1// Copyright John Maddock 2006.
2// Use, modification and distribution are subject to the
3// Boost Software License, Version 1.0. (See accompanying file
4// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
5
6#ifndef BOOST_STATS_WEIBULL_HPP
7#define BOOST_STATS_WEIBULL_HPP
8
9// http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm
10// http://mathworld.wolfram.com/WeibullDistribution.html
11
12#include <boost/math/distributions/fwd.hpp>
13#include <boost/math/special_functions/gamma.hpp>
14#include <boost/math/special_functions/log1p.hpp>
15#include <boost/math/special_functions/expm1.hpp>
16#include <boost/math/distributions/detail/common_error_handling.hpp>
17#include <boost/math/distributions/complement.hpp>
18
19#include <utility>
20
21namespace boost{ namespace math
22{
23namespace detail{
24
25template <class RealType, class Policy>
26inline bool check_weibull_shape(
27 const char* function,
28 RealType shape,
29 RealType* result, const Policy& pol)
30{
31 if((shape <= 0) || !(boost::math::isfinite)(shape))
32 {
33 *result = policies::raise_domain_error<RealType>(
34 function,
35 "Shape parameter is %1%, but must be > 0 !", shape, pol);
36 return false;
37 }
38 return true;
39}
40
41template <class RealType, class Policy>
42inline bool check_weibull_x(
43 const char* function,
44 RealType const& x,
45 RealType* result, const Policy& pol)
46{
47 if((x < 0) || !(boost::math::isfinite)(x))
48 {
49 *result = policies::raise_domain_error<RealType>(
50 function,
51 "Random variate is %1% but must be >= 0 !", x, pol);
52 return false;
53 }
54 return true;
55}
56
57template <class RealType, class Policy>
58inline bool check_weibull(
59 const char* function,
60 RealType scale,
61 RealType shape,
62 RealType* result, const Policy& pol)
63{
64 return check_scale(function, scale, result, pol) && check_weibull_shape(function, shape, result, pol);
65}
66
67} // namespace detail
68
69template <class RealType = double, class Policy = policies::policy<> >
70class weibull_distribution
71{
72public:
73 using value_type = RealType;
74 using policy_type = Policy;
75
76 explicit weibull_distribution(RealType l_shape, RealType l_scale = 1)
77 : m_shape(l_shape), m_scale(l_scale)
78 {
79 RealType result;
80 detail::check_weibull("boost::math::weibull_distribution<%1%>::weibull_distribution", l_scale, l_shape, &result, Policy());
81 }
82
83 RealType shape()const
84 {
85 return m_shape;
86 }
87
88 RealType scale()const
89 {
90 return m_scale;
91 }
92private:
93 //
94 // Data members:
95 //
96 RealType m_shape; // distribution shape
97 RealType m_scale; // distribution scale
98};
99
100using weibull = weibull_distribution<double>;
101
102#ifdef __cpp_deduction_guides
103template <class RealType>
104weibull_distribution(RealType)->weibull_distribution<typename boost::math::tools::promote_args<RealType>::type>;
105template <class RealType>
106weibull_distribution(RealType,RealType)->weibull_distribution<typename boost::math::tools::promote_args<RealType>::type>;
107#endif
108
109template <class RealType, class Policy>
110inline std::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/)
111{ // Range of permissible values for random variable x.
112 using boost::math::tools::max_value;
113 return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
114}
115
116template <class RealType, class Policy>
117inline std::pair<RealType, RealType> support(const weibull_distribution<RealType, Policy>& /*dist*/)
118{ // Range of supported values for random variable x.
119 // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
120 using boost::math::tools::max_value;
121 using boost::math::tools::min_value;
122 return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>());
123 // A discontinuity at x == 0, so only support down to min_value.
124}
125
126template <class RealType, class Policy>
127inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
128{
129 BOOST_MATH_STD_USING // for ADL of std functions
130
131 static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";
132
133 RealType shape = dist.shape();
134 RealType scale = dist.scale();
135
136 RealType result = 0;
137 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
138 return result;
139 if(false == detail::check_weibull_x(function, x, &result, Policy()))
140 return result;
141
142 if(x == 0)
143 {
144 if(shape == 1)
145 {
146 return 1 / scale;
147 }
148 if(shape > 1)
149 {
150 return 0;
151 }
152 return policies::raise_overflow_error<RealType>(function, 0, Policy());
153 }
154 result = exp(-pow(x / scale, shape));
155 result *= pow(x / scale, shape - 1) * shape / scale;
156
157 return result;
158}
159
160template <class RealType, class Policy>
161inline RealType logpdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
162{
163 BOOST_MATH_STD_USING // for ADL of std functions
164
165 static const char* function = "boost::math::logpdf(const weibull_distribution<%1%>, %1%)";
166
167 RealType shape = dist.shape();
168 RealType scale = dist.scale();
169
170 RealType result = 0;
171 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
172 return result;
173 if(false == detail::check_weibull_x(function, x, &result, Policy()))
174 return result;
175
176 if(x == 0)
177 {
178 if(shape == 1)
179 {
180 return log(1 / scale);
181 }
182 if(shape > 1)
183 {
184 return 0;
185 }
186 return policies::raise_overflow_error<RealType>(function, 0, Policy());
187 }
188
189 result = log(shape) - shape * log(scale) + log(x) * (shape - 1) - pow(x / scale, shape);
190
191 return result;
192}
193
194template <class RealType, class Policy>
195inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
196{
197 BOOST_MATH_STD_USING // for ADL of std functions
198
199 static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
200
201 RealType shape = dist.shape();
202 RealType scale = dist.scale();
203
204 RealType result = 0;
205 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
206 return result;
207 if(false == detail::check_weibull_x(function, x, &result, Policy()))
208 return result;
209
210 result = -boost::math::expm1(-pow(x / scale, shape), Policy());
211
212 return result;
213}
214
215template <class RealType, class Policy>
216inline RealType logcdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
217{
218 BOOST_MATH_STD_USING // for ADL of std functions
219
220 static const char* function = "boost::math::logcdf(const weibull_distribution<%1%>, %1%)";
221
222 RealType shape = dist.shape();
223 RealType scale = dist.scale();
224
225 RealType result = 0;
226 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
227 return result;
228 if(false == detail::check_weibull_x(function, x, &result, Policy()))
229 return result;
230
231 result = log1p(-exp(-pow(x / scale, shape)), Policy());
232
233 return result;
234}
235
236template <class RealType, class Policy>
237inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
238{
239 BOOST_MATH_STD_USING // for ADL of std functions
240
241 static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
242
243 RealType shape = dist.shape();
244 RealType scale = dist.scale();
245
246 RealType result = 0;
247 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
248 return result;
249 if(false == detail::check_probability(function, p, &result, Policy()))
250 return result;
251
252 if(p == 1)
253 return policies::raise_overflow_error<RealType>(function, 0, Policy());
254
255 result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);
256
257 return result;
258}
259
260template <class RealType, class Policy>
261inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
262{
263 BOOST_MATH_STD_USING // for ADL of std functions
264
265 static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
266
267 RealType shape = c.dist.shape();
268 RealType scale = c.dist.scale();
269
270 RealType result = 0;
271 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
272 return result;
273 if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
274 return result;
275
276 result = exp(-pow(c.param / scale, shape));
277
278 return result;
279}
280
281template <class RealType, class Policy>
282inline RealType logcdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
283{
284 BOOST_MATH_STD_USING // for ADL of std functions
285
286 static const char* function = "boost::math::logcdf(const weibull_distribution<%1%>, %1%)";
287
288 RealType shape = c.dist.shape();
289 RealType scale = c.dist.scale();
290
291 RealType result = 0;
292 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
293 return result;
294 if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
295 return result;
296
297 result = -pow(c.param / scale, shape);
298
299 return result;
300}
301
302template <class RealType, class Policy>
303inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
304{
305 BOOST_MATH_STD_USING // for ADL of std functions
306
307 static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
308
309 RealType shape = c.dist.shape();
310 RealType scale = c.dist.scale();
311 RealType q = c.param;
312
313 RealType result = 0;
314 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
315 return result;
316 if(false == detail::check_probability(function, q, &result, Policy()))
317 return result;
318
319 if(q == 0)
320 return policies::raise_overflow_error<RealType>(function, 0, Policy());
321
322 result = scale * pow(-log(q), 1 / shape);
323
324 return result;
325}
326
327template <class RealType, class Policy>
328inline RealType mean(const weibull_distribution<RealType, Policy>& dist)
329{
330 BOOST_MATH_STD_USING // for ADL of std functions
331
332 static const char* function = "boost::math::mean(const weibull_distribution<%1%>)";
333
334 RealType shape = dist.shape();
335 RealType scale = dist.scale();
336
337 RealType result = 0;
338 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
339 return result;
340
341 result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
342 return result;
343}
344
345template <class RealType, class Policy>
346inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
347{
348 RealType shape = dist.shape();
349 RealType scale = dist.scale();
350
351 static const char* function = "boost::math::variance(const weibull_distribution<%1%>)";
352
353 RealType result = 0;
354 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
355 {
356 return result;
357 }
358 result = boost::math::tgamma(1 + 1 / shape, Policy());
359 result *= -result;
360 result += boost::math::tgamma(1 + 2 / shape, Policy());
361 result *= scale * scale;
362 return result;
363}
364
365template <class RealType, class Policy>
366inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
367{
368 BOOST_MATH_STD_USING // for ADL of std function pow.
369
370 static const char* function = "boost::math::mode(const weibull_distribution<%1%>)";
371
372 RealType shape = dist.shape();
373 RealType scale = dist.scale();
374
375 RealType result = 0;
376 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
377 {
378 return result;
379 }
380 if(shape <= 1)
381 return 0;
382 result = scale * pow((shape - 1) / shape, 1 / shape);
383 return result;
384}
385
386template <class RealType, class Policy>
387inline RealType median(const weibull_distribution<RealType, Policy>& dist)
388{
389 BOOST_MATH_STD_USING // for ADL of std function pow.
390
391 static const char* function = "boost::math::median(const weibull_distribution<%1%>)";
392
393 RealType shape = dist.shape(); // Wikipedia k
394 RealType scale = dist.scale(); // Wikipedia lambda
395
396 RealType result = 0;
397 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
398 {
399 return result;
400 }
401 using boost::math::constants::ln_two;
402 result = scale * pow(ln_two<RealType>(), 1 / shape);
403 return result;
404}
405
406template <class RealType, class Policy>
407inline RealType skewness(const weibull_distribution<RealType, Policy>& dist)
408{
409 BOOST_MATH_STD_USING // for ADL of std functions
410
411 static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)";
412
413 RealType shape = dist.shape();
414 RealType scale = dist.scale();
415
416 RealType result = 0;
417 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
418 {
419 return result;
420 }
421
422 RealType g1 = boost::math::tgamma(1 + 1 / shape, Policy());
423 RealType g2 = boost::math::tgamma(1 + 2 / shape, Policy());
424 RealType g3 = boost::math::tgamma(1 + 3 / shape, Policy());
425 RealType d = pow(g2 - g1 * g1, RealType(1.5));
426
427 result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
428 return result;
429}
430
431template <class RealType, class Policy>
432inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist)
433{
434 BOOST_MATH_STD_USING // for ADL of std functions
435
436 static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";
437
438 RealType shape = dist.shape();
439 RealType scale = dist.scale();
440
441 RealType result = 0;
442 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
443 return result;
444
445 RealType g1 = boost::math::tgamma(1 + 1 / shape, Policy());
446 RealType g2 = boost::math::tgamma(1 + 2 / shape, Policy());
447 RealType g3 = boost::math::tgamma(1 + 3 / shape, Policy());
448 RealType g4 = boost::math::tgamma(1 + 4 / shape, Policy());
449 RealType g1_2 = g1 * g1;
450 RealType g1_4 = g1_2 * g1_2;
451 RealType d = g2 - g1_2;
452 d *= d;
453
454 result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
455 result /= d;
456 return result;
457}
458
459template <class RealType, class Policy>
460inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
461{
462 return kurtosis_excess(dist) + 3;
463}
464
465template <class RealType, class Policy>
466inline RealType entropy(const weibull_distribution<RealType, Policy>& dist)
467{
468 using std::log;
469 RealType k = dist.shape();
470 RealType lambda = dist.scale();
471 return constants::euler<RealType>()*(1-1/k) + log(lambda/k) + 1;
472}
473
474} // namespace math
475} // namespace boost
476
477// This include must be at the end, *after* the accessors
478// for this distribution have been defined, in order to
479// keep compilers that support two-phase lookup happy.
480#include <boost/math/distributions/detail/derived_accessors.hpp>
481
482#endif // BOOST_STATS_WEIBULL_HPP
483
484
485

source code of boost/libs/math/include/boost/math/distributions/weibull.hpp