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315 lines
12 KiB
C++
315 lines
12 KiB
C++
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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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// test_lognormal.cpp
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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/lognormal.hpp>
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using boost::math::lognormal_distribution;
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#include <boost/math/tools/test.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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using std::setprecision;
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#include <limits>
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using std::numeric_limits;
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#include <cassert>
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template <class RealType>
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void check_lognormal(RealType loc, RealType scale, RealType x, RealType p, RealType q, RealType tol)
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{
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BOOST_CHECK_CLOSE(
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::boost::math::cdf(
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lognormal_distribution<RealType>(loc, scale), // 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(
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::boost::math::cdf(
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complement(
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lognormal_distribution<RealType>(loc, scale), // 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(
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::boost::math::quantile(
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lognormal_distribution<RealType>(loc, scale), // 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(
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::boost::math::quantile(
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complement(
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lognormal_distribution<RealType>(loc, scale), // 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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}
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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 = 5e-3 * 100;
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// Some tests only pass at 1e-4 because values generated by
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// http://faculty.vassar.edu/lowry/VassarStats.html
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// give only 5 or 6 *fixed* places, so small values have fewer digits.
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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using std::exp;
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//
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// These test values were generated for the normal distribution
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// using the online calculator at http://faculty.vassar.edu/lowry/VassarStats.html
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// and then exponentiating the random variate x.
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//
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check_lognormal(
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static_cast<RealType>(0), // location
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static_cast<RealType>(5), // scale
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static_cast<RealType>(1), // x
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static_cast<RealType>(0.5), // p
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static_cast<RealType>(0.5), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(2), // location
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static_cast<RealType>(2), // scale
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static_cast<RealType>(exp(1.8)), // x
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static_cast<RealType>(0.46017), // p
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static_cast<RealType>(1-0.46017), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(2), // location
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static_cast<RealType>(2), // scale
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static_cast<RealType>(exp(2.2)), // x
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static_cast<RealType>(1-0.46017), // p
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static_cast<RealType>(0.46017), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(2), // location
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static_cast<RealType>(2), // scale
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static_cast<RealType>(exp(-1.4)), // x
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static_cast<RealType>(0.04457), // p
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static_cast<RealType>(1-0.04457), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(2), // location
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static_cast<RealType>(2), // scale
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static_cast<RealType>(exp(5.4)), // x
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static_cast<RealType>(1-0.04457), // p
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static_cast<RealType>(0.04457), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(-3), // location
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static_cast<RealType>(5), // scale
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static_cast<RealType>(exp(-5.0)), // x
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static_cast<RealType>(0.34458), // p
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static_cast<RealType>(1-0.34458), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(-3), // location
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static_cast<RealType>(5), // scale
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static_cast<RealType>(exp(-1.0)), // x
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static_cast<RealType>(1-0.34458), // p
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static_cast<RealType>(0.34458), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(-3), // location
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static_cast<RealType>(5), // scale
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static_cast<RealType>(exp(-9.0)), // x
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static_cast<RealType>(0.11507), // p
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static_cast<RealType>(1-0.11507), // q
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tolerance);
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check_lognormal(
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static_cast<RealType>(-3), // location
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static_cast<RealType>(5), // scale
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static_cast<RealType>(exp(3.0)), // x
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static_cast<RealType>(1-0.11507), // p
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static_cast<RealType>(0.11507), // q
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tolerance);
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//
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// Tests for PDF
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//
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tolerance = boost::math::tools::epsilon<RealType>() * 5 * 100; // 5 eps as a percentage
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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BOOST_CHECK_CLOSE(
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pdf(lognormal_distribution<RealType>(), static_cast<RealType>(1)),
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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(
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pdf(lognormal_distribution<RealType>(3), exp(static_cast<RealType>(3))),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L) / exp(static_cast<RealType>(3)),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(lognormal_distribution<RealType>(3, 5), exp(static_cast<RealType>(3))),
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static_cast<RealType>(0.3989422804014326779399460599343818684759L / (5 * exp(static_cast<RealType>(3)))),
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tolerance);
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//
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// Spot checks for location = -5, scale = 6,
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// use relation to normal to test:
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//
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for(RealType x = -15; x < 5; x += 0.125)
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{
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BOOST_CHECK_CLOSE(
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pdf(lognormal_distribution<RealType>(-5, 6), exp(x)),
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pdf(boost::math::normal_distribution<RealType>(-5, 6), x) / exp(x),
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tolerance);
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}
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//
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// These test values were obtained by punching numbers into
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// a calculator, using the formulas at http://mathworld.wolfram.com/LogNormalDistribution.html
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//
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tolerance = (std::max)(
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boost::math::tools::epsilon<RealType>(),
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static_cast<RealType>(boost::math::tools::epsilon<double>())) * 5 * 100; // 5 eps as a percentage
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cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
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lognormal_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>(268337.28652087445695647967378715L), tolerance);
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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>(583389737628117.49553037857325892L), tolerance);
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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>(24153462.228594009489719473727471L), tolerance);
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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)), tolerance);
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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))), tolerance);
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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), tolerance);
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// mode:
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BOOST_CHECK_CLOSE(
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mode(dist)
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, static_cast<RealType>(0.36787944117144232159552377016146L), tolerance);
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BOOST_CHECK_CLOSE(
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median(dist)
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, static_cast<RealType>(exp(dist.location())), tolerance);
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BOOST_CHECK_CLOSE(
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median(dist),
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quantile(dist, static_cast<RealType>(0.5)), tolerance);
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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>(729551.38304660255658441529235697L), tolerance);
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// kertosis:
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BOOST_CHECK_CLOSE(
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kurtosis(dist)
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, static_cast<RealType>(4312295840576303.2363383232038251L), tolerance);
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// kertosis excess:
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BOOST_CHECK_CLOSE(
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kurtosis_excess(dist)
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, static_cast<RealType>(4312295840576300.2363383232038251L), tolerance);
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BOOST_CHECK_CLOSE(
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range(dist).first
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, static_cast<RealType>(0), tolerance);
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//
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// Special cases:
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//
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BOOST_CHECK(pdf(dist, 0) == 0);
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BOOST_CHECK(cdf(dist, 0) == 0);
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BOOST_CHECK(cdf(complement(dist, 0)) == 1);
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BOOST_CHECK(quantile(dist, 0) == 0);
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BOOST_CHECK(quantile(complement(dist, 1)) == 0);
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//
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// Error checks:
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//
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BOOST_MATH_CHECK_THROW(lognormal_distribution<RealType>(0, 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(lognormal_distribution<RealType>(2, -1), std::domain_error);
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BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error);
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BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error);
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BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
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BOOST_MATH_CHECK_THROW(quantile(dist, 1), std::overflow_error);
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BOOST_MATH_CHECK_THROW(quantile(complement(dist, 0)), std::overflow_error);
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check_out_of_range<lognormal_distribution<RealType> >(1, 2);
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} // template <class RealType>void test_spots(RealType)
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BOOST_AUTO_TEST_CASE( test_main )
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{
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// Check that can generate lognormal distribution using the two convenience methods:
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boost::math::lognormal myf1(1., 2); // Using typedef
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lognormal_distribution<> myf2(1., 2); // Using default RealType double.
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// Test range and support using double only,
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// because it supports numeric_limits max for a pseudo-infinity.
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BOOST_CHECK_EQUAL(range(myf2).first, 0); // range 0 to +infinity
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BOOST_CHECK_EQUAL(range(myf2).second, (std::numeric_limits<double>::max)());
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BOOST_CHECK_EQUAL(support(myf2).first, 0); // support 0 to + infinity.
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BOOST_CHECK_EQUAL(support(myf2).second, (std::numeric_limits<double>::max)());
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// Basic sanity-check spot values.
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// (Parameter value, arbitrarily zero, only communicates the floating point type).
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test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
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test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
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#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
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test_spots(0.0L); // Test long double.
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#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
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test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
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#endif
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#else
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std::cout << "<note>The long double tests have been disabled on this platform "
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"either because the long double overloads of the usual math functions are "
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"not available at all, or because they are too inaccurate for these tests "
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"to pass.</note>" << std::endl;
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#endif
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} // BOOST_AUTO_TEST_CASE( test_main )
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/*
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Running 1 test case...
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Tolerance for type float is 0.5 %
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Tolerance for type float is 5.96046e-005 %
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Tolerance for type float is 5.96046e-005 %
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Tolerance for type double is 0.5 %
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Tolerance for type double is 1.11022e-013 %
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Tolerance for type double is 1.11022e-013 %
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Tolerance for type long double is 0.5 %
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Tolerance for type long double is 1.11022e-013 %
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Tolerance for type long double is 1.11022e-013 %
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Tolerance for type class boost::math::concepts::real_concept is 0.5 %
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Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 %
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Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 %
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*** No errors detected
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*/
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