| // Copyright John Maddock 2006. |
| // Copyright Paul A. Bristow 2007 |
| |
| // Use, modification and distribution are subject to the |
| // Boost Software License, Version 1.0. |
| // (See accompanying file LICENSE_1_0.txt |
| // or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| // test_lognormal.cpp |
| |
| #include <boost/math/concepts/real_concept.hpp> // for real_concept |
| #include <boost/test/test_exec_monitor.hpp> // Boost.Test |
| #include <boost/test/floating_point_comparison.hpp> |
| |
| #include <boost/math/distributions/lognormal.hpp> |
| using boost::math::lognormal_distribution; |
| #include <boost/math/tools/test.hpp> |
| |
| #include <iostream> |
| using std::cout; |
| using std::endl; |
| using std::setprecision; |
| #include <limits> |
| using std::numeric_limits; |
| #include <cassert> |
| |
| template <class RealType> |
| void check_lognormal(RealType loc, RealType scale, RealType x, RealType p, RealType q, RealType tol) |
| { |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| lognormal_distribution<RealType>(loc, scale), // distribution. |
| x), // random variable. |
| p, // probability. |
| tol); // %tolerance. |
| BOOST_CHECK_CLOSE( |
| ::boost::math::cdf( |
| complement( |
| lognormal_distribution<RealType>(loc, scale), // distribution. |
| x)), // random variable. |
| q, // probability complement. |
| tol); // %tolerance. |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| lognormal_distribution<RealType>(loc, scale), // distribution. |
| p), // probability. |
| x, // random variable. |
| tol); // %tolerance. |
| BOOST_CHECK_CLOSE( |
| ::boost::math::quantile( |
| complement( |
| lognormal_distribution<RealType>(loc, scale), // distribution. |
| q)), // probability complement. |
| x, // random variable. |
| tol); // %tolerance. |
| } |
| |
| template <class RealType> |
| void test_spots(RealType) |
| { |
| |
| // Basic sanity checks. |
| RealType tolerance = 5e-3 * 100; |
| // Some tests only pass at 1e-4 because values generated by |
| // http://faculty.vassar.edu/lowry/VassarStats.html |
| // give only 5 or 6 *fixed* places, so small values have fewer digits. |
| |
| cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl; |
| |
| using std::exp; |
| |
| // |
| // These test values were generated for the normal distribution |
| // using the online calculator at http://faculty.vassar.edu/lowry/VassarStats.html |
| // and then exponentiating the random variate x. |
| // |
| |
| check_lognormal( |
| static_cast<RealType>(0), // location |
| static_cast<RealType>(5), // scale |
| static_cast<RealType>(1), // x |
| static_cast<RealType>(0.5), // p |
| static_cast<RealType>(0.5), // q |
| tolerance); |
| check_lognormal( |
| static_cast<RealType>(2), // location |
| static_cast<RealType>(2), // scale |
| static_cast<RealType>(exp(1.8)), // x |
| static_cast<RealType>(0.46017), // p |
| static_cast<RealType>(1-0.46017), // q |
| tolerance); |
| check_lognormal( |
| static_cast<RealType>(2), // location |
| static_cast<RealType>(2), // scale |
| static_cast<RealType>(exp(2.2)), // x |
| static_cast<RealType>(1-0.46017), // p |
| static_cast<RealType>(0.46017), // q |
| tolerance); |
| check_lognormal( |
| static_cast<RealType>(2), // location |
| static_cast<RealType>(2), // scale |
| static_cast<RealType>(exp(-1.4)), // x |
| static_cast<RealType>(0.04457), // p |
| static_cast<RealType>(1-0.04457), // q |
| tolerance); |
| check_lognormal( |
| static_cast<RealType>(2), // location |
| static_cast<RealType>(2), // scale |
| static_cast<RealType>(exp(5.4)), // x |
| static_cast<RealType>(1-0.04457), // p |
| static_cast<RealType>(0.04457), // q |
| tolerance); |
| |
| check_lognormal( |
| static_cast<RealType>(-3), // location |
| static_cast<RealType>(5), // scale |
| static_cast<RealType>(exp(-5.0)), // x |
| static_cast<RealType>(0.34458), // p |
| static_cast<RealType>(1-0.34458), // q |
| tolerance); |
| check_lognormal( |
| static_cast<RealType>(-3), // location |
| static_cast<RealType>(5), // scale |
| static_cast<RealType>(exp(-1.0)), // x |
| static_cast<RealType>(1-0.34458), // p |
| static_cast<RealType>(0.34458), // q |
| tolerance); |
| check_lognormal( |
| static_cast<RealType>(-3), // location |
| static_cast<RealType>(5), // scale |
| static_cast<RealType>(exp(-9.0)), // x |
| static_cast<RealType>(0.11507), // p |
| static_cast<RealType>(1-0.11507), // q |
| tolerance); |
| check_lognormal( |
| static_cast<RealType>(-3), // location |
| static_cast<RealType>(5), // scale |
| static_cast<RealType>(exp(3.0)), // x |
| static_cast<RealType>(1-0.11507), // p |
| static_cast<RealType>(0.11507), // q |
| tolerance); |
| |
| // |
| // Tests for PDF |
| // |
| tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage |
| cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl; |
| BOOST_CHECK_CLOSE( |
| pdf(lognormal_distribution<RealType>(), static_cast<RealType>(1)), |
| static_cast<RealType>(0.3989422804014326779399460599343818684759L), // 1/sqrt(2*pi) |
| tolerance); |
| BOOST_CHECK_CLOSE( |
| pdf(lognormal_distribution<RealType>(3), exp(static_cast<RealType>(3))), |
| static_cast<RealType>(0.3989422804014326779399460599343818684759L) / exp(static_cast<RealType>(3)), |
| tolerance); |
| BOOST_CHECK_CLOSE( |
| pdf(lognormal_distribution<RealType>(3, 5), exp(static_cast<RealType>(3))), |
| static_cast<RealType>(0.3989422804014326779399460599343818684759L / (5 * exp(static_cast<RealType>(3)))), |
| tolerance); |
| // |
| // Spot checks for location = -5, scale = 6, |
| // use relation to normal to test: |
| // |
| for(RealType x = -15; x < 5; x += 0.125) |
| { |
| BOOST_CHECK_CLOSE( |
| pdf(lognormal_distribution<RealType>(-5, 6), exp(x)), |
| pdf(boost::math::normal_distribution<RealType>(-5, 6), x) / exp(x), |
| tolerance); |
| } |
| |
| // |
| // These test values were obtained by punching numbers into |
| // a calculator, using the formulas at http://mathworld.wolfram.com/LogNormalDistribution.html |
| // |
| tolerance = (std::max)( |
| boost::math::tools::epsilon<RealType>(), |
| static_cast<RealType>(boost::math::tools::epsilon<double>())) * 5 * 100; // 5 eps as a percentage |
| cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl; |
| lognormal_distribution<RealType> dist(8, 3); |
| RealType x = static_cast<RealType>(0.125); |
| using namespace std; // ADL of std names. |
| // mean: |
| BOOST_CHECK_CLOSE( |
| mean(dist) |
| , static_cast<RealType>(268337.28652087445695647967378715L), tolerance); |
| // variance: |
| BOOST_CHECK_CLOSE( |
| variance(dist) |
| , static_cast<RealType>(583389737628117.49553037857325892L), tolerance); |
| // std deviation: |
| BOOST_CHECK_CLOSE( |
| standard_deviation(dist) |
| , static_cast<RealType>(24153462.228594009489719473727471L), tolerance); |
| // hazard: |
| BOOST_CHECK_CLOSE( |
| hazard(dist, x) |
| , pdf(dist, x) / cdf(complement(dist, x)), tolerance); |
| // cumulative hazard: |
| BOOST_CHECK_CLOSE( |
| chf(dist, x) |
| , -log(cdf(complement(dist, x))), tolerance); |
| // coefficient_of_variation: |
| BOOST_CHECK_CLOSE( |
| coefficient_of_variation(dist) |
| , standard_deviation(dist) / mean(dist), tolerance); |
| // mode: |
| BOOST_CHECK_CLOSE( |
| mode(dist) |
| , static_cast<RealType>(0.36787944117144232159552377016146L), tolerance); |
| |
| BOOST_CHECK_CLOSE( |
| median(dist) |
| , static_cast<RealType>(exp(dist.location())), tolerance); |
| |
| BOOST_CHECK_CLOSE( |
| median(dist), |
| quantile(dist, static_cast<RealType>(0.5)), tolerance); |
| |
| // skewness: |
| BOOST_CHECK_CLOSE( |
| skewness(dist) |
| , static_cast<RealType>(729551.38304660255658441529235697L), tolerance); |
| // kertosis: |
| BOOST_CHECK_CLOSE( |
| kurtosis(dist) |
| , static_cast<RealType>(4312295840576303.2363383232038251L), tolerance); |
| // kertosis excess: |
| BOOST_CHECK_CLOSE( |
| kurtosis_excess(dist) |
| , static_cast<RealType>(4312295840576300.2363383232038251L), tolerance); |
| |
| BOOST_CHECK_CLOSE( |
| range(dist).first |
| , static_cast<RealType>(0), tolerance); |
| |
| // |
| // Special cases: |
| // |
| BOOST_CHECK(pdf(dist, 0) == 0); |
| BOOST_CHECK(cdf(dist, 0) == 0); |
| BOOST_CHECK(cdf(complement(dist, 0)) == 1); |
| BOOST_CHECK(quantile(dist, 0) == 0); |
| BOOST_CHECK(quantile(complement(dist, 1)) == 0); |
| |
| // |
| // Error checks: |
| // |
| BOOST_CHECK_THROW(lognormal_distribution<RealType>(0, -1), std::domain_error); |
| BOOST_CHECK_THROW(pdf(dist, -1), std::domain_error); |
| BOOST_CHECK_THROW(cdf(dist, -1), std::domain_error); |
| BOOST_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error); |
| BOOST_CHECK_THROW(quantile(dist, 1), std::overflow_error); |
| BOOST_CHECK_THROW(quantile(complement(dist, 0)), std::overflow_error); |
| |
| } // template <class RealType>void test_spots(RealType) |
| |
| int test_main(int, char* []) |
| { |
| |
| // Check that can generate lognormal distribution using the two convenience methods: |
| boost::math::lognormal myf1(1., 2); // Using typedef |
| lognormal_distribution<> myf2(1., 2); // Using default RealType double. |
| |
| // Test range and support using double only, |
| // because it supports numeric_limits max for a pseudo-infinity. |
| BOOST_CHECK_EQUAL(range(myf2).first, 0); // range 0 to +infinity |
| BOOST_CHECK_EQUAL(range(myf2).second, (std::numeric_limits<double>::max)()); |
| BOOST_CHECK_EQUAL(support(myf2).first, 0); // support 0 to + infinity. |
| BOOST_CHECK_EQUAL(support(myf2).second, (std::numeric_limits<double>::max)()); |
| |
| // Basic sanity-check spot values. |
| // (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. |
| #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582)) |
| 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 |
| |
| return 0; |
| } // int test_main(int, char* []) |
| |
| /* |
| Running 1 test case... |
| Tolerance for type float is 0.5 % |
| Tolerance for type float is 5.96046e-005 % |
| Tolerance for type float is 5.96046e-005 % |
| Tolerance for type double is 0.5 % |
| Tolerance for type double is 1.11022e-013 % |
| Tolerance for type double is 1.11022e-013 % |
| Tolerance for type long double is 0.5 % |
| Tolerance for type long double is 1.11022e-013 % |
| Tolerance for type long double is 1.11022e-013 % |
| Tolerance for type class boost::math::concepts::real_concept is 0.5 % |
| Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 % |
| Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 % |
| *** No errors detected |
| */ |
| |
| |
