mirror of
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400 lines
15 KiB
C++
400 lines
15 KiB
C++
// Copyright John Maddock 2006, 2012.
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// Copyright Paul A. Bristow 2007, 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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// test_weibull.cpp
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#ifdef _MSC_VER
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# pragma warning (disable : 4127) // conditional expression is constant.
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#endif
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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/weibull.hpp>
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using boost::math::weibull_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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template <class RealType>
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void check_weibull(RealType shape, 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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weibull_distribution<RealType>(shape, 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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weibull_distribution<RealType>(shape, 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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weibull_distribution<RealType>(shape, 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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weibull_distribution<RealType>(shape, 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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//
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// These test values were generated for the normal distribution
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// using the online calculator at
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// http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
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//
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// Tolerance is just over 5 decimal digits expressed as a persentage:
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// that's the limit of the test data.
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RealType tolerance = 2e-5f * 100;
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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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check_weibull(
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static_cast<RealType>(0.25), // shape
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static_cast<RealType>(0.5), // scale
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static_cast<RealType>(0.1), // x
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static_cast<RealType>(0.487646), // p
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static_cast<RealType>(1-0.487646), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.25), // shape
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static_cast<RealType>(0.5), // scale
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static_cast<RealType>(0.5), // x
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static_cast<RealType>(1-0.367879), // p
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static_cast<RealType>(0.367879), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.25), // shape
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static_cast<RealType>(0.5), // scale
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static_cast<RealType>(1), // x
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static_cast<RealType>(1-0.304463), // p
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static_cast<RealType>(0.304463), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.25), // shape
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static_cast<RealType>(0.5), // scale
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static_cast<RealType>(2), // x
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static_cast<RealType>(1-0.243117), // p
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static_cast<RealType>(0.243117), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.25), // shape
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static_cast<RealType>(0.5), // scale
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static_cast<RealType>(5), // x
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static_cast<RealType>(1-0.168929), // p
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static_cast<RealType>(0.168929), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.5), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(0.1), // x
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static_cast<RealType>(0.200371), // p
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static_cast<RealType>(1-0.200371), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.5), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(0.5), // x
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static_cast<RealType>(0.393469), // p
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static_cast<RealType>(1-0.393469), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.5), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(1), // x
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static_cast<RealType>(1-0.493069), // p
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static_cast<RealType>(0.493069), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.5), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(2), // x
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static_cast<RealType>(1-0.367879), // p
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static_cast<RealType>(0.367879), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(0.5), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(5), // x
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static_cast<RealType>(1-0.205741), // p
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static_cast<RealType>(0.205741), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(2), // shape
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static_cast<RealType>(0.25), // scale
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static_cast<RealType>(0.1), // x
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static_cast<RealType>(0.147856), // p
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static_cast<RealType>(1-0.147856), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(2), // shape
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static_cast<RealType>(0.25), // scale
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static_cast<RealType>(0.5), // x
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static_cast<RealType>(1-0.018316), // p
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static_cast<RealType>(0.018316), // q
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tolerance);
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/*
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This test value came from
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http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
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but appears to be grossly incorrect: certainly it does not agree with the values
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I get from pushing numbers into a calculator (0.0001249921878255106610615995196123).
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Strangely other test values generated for the same shape and scale parameters do look OK.
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check_weibull(
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static_cast<RealType>(3), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(0.1), // x
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static_cast<RealType>(1.25E-40), // p
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static_cast<RealType>(1-1.25E-40), // q
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tolerance);
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*/
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check_weibull(
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static_cast<RealType>(3), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(0.5), // x
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static_cast<RealType>(0.015504), // p
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static_cast<RealType>(1-0.015504), // q
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tolerance * 10); // few digits in test value
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check_weibull(
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static_cast<RealType>(3), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(1), // x
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static_cast<RealType>(0.117503), // p
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static_cast<RealType>(1-0.117503), // q
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tolerance);
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check_weibull(
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static_cast<RealType>(3), // shape
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static_cast<RealType>(2), // scale
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static_cast<RealType>(2), // x
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static_cast<RealType>(1-0.367879), // p
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static_cast<RealType>(0.367879), // 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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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(0.25, 0.5), static_cast<RealType>(0.1)),
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static_cast<RealType>(0.856579),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(0.25, 0.5), static_cast<RealType>(0.5)),
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static_cast<RealType>(0.183940),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(0.25, 0.5), static_cast<RealType>(5)),
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static_cast<RealType>(0.015020),
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tolerance * 10); // fewer digits in test value
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(0.5, 2), static_cast<RealType>(0.1)),
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static_cast<RealType>(0.894013),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(0.5, 2), static_cast<RealType>(0.5)),
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static_cast<RealType>(0.303265),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(0.5, 2), static_cast<RealType>(1)),
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static_cast<RealType>(0.174326),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(2, 0.25), static_cast<RealType>(0.1)),
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static_cast<RealType>(2.726860),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(2, 0.25), static_cast<RealType>(0.5)),
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static_cast<RealType>(0.293050),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(3, 2), static_cast<RealType>(1)),
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static_cast<RealType>(0.330936),
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tolerance);
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BOOST_CHECK_CLOSE(
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pdf(weibull_distribution<RealType>(3, 2), static_cast<RealType>(2)),
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static_cast<RealType>(0.551819),
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tolerance);
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//
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// These test values were obtained using the formulas at
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// http://en.wikipedia.org/wiki/Weibull_distribution
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// which are subtly different to (though mathematically
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// the same as) the ones on the Mathworld site
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// http://mathworld.wolfram.com/WeibullDistribution.html
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// which are the ones used in the implementation.
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// The assumption is that if both computation methods
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// agree then the implementation is probably correct...
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// What's not clear is which method is more accurate.
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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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weibull_distribution<RealType> dist(2, 3);
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RealType x = static_cast<RealType>(0.125);
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BOOST_MATH_STD_USING // ADL of std lib math functions
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// mean:
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BOOST_CHECK_CLOSE(
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mean(dist)
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, dist.scale() * boost::math::tgamma(1 + 1 / dist.shape()), tolerance);
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// variance:
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BOOST_CHECK_CLOSE(
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variance(dist)
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, dist.scale() * dist.scale() * boost::math::tgamma(1 + 2 / dist.shape()) - mean(dist) * mean(dist), 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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, sqrt(variance(dist)), 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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, dist.scale() * pow((dist.shape() - 1) / dist.shape(), 1/dist.shape()), tolerance);
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// median:
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BOOST_CHECK_CLOSE(
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median(dist)
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, dist.scale() * pow(log(static_cast<RealType>(2)), 1 / dist.shape()), tolerance);
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// skewness:
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BOOST_CHECK_CLOSE(
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skewness(dist),
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(boost::math::tgamma(1 + 3/dist.shape()) * pow(dist.scale(), RealType(3)) - 3 * mean(dist) * variance(dist) - pow(mean(dist), RealType(3))) / pow(standard_deviation(dist), RealType(3)),
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tolerance * 100);
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// kertosis:
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BOOST_CHECK_CLOSE(
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kurtosis(dist)
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, kurtosis_excess(dist) + 3, 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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(pow(dist.scale(), RealType(4)) * boost::math::tgamma(1 + 4/dist.shape())
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- 3 * variance(dist) * variance(dist)
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- 4 * skewness(dist) * variance(dist) * standard_deviation(dist) * mean(dist)
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- 6 * variance(dist) * mean(dist) * mean(dist)
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- pow(mean(dist), RealType(4))) / (variance(dist) * variance(dist)),
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tolerance * 1000);
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//
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// Special cases:
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//
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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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BOOST_CHECK_EQUAL(pdf(weibull_distribution<RealType>(1, 1), 0), 1);
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//
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// Error checks:
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//
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BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(1, -1), std::domain_error);
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BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(-1, 1), std::domain_error);
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BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(1, 0), std::domain_error);
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BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(0, 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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BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
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BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
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BOOST_CHECK_EQUAL(pdf(dist, 0), exp(-pow(RealType(0) / RealType(3), RealType(2))) * pow(RealType(0), RealType(1)) * RealType(2) / RealType(3));
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BOOST_CHECK_EQUAL(pdf(weibull_distribution<RealType>(1, 3), 0), exp(-pow(RealType(0) / RealType(3), RealType(1))) * pow(RealType(0), RealType(0)) * RealType(1) / RealType(3));
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BOOST_MATH_CHECK_THROW(pdf(weibull_distribution<RealType>(0.5, 3), 0), std::overflow_error);
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check_out_of_range<weibull_distribution<RealType> >(1, 1);
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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 construct weibull distribution using the two convenience methods:
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using namespace boost::math;
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weibull myw1(2); // Using typedef
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weibull_distribution<> myw2(2); // Using default RealType double.
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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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Output:
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Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_weibull.exe"
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Running 1 test case...
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Tolerance for type float is 0.002 %
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Tolerance for type float is 5.96046e-005 %
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Tolerance for type double is 0.002 %
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Tolerance for type double is 1.11022e-013 %
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Tolerance for type long double is 0.002 %
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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 0.002 %
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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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