| // Copyright Paul A. Bristow 2012. |
| // Copyright John Maddock 2012. |
| // Copyright Benjamin Sobotta 2012 |
| |
| // 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) |
| |
| #ifdef _MSC_VER |
| # pragma warning (disable : 4127) // conditional expression is constant. |
| # pragma warning (disable : 4305) // 'initializing' : truncation from 'double' to 'const float'. |
| # pragma warning (disable : 4310) // cast truncates constant value. |
| # pragma warning (disable : 4512) // assignment operator could not be generated. |
| #endif |
| |
| //#include <pch.hpp> // include directory libs/math/src/tr1/ is needed. |
| |
| #include <boost/math/concepts/real_concept.hpp> // for real_concept |
| #define BOOST_TEST_MAIN |
| #include <boost/test/unit_test.hpp> // Boost.Test |
| #include <boost/test/floating_point_comparison.hpp> |
| |
| #include <boost/math/distributions/skew_normal.hpp> |
| using boost::math::skew_normal_distribution; |
| using boost::math::skew_normal; |
| |
| #include <iostream> |
| #include <iomanip> |
| using std::cout; |
| using std::endl; |
| using std::setprecision; |
| #include <limits> |
| using std::numeric_limits; |
| #include "test_out_of_range.hpp" |
| |
| template <class RealType> |
| void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol) |
| { |
| using boost::math::skew_normal_distribution; |
| |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::cdf( // Check cdf |
| skew_normal_distribution<RealType>(mean, scale, shape), // distribution. |
| x), // random variable. |
| p, // probability. |
| tol); // tolerance. |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::cdf( // Check cdf complement |
| complement( |
| skew_normal_distribution<RealType>(mean, scale, shape), // distribution. |
| x)), // random variable. |
| q, // probability complement. |
| tol); // %tolerance. |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::quantile( // Check quantile |
| skew_normal_distribution<RealType>(mean, scale, shape), // distribution. |
| p), // probability. |
| x, // random variable. |
| tol); // tolerance. |
| BOOST_CHECK_CLOSE_FRACTION( |
| ::boost::math::quantile( // Check quantile complement |
| complement( |
| skew_normal_distribution<RealType>(mean, scale, shape), // distribution. |
| q)), // probability complement. |
| x, // random variable. |
| tol); // tolerance. |
| |
| skew_normal_distribution<RealType> dist (mean, scale, shape); |
| |
| if((p < 0.999) && (q < 0.999)) |
| { // We can only check this if P is not too close to 1, |
| // so that we can guarantee Q is accurate: |
| BOOST_CHECK_CLOSE_FRACTION( |
| cdf(complement(dist, x)), q, tol); // 1 - cdf |
| BOOST_CHECK_CLOSE_FRACTION( |
| quantile(dist, p), x, tol); // quantile(cdf) = x |
| BOOST_CHECK_CLOSE_FRACTION( |
| quantile(complement(dist, q)), x, tol); // quantile(complement(1 - cdf)) = x |
| } |
| } // template <class RealType>void check_skew_normal() |
| |
| |
| template <class RealType> |
| void test_spots(RealType) |
| { |
| // Basic sanity checks |
| RealType tolerance = 1e-4f; // 1e-4 (as %) |
| |
| // Check some bad parameters to the distribution, |
| |
| BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, 0), std::domain_error); // zero sd |
| BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(0, -1), std::domain_error); // negative sd |
| |
| // Tests on extreme values of random variate x, if has numeric_limit infinity etc. |
| skew_normal_distribution<RealType> N01; |
| if(std::numeric_limits<RealType>::has_infinity) |
| { |
| BOOST_CHECK_EQUAL(pdf(N01, +std::numeric_limits<RealType>::infinity()), 0); // x = + infinity, pdf = 0 |
| BOOST_CHECK_EQUAL(pdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, pdf = 0 |
| BOOST_CHECK_EQUAL(cdf(N01, +std::numeric_limits<RealType>::infinity()), 1); // x = + infinity, cdf = 1 |
| BOOST_CHECK_EQUAL(cdf(N01, -std::numeric_limits<RealType>::infinity()), 0); // x = - infinity, cdf = 0 |
| BOOST_CHECK_EQUAL(cdf(complement(N01, +std::numeric_limits<RealType>::infinity())), 0); // x = + infinity, c cdf = 0 |
| BOOST_CHECK_EQUAL(cdf(complement(N01, -std::numeric_limits<RealType>::infinity())), 1); // x = - infinity, c cdf = 1 |
| BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // +infinite mean |
| BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(-std::numeric_limits<RealType>::infinity(), static_cast<RealType>(1)), std::domain_error); // -infinite mean |
| BOOST_CHECK_THROW(boost::math::skew_normal_distribution<RealType> nbad1(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()), std::domain_error); // infinite sd |
| } |
| |
| if (std::numeric_limits<RealType>::has_quiet_NaN) |
| { |
| // No longer allow x to be NaN, then these tests should throw. |
| BOOST_CHECK_THROW(pdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN |
| BOOST_CHECK_THROW(cdf(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // x = NaN |
| BOOST_CHECK_THROW(cdf(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // x = + infinity |
| BOOST_CHECK_THROW(quantile(N01, +std::numeric_limits<RealType>::quiet_NaN()), std::domain_error); // p = + infinity |
| BOOST_CHECK_THROW(quantile(complement(N01, +std::numeric_limits<RealType>::quiet_NaN())), std::domain_error); // p = + infinity |
| } |
| |
| cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl; |
| |
| // Tests where shape = 0, so same as normal tests. |
| // (These might be removed later). |
| check_skew_normal( |
| static_cast<RealType>(5), |
| static_cast<RealType>(2), |
| static_cast<RealType>(0), |
| static_cast<RealType>(4.8), |
| static_cast<RealType>(0.46017), |
| static_cast<RealType>(1 - 0.46017), |
| tolerance); |
| |
| check_skew_normal( |
| static_cast<RealType>(5), |
| static_cast<RealType>(2), |
| static_cast<RealType>(0), |
| static_cast<RealType>(5.2), |
| static_cast<RealType>(1 - 0.46017), |
| static_cast<RealType>(0.46017), |
| tolerance); |
| |
| check_skew_normal( |
| static_cast<RealType>(5), |
| static_cast<RealType>(2), |
| static_cast<RealType>(0), |
| static_cast<RealType>(2.2), |
| static_cast<RealType>(0.08076), |
| static_cast<RealType>(1 - 0.08076), |
| tolerance); |
| |
| check_skew_normal( |
| static_cast<RealType>(5), |
| static_cast<RealType>(2), |
| static_cast<RealType>(0), |
| static_cast<RealType>(7.8), |
| static_cast<RealType>(1 - 0.08076), |
| static_cast<RealType>(0.08076), |
| tolerance); |
| |
| check_skew_normal( |
| static_cast<RealType>(-3), |
| static_cast<RealType>(5), |
| static_cast<RealType>(0), |
| static_cast<RealType>(-4.5), |
| static_cast<RealType>(0.38209), |
| static_cast<RealType>(1 - 0.38209), |
| tolerance); |
| |
| check_skew_normal( |
| static_cast<RealType>(-3), |
| static_cast<RealType>(5), |
| static_cast<RealType>(0), |
| static_cast<RealType>(-1.5), |
| static_cast<RealType>(1 - 0.38209), |
| static_cast<RealType>(0.38209), |
| tolerance); |
| |
| check_skew_normal( |
| static_cast<RealType>(-3), |
| static_cast<RealType>(5), |
| static_cast<RealType>(0), |
| static_cast<RealType>(-8.5), |
| static_cast<RealType>(0.13567), |
| static_cast<RealType>(1 - 0.13567), |
| tolerance); |
| |
| check_skew_normal( |
| static_cast<RealType>(-3), |
| static_cast<RealType>(5), |
| static_cast<RealType>(0), |
| static_cast<RealType>(2.5), |
| static_cast<RealType>(1 - 0.13567), |
| static_cast<RealType>(0.13567), |
| tolerance); |
| |
| // Tests where shape != 0, specific to skew_normal distribution. |
| //void check_skew_normal(RealType mean, RealType scale, RealType shape, RealType x, RealType p, RealType q, RealType tol) |
| check_skew_normal( // 1st R example. |
| static_cast<RealType>(1.1), |
| static_cast<RealType>(2.2), |
| static_cast<RealType>(-3.3), |
| static_cast<RealType>(0.4), // x |
| static_cast<RealType>(0.733918618927874), // p == psn |
| static_cast<RealType>(1 - 0.733918618927874), // q |
| tolerance); |
| |
| // Not sure about these yet. |
| //check_skew_normal( // 2nd R example. |
| //static_cast<RealType>(1.1), |
| //static_cast<RealType>(0.02), |
| //static_cast<RealType>(0.03), |
| //static_cast<RealType>(1.3), // x |
| //static_cast<RealType>(0.01), // p |
| //static_cast<RealType>(0.09), // q |
| //tolerance); |
| //check_skew_normal( // 3nd R example. |
| //static_cast<RealType>(10.1), |
| //static_cast<RealType>(5.), |
| //static_cast<RealType>(-0.03), |
| //static_cast<RealType>(-1.3), // x |
| //static_cast<RealType>(0.01201290665838824), // p |
| //static_cast<RealType>(1. - 0.01201290665838824), // q 0.987987101 |
| //tolerance); |
| |
| // Tests for PDF: we know that the normal peak value is at 1/sqrt(2*pi) |
| // |
| tolerance = boost::math::tools::epsilon<RealType>() * 5; // 5 eps as a fraction |
| BOOST_CHECK_CLOSE_FRACTION( |
| pdf(skew_normal_distribution<RealType>(), static_cast<RealType>(0)), |
| static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi) |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( |
| pdf(skew_normal_distribution<RealType>(3), static_cast<RealType>(3)), |
| static_cast<RealType>(0.3989422804014326779399460599343818684759L), |
| tolerance); |
| BOOST_CHECK_CLOSE_FRACTION( |
| pdf(skew_normal_distribution<RealType>(3, 5), static_cast<RealType>(3)), |
| static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5), |
| tolerance); |
| |
| // Shape != 0. |
| BOOST_CHECK_CLOSE_FRACTION( |
| pdf(skew_normal_distribution<RealType>(3,5,1e-6), static_cast<RealType>(3)), |
| static_cast<RealType>(0.3989422804014326779399460599343818684759L / 5), |
| tolerance); |
| |
| |
| // Checks on mean, variance cumulants etc. |
| // Checks on shape ==0 |
| |
| RealType tol5 = boost::math::tools::epsilon<RealType>() * 5; |
| skew_normal_distribution<RealType> dist(8, 3); |
| RealType x = static_cast<RealType>(0.125); |
| |
| BOOST_MATH_STD_USING // ADL of std math lib names |
| |
| // mean: |
| BOOST_CHECK_CLOSE( |
| mean(dist) |
| , static_cast<RealType>(8), tol5); |
| // variance: |
| BOOST_CHECK_CLOSE( |
| variance(dist) |
| , static_cast<RealType>(9), tol5); |
| // std deviation: |
| BOOST_CHECK_CLOSE( |
| standard_deviation(dist) |
| , static_cast<RealType>(3), tol5); |
| // hazard: |
| BOOST_CHECK_CLOSE( |
| hazard(dist, x) |
| , pdf(dist, x) / cdf(complement(dist, x)), tol5); |
| // cumulative hazard: |
| BOOST_CHECK_CLOSE( |
| chf(dist, x) |
| , -log(cdf(complement(dist, x))), tol5); |
| // coefficient_of_variation: |
| BOOST_CHECK_CLOSE( |
| coefficient_of_variation(dist) |
| , standard_deviation(dist) / mean(dist), tol5); |
| // mode: |
| BOOST_CHECK_CLOSE_FRACTION(mode(dist), static_cast<RealType>(8), 0.001f); |
| |
| BOOST_CHECK_CLOSE( |
| median(dist) |
| , static_cast<RealType>(8), tol5); |
| |
| // skewness: |
| BOOST_CHECK_CLOSE( |
| skewness(dist) |
| , static_cast<RealType>(0), tol5); |
| // kurtosis: |
| BOOST_CHECK_CLOSE( |
| kurtosis(dist) |
| , static_cast<RealType>(3), tol5); |
| // kurtosis excess: |
| BOOST_CHECK_CLOSE( |
| kurtosis_excess(dist) |
| , static_cast<RealType>(0), tol5); |
| |
| skew_normal_distribution<RealType> norm01(0, 1); // Test default (0, 1) |
| BOOST_CHECK_CLOSE( |
| mean(norm01), |
| static_cast<RealType>(0), 0); // Mean == zero |
| |
| skew_normal_distribution<RealType> defsd_norm01(0); // Test default (0, sd = 1) |
| BOOST_CHECK_CLOSE( |
| mean(defsd_norm01), |
| static_cast<RealType>(0), 0); // Mean == zero |
| |
| skew_normal_distribution<RealType> def_norm01; // Test default (0, sd = 1) |
| BOOST_CHECK_CLOSE( |
| mean(def_norm01), |
| static_cast<RealType>(0), 0); // Mean == zero |
| |
| BOOST_CHECK_CLOSE( |
| standard_deviation(def_norm01), |
| static_cast<RealType>(1), 0); // |
| |
| BOOST_CHECK_CLOSE( |
| mode(def_norm01), |
| static_cast<RealType>(0), 0); // Mode == zero |
| |
| |
| // Skew_normal tests with shape != 0. |
| { |
| // Note these tolerances are expressed as percentages, hence the extra * 100 on the end: |
| RealType tol10 = boost::math::tools::epsilon<RealType>() * 10 * 100; |
| RealType tol100 = boost::math::tools::epsilon<RealType>() * 100 * 100; |
| |
| //skew_normal_distribution<RealType> dist(1.1, 0.02, 0.03); |
| |
| BOOST_MATH_STD_USING // ADL of std math lib names. |
| |
| // Test values from R = see skew_normal_drv.cpp which included the R code used. |
| { |
| dist = skew_normal_distribution<RealType>(static_cast<RealType>(1.1l), static_cast<RealType>(2.2l), static_cast<RealType>(-3.3l)); |
| |
| BOOST_CHECK_CLOSE( // mean: |
| mean(dist) |
| , static_cast<RealType>(-0.579908992539856825862549L), tol10 * 2); |
| |
| std::cout << std::setprecision(17) << "Variance = " << variance(dist) << std::endl; |
| BOOST_CHECK_CLOSE( // variance: N[variance[skewnormaldistribution[1.1, 2.2, -3.3]], 50] |
| variance(dist) |
| , static_cast<RealType>(2.0179057767837232633904061072049998357047989154484L), tol10); |
| |
| BOOST_CHECK_CLOSE( // skewness: |
| skewness(dist) |
| , static_cast<RealType>(-0.709854548171537509192897824663L), tol100); |
| BOOST_CHECK_CLOSE( // kurtosis: |
| kurtosis(dist) |
| , static_cast<RealType>(3.5538752625241790601377L), tol100); |
| BOOST_CHECK_CLOSE( // kurtosis excess: |
| kurtosis_excess(dist) |
| , static_cast<RealType>(0.5538752625241790601377L), tol100); |
| |
| BOOST_CHECK_CLOSE( |
| pdf(dist, static_cast<RealType>(0.4L)), |
| static_cast<RealType>(0.294140110156599539564571L), |
| tol10); |
| |
| BOOST_CHECK_CLOSE( |
| cdf(dist, static_cast<RealType>(0.4L)), |
| static_cast<RealType>(0.7339186189278737976326676452L), |
| tol100); |
| |
| BOOST_CHECK_CLOSE( |
| quantile(dist, static_cast<RealType>(0.3L)), |
| static_cast<RealType>(-1.180104068086875314419247L), |
| tol100); |
| |
| |
| { // mode tests |
| |
| dist = skew_normal_distribution<RealType>(static_cast<RealType>(0.l), static_cast<RealType>(1.l), static_cast<RealType>(4.l)); |
| |
| // cout << "pdf(dist, 0) = " << pdf(dist, 0) << ", pdf(dist, 0.45) = " << pdf(dist, 0.45) << endl; |
| // BOOST_CHECK_CLOSE(mode(dist), boost::math::constants::root_two<RealType>() / 2, tol5); |
| BOOST_CHECK_CLOSE(mode(dist), static_cast<RealType>(0.41697299497388863932L), tol100); |
| } |
| |
| |
| } |
| { |
| dist = skew_normal_distribution<RealType>(static_cast<RealType>(1.1l), static_cast<RealType>(0.02l), static_cast<RealType>(0.03l)); |
| |
| BOOST_CHECK_CLOSE( // mean: |
| mean(dist) |
| , static_cast<RealType>(1.1004785154529557886162L), tol10); |
| BOOST_CHECK_CLOSE( // variance: |
| variance(dist) |
| , static_cast<RealType>(0.00039977102296128251645L), tol10); |
| |
| BOOST_CHECK_CLOSE( // skewness: |
| skewness(dist) |
| , static_cast<RealType>(5.8834811259890359782e-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>(-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_CHECK_THROW(cdf(skew_normal_distribution<RealType>(0, 0, 0), 0), std::domain_error); |
| BOOST_CHECK_THROW(cdf(skew_normal_distribution<RealType>(0, -1, 0), 0), std::domain_error); |
| BOOST_CHECK_THROW(quantile(skew_normal_distribution<RealType>(0, 1, 0), -1), std::domain_error); |
| BOOST_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::cout; |
| #endif |
| /* */ |
| |
| } // BOOST_AUTO_TEST_CASE( test_main ) |
| |
| /* |
| |
| Output: |
| |
| |
| */ |
| |
| |
