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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 percentage:
// 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);
// kurtosis:
BOOST_CHECK_CLOSE(
kurtosis(dist)
, kurtosis_excess(dist) + 3, tolerance);
// kurtosis 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);
RealType expected_entropy = boost::math::constants::euler<RealType>()*(1-1/dist.shape()) + log(dist.scale()/dist.shape()) + 1;
BOOST_CHECK_CLOSE(
entropy(dist)
, expected_entropy, tolerance);
//
// 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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