[ceph.git] / ceph / src / boost / libs / math / test / test_weibull.cpp

// 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(BOOST_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


*/
Commit	Line	Data
7c673cae FG	1	// Copyright John Maddock 2006, 2012.
	2	// Copyright Paul A. Bristow 2007, 2012.
	3
	4	// Use, modification and distribution are subject to the
	5	// Boost Software License, Version 1.0.
	6	// (See accompanying file LICENSE_1_0.txt
	7	// or copy at http://www.boost.org/LICENSE_1_0.txt)
	8
	9	// test_weibull.cpp
	10
	11	#ifdef _MSC_VER
	12	# pragma warning (disable : 4127) // conditional expression is constant.
	13	#endif
	14
	15
	16	#include <boost/math/concepts/real_concept.hpp> // for real_concept
	17	#define BOOST_TEST_MAIN
	18	#include <boost/test/unit_test.hpp> // Boost.Test
92f5a8d4	19	#include <boost/test/tools/floating_point_comparison.hpp>
7c673cae FG	20
	21	#include <boost/math/distributions/weibull.hpp>
	22	using boost::math::weibull_distribution;
	23	#include <boost/math/tools/test.hpp>
	24	#include "test_out_of_range.hpp"
	25
	26	#include <iostream>
	27	using std::cout;
	28	using std::endl;
	29	using std::setprecision;
	30	#include <limits>
	31	using std::numeric_limits;
	32
	33	template <class RealType>
	34	void check_weibull(RealType shape, RealType scale, RealType x, RealType p, RealType q, RealType tol)
	35	{
	36	BOOST_CHECK_CLOSE(
	37	::boost::math::cdf(
	38	weibull_distribution<RealType>(shape, scale), // distribution.
	39	x), // random variable.
	40	p, // probability.
	41	tol); // %tolerance.
	42	BOOST_CHECK_CLOSE(
	43	::boost::math::cdf(
	44	complement(
	45	weibull_distribution<RealType>(shape, scale), // distribution.
	46	x)), // random variable.
	47	q, // probability complement.
	48	tol); // %tolerance.
	49	BOOST_CHECK_CLOSE(
	50	::boost::math::quantile(
	51	weibull_distribution<RealType>(shape, scale), // distribution.
	52	p), // probability.
	53	x, // random variable.
	54	tol); // %tolerance.
	55	BOOST_CHECK_CLOSE(
	56	::boost::math::quantile(
	57	complement(
	58	weibull_distribution<RealType>(shape, scale), // distribution.
	59	q)), // probability complement.
	60	x, // random variable.
	61	tol); // %tolerance.
	62	}
	63
	64	template <class RealType>
	65	void test_spots(RealType)
	66	{
	67	// Basic sanity checks
	68	//
	69	// These test values were generated for the normal distribution
	70	// using the online calculator at
	71	// http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
	72	//
f67539c2	73	// Tolerance is just over 5 decimal digits expressed as a percentage:
7c673cae FG	74	// that's the limit of the test data.
	75	RealType tolerance = 2e-5f * 100;
	76	cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
	77
	78	using std::exp;
	79
	80	check_weibull(
	81	static_cast<RealType>(0.25), // shape
	82	static_cast<RealType>(0.5), // scale
	83	static_cast<RealType>(0.1), // x
	84	static_cast<RealType>(0.487646), // p
	85	static_cast<RealType>(1-0.487646), // q
	86	tolerance);
	87	check_weibull(
	88	static_cast<RealType>(0.25), // shape
	89	static_cast<RealType>(0.5), // scale
	90	static_cast<RealType>(0.5), // x
	91	static_cast<RealType>(1-0.367879), // p
	92	static_cast<RealType>(0.367879), // q
	93	tolerance);
	94	check_weibull(
	95	static_cast<RealType>(0.25), // shape
	96	static_cast<RealType>(0.5), // scale
	97	static_cast<RealType>(1), // x
	98	static_cast<RealType>(1-0.304463), // p
	99	static_cast<RealType>(0.304463), // q
	100	tolerance);
	101	check_weibull(
	102	static_cast<RealType>(0.25), // shape
	103	static_cast<RealType>(0.5), // scale
	104	static_cast<RealType>(2), // x
	105	static_cast<RealType>(1-0.243117), // p
	106	static_cast<RealType>(0.243117), // q
	107	tolerance);
	108	check_weibull(
	109	static_cast<RealType>(0.25), // shape
	110	static_cast<RealType>(0.5), // scale
	111	static_cast<RealType>(5), // x
	112	static_cast<RealType>(1-0.168929), // p
	113	static_cast<RealType>(0.168929), // q
	114	tolerance);
	115
	116	check_weibull(
	117	static_cast<RealType>(0.5), // shape
	118	static_cast<RealType>(2), // scale
	119	static_cast<RealType>(0.1), // x
	120	static_cast<RealType>(0.200371), // p
	121	static_cast<RealType>(1-0.200371), // q
	122	tolerance);
	123	check_weibull(
	124	static_cast<RealType>(0.5), // shape
	125	static_cast<RealType>(2), // scale
	126	static_cast<RealType>(0.5), // x
	127	static_cast<RealType>(0.393469), // p
	128	static_cast<RealType>(1-0.393469), // q
	129	tolerance);
	130	check_weibull(
	131	static_cast<RealType>(0.5), // shape
	132	static_cast<RealType>(2), // scale
	133	static_cast<RealType>(1), // x
	134	static_cast<RealType>(1-0.493069), // p
	135	static_cast<RealType>(0.493069), // q
	136	tolerance);
	137	check_weibull(
138	static_cast<RealType>(0.5), // shape
139	static_cast<RealType>(2), // scale
140	static_cast<RealType>(2), // x
141	static_cast<RealType>(1-0.367879), // p
142	static_cast<RealType>(0.367879), // q
143	tolerance);
144	check_weibull(
145	static_cast<RealType>(0.5), // shape
146	static_cast<RealType>(2), // scale
147	static_cast<RealType>(5), // x
148	static_cast<RealType>(1-0.205741), // p
149	static_cast<RealType>(0.205741), // q
150	tolerance);
151
152	check_weibull(
153	static_cast<RealType>(2), // shape
154	static_cast<RealType>(0.25), // scale
155	static_cast<RealType>(0.1), // x
156	static_cast<RealType>(0.147856), // p
157	static_cast<RealType>(1-0.147856), // q
158	tolerance);
159	check_weibull(
160	static_cast<RealType>(2), // shape
161	static_cast<RealType>(0.25), // scale
162	static_cast<RealType>(0.5), // x
163	static_cast<RealType>(1-0.018316), // p
164	static_cast<RealType>(0.018316), // q
165	tolerance);
166
167	/*
168	This test value came from
169	http://espse.ed.psu.edu/edpsych/faculty/rhale/hale/507Mat/statlets/free/pdist.htm
170	but appears to be grossly incorrect: certainly it does not agree with the values
171	I get from pushing numbers into a calculator (0.0001249921878255106610615995196123).
172	Strangely other test values generated for the same shape and scale parameters do look OK.
173	check_weibull(
174	static_cast<RealType>(3), // shape
175	static_cast<RealType>(2), // scale
176	static_cast<RealType>(0.1), // x
177	static_cast<RealType>(1.25E-40), // p
178	static_cast<RealType>(1-1.25E-40), // q
179	tolerance);
180	*/
181	check_weibull(
182	static_cast<RealType>(3), // shape
183	static_cast<RealType>(2), // scale
184	static_cast<RealType>(0.5), // x
185	static_cast<RealType>(0.015504), // p
186	static_cast<RealType>(1-0.015504), // q
187	tolerance * 10); // few digits in test value
188	check_weibull(
189	static_cast<RealType>(3), // shape
190	static_cast<RealType>(2), // scale
191	static_cast<RealType>(1), // x
192	static_cast<RealType>(0.117503), // p
193	static_cast<RealType>(1-0.117503), // q
194	tolerance);
195	check_weibull(
196	static_cast<RealType>(3), // shape
197	static_cast<RealType>(2), // scale
198	static_cast<RealType>(2), // x
199	static_cast<RealType>(1-0.367879), // p
200	static_cast<RealType>(0.367879), // q
201	tolerance);
202
203	//
204	// Tests for PDF
205	//
206	BOOST_CHECK_CLOSE(
207	pdf(weibull_distribution<RealType>(0.25, 0.5), static_cast<RealType>(0.1)),
208	static_cast<RealType>(0.856579),
209	tolerance);
210	BOOST_CHECK_CLOSE(
211	pdf(weibull_distribution<RealType>(0.25, 0.5), static_cast<RealType>(0.5)),
212	static_cast<RealType>(0.183940),
213	tolerance);
214	BOOST_CHECK_CLOSE(
215	pdf(weibull_distribution<RealType>(0.25, 0.5), static_cast<RealType>(5)),
216	static_cast<RealType>(0.015020),
217	tolerance * 10); // fewer digits in test value
218	BOOST_CHECK_CLOSE(
219	pdf(weibull_distribution<RealType>(0.5, 2), static_cast<RealType>(0.1)),
220	static_cast<RealType>(0.894013),
221	tolerance);
222	BOOST_CHECK_CLOSE(
223	pdf(weibull_distribution<RealType>(0.5, 2), static_cast<RealType>(0.5)),
224	static_cast<RealType>(0.303265),
225	tolerance);
226	BOOST_CHECK_CLOSE(
227	pdf(weibull_distribution<RealType>(0.5, 2), static_cast<RealType>(1)),
228	static_cast<RealType>(0.174326),
229	tolerance);
230	BOOST_CHECK_CLOSE(
231	pdf(weibull_distribution<RealType>(2, 0.25), static_cast<RealType>(0.1)),
232	static_cast<RealType>(2.726860),
233	tolerance);
234	BOOST_CHECK_CLOSE(
235	pdf(weibull_distribution<RealType>(2, 0.25), static_cast<RealType>(0.5)),
236	static_cast<RealType>(0.293050),
237	tolerance);
238	BOOST_CHECK_CLOSE(
239	pdf(weibull_distribution<RealType>(3, 2), static_cast<RealType>(1)),
240	static_cast<RealType>(0.330936),
241	tolerance);
242	BOOST_CHECK_CLOSE(
243	pdf(weibull_distribution<RealType>(3, 2), static_cast<RealType>(2)),
244	static_cast<RealType>(0.551819),
245	tolerance);
246
247	//
248	// These test values were obtained using the formulas at
249	// http://en.wikipedia.org/wiki/Weibull_distribution
250	// which are subtly different to (though mathematically
251	// the same as) the ones on the Mathworld site
252	// http://mathworld.wolfram.com/WeibullDistribution.html
253	// which are the ones used in the implementation.
254	// The assumption is that if both computation methods
255	// agree then the implementation is probably correct...
256	// What's not clear is which method is more accurate.
257	//
258	tolerance = (std::max)(
259	boost::math::tools::epsilon<RealType>(),
260	static_cast<RealType>(boost::math::tools::epsilon<double>())) * 5 * 100; // 5 eps as a percentage
261	cout << "Tolerance for type " << typeid(RealType).name() << " is " << tolerance << " %" << endl;
262	weibull_distribution<RealType> dist(2, 3);
263	RealType x = static_cast<RealType>(0.125);
264
265	BOOST_MATH_STD_USING // ADL of std lib math functions
266
267	// mean:
268	BOOST_CHECK_CLOSE(
269	mean(dist)
270	, dist.scale() * boost::math::tgamma(1 + 1 / dist.shape()), tolerance);
271	// variance:
272	BOOST_CHECK_CLOSE(
273	variance(dist)
274	, dist.scale() * dist.scale() * boost::math::tgamma(1 + 2 / dist.shape()) - mean(dist) * mean(dist), tolerance);
275	// std deviation:
276	BOOST_CHECK_CLOSE(
277	standard_deviation(dist)
278	, sqrt(variance(dist)), tolerance);
279	// hazard:
280	BOOST_CHECK_CLOSE(
281	hazard(dist, x)
282	, pdf(dist, x) / cdf(complement(dist, x)), tolerance);
283	// cumulative hazard:
284	BOOST_CHECK_CLOSE(
285	chf(dist, x)
286	, -log(cdf(complement(dist, x))), tolerance);
287	// coefficient_of_variation:
288	BOOST_CHECK_CLOSE(
289	coefficient_of_variation(dist)
290	, standard_deviation(dist) / mean(dist), tolerance);
291	// mode:
292	BOOST_CHECK_CLOSE(
293	mode(dist)
294	, dist.scale() * pow((dist.shape() - 1) / dist.shape(), 1/dist.shape()), tolerance);
295	// median:
296	BOOST_CHECK_CLOSE(
297	median(dist)
298	, dist.scale() * pow(log(static_cast<RealType>(2)), 1 / dist.shape()), tolerance);
299	// skewness:
300	BOOST_CHECK_CLOSE(
301	skewness(dist),
302	(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)),
303	tolerance * 100);
f67539c2	304	// kurtosis:
7c673cae FG	305	BOOST_CHECK_CLOSE(
	306	kurtosis(dist)
	307	, kurtosis_excess(dist) + 3, tolerance);
f67539c2	308	// kurtosis excess:
7c673cae FG	309	BOOST_CHECK_CLOSE(
	310	kurtosis_excess(dist),
	311	(pow(dist.scale(), RealType(4)) * boost::math::tgamma(1 + 4/dist.shape())
	312	- 3 * variance(dist) * variance(dist)
	313	- 4 * skewness(dist) * variance(dist) * standard_deviation(dist) * mean(dist)
	314	- 6 * variance(dist) * mean(dist) * mean(dist)
	315	- pow(mean(dist), RealType(4))) / (variance(dist) * variance(dist)),
	316	tolerance * 1000);
	317
f67539c2 TL	318	RealType expected_entropy = boost::math::constants::euler<RealType>()*(1-1/dist.shape()) + log(dist.scale()/dist.shape()) + 1;
	319	BOOST_CHECK_CLOSE(
	320	entropy(dist)
	321	, expected_entropy, tolerance);
	322
7c673cae FG	323	//
	324	// Special cases:
	325	//
	326	BOOST_CHECK(cdf(dist, 0) == 0);
	327	BOOST_CHECK(cdf(complement(dist, 0)) == 1);
	328	BOOST_CHECK(quantile(dist, 0) == 0);
	329	BOOST_CHECK(quantile(complement(dist, 1)) == 0);
	330
	331	BOOST_CHECK_EQUAL(pdf(weibull_distribution<RealType>(1, 1), 0), 1);
	332
	333	//
	334	// Error checks:
	335	//
	336	BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(1, -1), std::domain_error);
	337	BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(-1, 1), std::domain_error);
	338	BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(1, 0), std::domain_error);
	339	BOOST_MATH_CHECK_THROW(weibull_distribution<RealType>(0, 1), std::domain_error);
	340	BOOST_MATH_CHECK_THROW(pdf(dist, -1), std::domain_error);
	341	BOOST_MATH_CHECK_THROW(cdf(dist, -1), std::domain_error);
	342	BOOST_MATH_CHECK_THROW(cdf(complement(dist, -1)), std::domain_error);
	343	BOOST_MATH_CHECK_THROW(quantile(dist, 1), std::overflow_error);
	344	BOOST_MATH_CHECK_THROW(quantile(complement(dist, 0)), std::overflow_error);
	345	BOOST_MATH_CHECK_THROW(quantile(dist, -1), std::domain_error);
	346	BOOST_MATH_CHECK_THROW(quantile(complement(dist, -1)), std::domain_error);
	347
	348	BOOST_CHECK_EQUAL(pdf(dist, 0), exp(-pow(RealType(0) / RealType(3), RealType(2))) * pow(RealType(0), RealType(1)) * RealType(2) / RealType(3));
	349	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));
	350	BOOST_MATH_CHECK_THROW(pdf(weibull_distribution<RealType>(0.5, 3), 0), std::overflow_error);
	351
	352	check_out_of_range<weibull_distribution<RealType> >(1, 1);
	353	} // template <class RealType>void test_spots(RealType)
	354
	355	BOOST_AUTO_TEST_CASE( test_main )
	356	{
	357
	358	// Check that can construct weibull distribution using the two convenience methods:
	359	using namespace boost::math;
	360	weibull myw1(2); // Using typedef
	361	weibull_distribution<> myw2(2); // Using default RealType double.
	362
	363	// Basic sanity-check spot values.
	364	// (Parameter value, arbitrarily zero, only communicates the floating point type).
	365	test_spots(0.0F); // Test float. OK at decdigits = 0 tolerance = 0.0001 %
	366	test_spots(0.0); // Test double. OK at decdigits 7, tolerance = 1e07 %
	367	#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
	368	test_spots(0.0L); // Test long double.
20effc67	369	#if !BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x0582))
7c673cae FG	370	test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
	371	#endif
	372	#else
	373	std::cout << "<note>The long double tests have been disabled on this platform "
	374	"either because the long double overloads of the usual math functions are "
	375	"not available at all, or because they are too inaccurate for these tests "
	376	"to pass.</note>" << std::endl;
	377	#endif
	378
	379
	380	} // BOOST_AUTO_TEST_CASE( test_main )
	381
	382	/*
	383
	384	Output:
	385
	386	Description: Autorun "J:\Cpp\MathToolkit\test\Math_test\Debug\test_weibull.exe"
	387	Running 1 test case...
	388	Tolerance for type float is 0.002 %
	389	Tolerance for type float is 5.96046e-005 %
	390	Tolerance for type double is 0.002 %
	391	Tolerance for type double is 1.11022e-013 %
	392	Tolerance for type long double is 0.002 %
	393	Tolerance for type long double is 1.11022e-013 %
	394	Tolerance for type class boost::math::concepts::real_concept is 0.002 %
	395	Tolerance for type class boost::math::concepts::real_concept is 1.11022e-013 %
	396
	397	*** No errors detected
	398
	399
	400	*/
	401
	402
	403
	404