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- // 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
- #define BOOST_TEST_MAIN
- #include <boost/test/unit_test.hpp> // Boost.Test
- #include <boost/test/tools/floating_point_comparison.hpp>
- #include <boost/math/distributions/lognormal.hpp>
- using boost::math::lognormal_distribution;
- #include <boost/math/tools/test.hpp>
- #include "test_out_of_range.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);
- BOOST_MATH_STD_USING // ADL of std math lib 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_MATH_CHECK_THROW(lognormal_distribution<RealType>(0, 0), std::domain_error);
- BOOST_MATH_CHECK_THROW(lognormal_distribution<RealType>(2, -1), std::domain_error);
- BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error);
- BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error);
- BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
- BOOST_MATH_CHECK_THROW(quantile(dist, 1), std::overflow_error);
- BOOST_MATH_CHECK_THROW(quantile(complement(dist, 0)), std::overflow_error);
- check_out_of_range<lognormal_distribution<RealType> >(1, 2);
- } // template <class RealType>void test_spots(RealType)
- BOOST_AUTO_TEST_CASE( test_main )
- {
- // 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::endl;
- #endif
-
- } // BOOST_AUTO_TEST_CASE( test_main )
- /*
- 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
- */
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