOOST_CHECK_CLOSE(
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skewness(dist)
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, static_cast<RealType>(0), tol5);
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// kurtosis:
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BOOST_CHECK_CLOSE(
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kurtosis(dist)
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, static_cast<RealType>(3), tol5);
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// kurtosis excess:
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BOOST_CHECK_CLOSE(
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kurtosis_excess(dist)
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, static_cast<RealType>(0), tol5);
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skew_normal_distribution<RealType> norm01(0, 1); // Test default (0, 1)
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BOOST_CHECK_CLOSE(
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mean(norm01),
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static_cast<RealType>(0), 0); // Mean == zero
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skew_normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1)
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BOOST_CHECK_CLOSE(
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mean(defsd_norm01),
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static_cast<RealType>(0), 0); // Mean == zero
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skew_normal_distribution<RealType> def_norm01; // Test default (0, sd = 1)
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BOOST_CHECK_CLOSE(
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mean(def_norm01),
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static_cast<RealType>(0), 0); // Mean == zero
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BOOST_CHECK_CLOSE(
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standard_deviation(def_norm01),
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static_cast<RealType>(1), 0); //
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BOOST_CHECK_CLOSE(
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mode(def_norm01),
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static_cast<RealType>(0), 0); // Mode == zero
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// Skew_normal tests with shape != 0.
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{
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// Note these tolerances are expressed as percentages, hence the extra * 100 on the end:
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RealType tol10 = boost::math::tools::epsilon<RealType>() * 10 * 100;
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RealType tol100 = boost::math::tools::epsilon<RealType>() * 100 * 100;
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//skew_normal_distribution<RealType> dist(1.1, 0.02, 0.03);
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BOOST_MATH_STD_USING // ADL of std math lib names.
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// Test values from R = see skew_normal_drv.cpp which included the R code used.
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{
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dist = skew_normal_distribution<RealType>(static_cast<RealType>(1.1l), static_cast<RealType>(2.2l), static_cast<RealType>(-3.3l));
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BOOST_CHECK_CLOSE( // mean:
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mean(dist)
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, static_cast<RealType>(-0.579908992539856825862549L), tol10 * 2);
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std::cout << std::setprecision(17) << "Variance = " << variance(dist) << std::endl;
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BOOST_CHECK_CLOSE( // variance: N[variance[skewnormaldistribution[1.1, 2.2, -3.3]], 50]
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variance(dist)
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, static_cast<RealType>(2.0179057767837232633904061072049998357047989154484L), tol10);
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BOOST_CHECK_CLOSE( // skewness:
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skewness(dist)
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, static_cast<RealType>(-0.709854548171537509192897824663L), tol100);
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BOOST_CHECK_CLOSE( // kurtosis:
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kurtosis(dist)
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, static_cast<RealType>(3.5538752625241790601377L), tol100);
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BOOST_CHECK_CLOSE( // kurtosis excess:
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kurtosis_excess(dist)
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, static_cast<RealType>(0.5538752625241790601377L), tol100);
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BOOST_CHECK_CLOSE(
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pdf(dist, static_cast<RealType>(0.4L)),
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static_cast<RealType>(0.294140110156599539564571L),
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tol10);
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BOOST_CHECK_CLOSE(
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cdf(dist, static_cast<RealType>(0.4L)),
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static_cast<RealType>(0.7339186189278737976326676452L),
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tol100);
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BOOST_CHECK_CLOSE(
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quantile(dist, static_cast<RealType>(0.3L)),
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static_cast<RealType>(-1.180104068086875314419247L),
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tol100);
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{ // mode tests
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dist = skew_normal_distribution<RealType>(static_cast<RealType>(0.l), static_cast<RealType>(1.l), static_cast<RealType>(4.l));
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// cout << "pdf(dist, 0) = " << pdf(dist, 0) << ", pdf(dist, 0.45) = " << pdf(dist, 0.45) << endl;
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// BOOST_CHECK_CLOSE(mode(dist), boost::math::constants::root_two<RealType>() / 2, tol5);
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BOOST_CHECK_CLOSE(mode(dist), static_cast<RealType>(0.41697299497388863932L), tol100);
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}
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}
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{
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dist = skew_normal_distribution<RealType>(static_cast<RealType>(1.1l), static_cast<RealType>(0.02l), static_cast<RealType>(0.03l));
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BOOST_CHECK_CLOSE( // mean:
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mean(dist)
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, static_cast<RealType>(1.1004785154529557886162L), tol10);
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BOOST_CHECK_CLOSE( // variance:
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variance(dist)
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, static_cast<RealType>(0.00039977102296128251645L), tol10);
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BOOST_CHECK_CLOSE( // skewness:
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skewness(dist)
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, static_cast<RealType>(5.8834811259890359782e-006L), tol100);
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BOOST_CHECK_CLOSE( // kurtosis:
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kurtosis(dist)
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, static_cast<RealType>(3.L + 9.2903475812137800239002e-008L), tol100);
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BOOST_CHECK_CLOSE( // kurtosis excess:
|
|
kurtosis_excess(dist)
|
|
, static_cast<RealType>(9.2903475812137800239002e-008L), tol100);
|
|
}
|
|
{
|
|
dist = skew_normal_distribution<RealType>(static_cast<RealType>(10.1l), static_cast<RealType>(5.l), static_cast<RealType>(-0.03l));
|
|
BOOST_CHECK_CLOSE( // mean:
|
|
mean(dist)
|
|
, static_cast<RealType>(9.9803711367610528459485937L), tol10);
|
|
BOOST_CHECK_CLOSE( // variance:
|
|
variance(dist)
|
|
, static_cast<RealType>(24.98568893508015727823L), tol10);
|
|
|
|
BOOST_CHECK_CLOSE( // skewness:
|
|
skewness(dist)
|
|
, static_cast<RealType>(-5.8834811259890359782085e-006L), tol100);
|
|
BOOST_CHECK_CLOSE( // kurtosis:
|
|
kurtosis(dist)
|
|
, static_cast<RealType>(3.L + 9.2903475812137800239002e-008L), tol100);
|
|
BOOST_CHECK_CLOSE( // kurtosis excess:
|
|
kurtosis_excess(dist)
|
|
, static_cast<RealType>(9.2903475812137800239002e-008L), tol100);
|
|
}
|
|
{
|
|
dist = skew_normal_distribution<RealType>(static_cast<RealType>(-10.1l), static_cast<RealType>(5.l), static_cast<RealType>(30.l));
|
|
BOOST_CHECK_CLOSE( // mean:
|
|
mean(dist)
|
|
, static_cast<RealType>(-6.11279169674138408531365L), 2 * tol10);
|
|
BOOST_CHECK_CLOSE( // variance:
|
|
variance(dist)
|
|
, static_cast<RealType>(9.10216994642554914628242L), tol10 * 2);
|
|
|
|
BOOST_CHECK_CLOSE( // skewness:
|
|
skewness(dist)
|
|
, static_cast<RealType>(0.99072425443686904424L), tol100);
|
|
BOOST_CHECK_CLOSE( // kurtosis:
|
|
kurtosis(dist)
|
|
, static_cast<RealType>(3.L + 0.8638862008406084244563L), tol100);
|
|
BOOST_CHECK_CLOSE( // kurtosis excess:
|
|
kurtosis_excess(dist)
|
|
, static_cast<RealType>(0.8638862008406084244563L), tol100);
|
|
}
|
|
|
|
BOOST_MATH_CHECK_THROW(cdf(skew_normal_distribution<RealType>(0, 0, 0), 0), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(cdf(skew_normal_distribution<RealType>(0, -1, 0), 0), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(quantile(skew_normal_distribution<RealType>(0, 1, 0), -1), std::domain_error);
|
|
BOOST_MATH_CHECK_THROW(quantile(skew_normal_distribution<RealType>(0, 1, 0), 2), std::domain_error);
|
|
check_out_of_range<skew_normal_distribution<RealType> >(1, 1, 1);
|
|
}
|
|
|
|
|
|
} // template <class RealType>void test_spots(RealType)
|
|
|
|
BOOST_AUTO_TEST_CASE( test_main )
|
|
{
|
|
|
|
|
|
using boost::math::skew_normal;
|
|
using boost::math::skew_normal_distribution;
|
|
|
|
//int precision = 17; // std::numeric_limits<double::max_digits10;
|
|
double tolfeweps = numeric_limits<double>::epsilon() * 5;
|
|
//double tol6decdigits = numeric_limits<float>::epsilon() * 2;
|
|
// Check that can generate skew_normal distribution using the two convenience methods:
|
|
boost::math::skew_normal w12(1., 2); // Using typedef.
|
|
boost::math::skew_normal_distribution<> w01; // Use default unity values for mean and scale.
|
|
// Note NOT myn01() as the compiler will interpret as a function!
|
|
|
|
// Checks on constructors.
|
|
// Default parameters.
|
|
BOOST_CHECK_EQUAL(w01.location(), 0);
|
|
BOOST_CHECK_EQUAL(w01.scale(), 1);
|
|
BOOST_CHECK_EQUAL(w01.shape(), 0);
|
|
|
|
skew_normal_distribution<> w23(2., 3); // Using default RealType double.
|
|
BOOST_CHECK_EQUAL(w23.scale(), 3);
|
|
BOOST_CHECK_EQUAL(w23.shape(), 0);
|
|
|
|
skew_normal_distribution<> w123(1., 2., 3.); // Using default RealType double.
|
|
BOOST_CHECK_EQUAL(w123.location(), 1.);
|
|
BOOST_CHECK_EQUAL(w123.scale(), 2.);
|
|
BOOST_CHECK_EQUAL(w123.shape(), 3.);
|
|
|
|
BOOST_CHECK_CLOSE_FRACTION(mean(w01), static_cast<double>(0), tolfeweps); // Default mean == zero
|
|
BOOST_CHECK_CLOSE_FRACTION(scale(w01), static_cast<double>(1), tolfeweps); // Default scale == unity
|
|
|
|
// Basic sanity-check spot values for all floating-point types..
|
|
// (Parameter value, arbitrarily zero, only communicates the floating point type).
|
|
test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
|
|
test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
|
|
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
|
|
test_spots(0.0L); // Test long double.
|
|
#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS
|
|
test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
|
|
#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:
|
|
|
|
|
|
*/
|
|
|
|
|