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
19 #include <boost/test/tools/floating_point_comparison.hpp>
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>
check_weibull(RealType shape,RealType scale,RealType x,RealType p,RealType q,RealType tol)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>
test_spots(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 //
73 // Tolerance is just over 5 decimal digits expressed as a percentage:
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);
304 // kurtosis:
305 BOOST_CHECK_CLOSE(
306 kurtosis(dist)
307 , kurtosis_excess(dist) + 3, tolerance);
308 // kurtosis excess:
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
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
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
BOOST_AUTO_TEST_CASE(test_main)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.
369 #if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
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
405