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