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
21 namespace boost{ namespace math
22 {
23 namespace detail{
24
25 template <class RealType, class Policy>
check_weibull_shape(const char * function,RealType shape,RealType * result,const Policy & pol)26 inline 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
41 template <class RealType, class Policy>
check_weibull_x(const char * function,RealType const & x,RealType * result,const Policy & pol)42 inline 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
57 template <class RealType, class Policy>
check_weibull(const char * function,RealType scale,RealType shape,RealType * result,const Policy & pol)58 inline 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
69 template <class RealType = double, class Policy = policies::policy<> >
70 class weibull_distribution
71 {
72 public:
73 typedef RealType value_type;
74 typedef Policy policy_type;
75
weibull_distribution(RealType l_shape,RealType l_scale=1)76 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
shape() const83 RealType shape()const
84 {
85 return m_shape;
86 }
87
scale() const88 RealType scale()const
89 {
90 return m_scale;
91 }
92 private:
93 //
94 // Data members:
95 //
96 RealType m_shape; // distribution shape
97 RealType m_scale; // distribution scale
98 };
99
100 typedef weibull_distribution<double> weibull;
101
102 template <class RealType, class Policy>
range(const weibull_distribution<RealType,Policy> &)103 inline const std::pair<RealType, RealType> range(const weibull_distribution<RealType, Policy>& /*dist*/)
104 { // Range of permissible values for random variable x.
105 using boost::math::tools::max_value;
106 return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>());
107 }
108
109 template <class RealType, class Policy>
support(const weibull_distribution<RealType,Policy> &)110 inline const std::pair<RealType, RealType> support(const weibull_distribution<RealType, Policy>& /*dist*/)
111 { // Range of supported values for random variable x.
112 // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
113 using boost::math::tools::max_value;
114 using boost::math::tools::min_value;
115 return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>());
116 // A discontinuity at x == 0, so only support down to min_value.
117 }
118
119 template <class RealType, class Policy>
pdf(const weibull_distribution<RealType,Policy> & dist,const RealType & x)120 inline RealType pdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
121 {
122 BOOST_MATH_STD_USING // for ADL of std functions
123
124 static const char* function = "boost::math::pdf(const weibull_distribution<%1%>, %1%)";
125
126 RealType shape = dist.shape();
127 RealType scale = dist.scale();
128
129 RealType result = 0;
130 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
131 return result;
132 if(false == detail::check_weibull_x(function, x, &result, Policy()))
133 return result;
134
135 if(x == 0)
136 {
137 if(shape == 1)
138 {
139 return 1 / scale;
140 }
141 if(shape > 1)
142 {
143 return 0;
144 }
145 return policies::raise_overflow_error<RealType>(function, 0, Policy());
146 }
147 result = exp(-pow(x / scale, shape));
148 result *= pow(x / scale, shape - 1) * shape / scale;
149
150 return result;
151 }
152
153 template <class RealType, class Policy>
cdf(const weibull_distribution<RealType,Policy> & dist,const RealType & x)154 inline RealType cdf(const weibull_distribution<RealType, Policy>& dist, const RealType& x)
155 {
156 BOOST_MATH_STD_USING // for ADL of std functions
157
158 static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
159
160 RealType shape = dist.shape();
161 RealType scale = dist.scale();
162
163 RealType result = 0;
164 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
165 return result;
166 if(false == detail::check_weibull_x(function, x, &result, Policy()))
167 return result;
168
169 result = -boost::math::expm1(-pow(x / scale, shape), Policy());
170
171 return result;
172 }
173
174 template <class RealType, class Policy>
quantile(const weibull_distribution<RealType,Policy> & dist,const RealType & p)175 inline RealType quantile(const weibull_distribution<RealType, Policy>& dist, const RealType& p)
176 {
177 BOOST_MATH_STD_USING // for ADL of std functions
178
179 static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
180
181 RealType shape = dist.shape();
182 RealType scale = dist.scale();
183
184 RealType result = 0;
185 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
186 return result;
187 if(false == detail::check_probability(function, p, &result, Policy()))
188 return result;
189
190 if(p == 1)
191 return policies::raise_overflow_error<RealType>(function, 0, Policy());
192
193 result = scale * pow(-boost::math::log1p(-p, Policy()), 1 / shape);
194
195 return result;
196 }
197
198 template <class RealType, class Policy>
cdf(const complemented2_type<weibull_distribution<RealType,Policy>,RealType> & c)199 inline RealType cdf(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
200 {
201 BOOST_MATH_STD_USING // for ADL of std functions
202
203 static const char* function = "boost::math::cdf(const weibull_distribution<%1%>, %1%)";
204
205 RealType shape = c.dist.shape();
206 RealType scale = c.dist.scale();
207
208 RealType result = 0;
209 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
210 return result;
211 if(false == detail::check_weibull_x(function, c.param, &result, Policy()))
212 return result;
213
214 result = exp(-pow(c.param / scale, shape));
215
216 return result;
217 }
218
219 template <class RealType, class Policy>
quantile(const complemented2_type<weibull_distribution<RealType,Policy>,RealType> & c)220 inline RealType quantile(const complemented2_type<weibull_distribution<RealType, Policy>, RealType>& c)
221 {
222 BOOST_MATH_STD_USING // for ADL of std functions
223
224 static const char* function = "boost::math::quantile(const weibull_distribution<%1%>, %1%)";
225
226 RealType shape = c.dist.shape();
227 RealType scale = c.dist.scale();
228 RealType q = c.param;
229
230 RealType result = 0;
231 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
232 return result;
233 if(false == detail::check_probability(function, q, &result, Policy()))
234 return result;
235
236 if(q == 0)
237 return policies::raise_overflow_error<RealType>(function, 0, Policy());
238
239 result = scale * pow(-log(q), 1 / shape);
240
241 return result;
242 }
243
244 template <class RealType, class Policy>
mean(const weibull_distribution<RealType,Policy> & dist)245 inline RealType mean(const weibull_distribution<RealType, Policy>& dist)
246 {
247 BOOST_MATH_STD_USING // for ADL of std functions
248
249 static const char* function = "boost::math::mean(const weibull_distribution<%1%>)";
250
251 RealType shape = dist.shape();
252 RealType scale = dist.scale();
253
254 RealType result = 0;
255 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
256 return result;
257
258 result = scale * boost::math::tgamma(1 + 1 / shape, Policy());
259 return result;
260 }
261
262 template <class RealType, class Policy>
variance(const weibull_distribution<RealType,Policy> & dist)263 inline RealType variance(const weibull_distribution<RealType, Policy>& dist)
264 {
265 RealType shape = dist.shape();
266 RealType scale = dist.scale();
267
268 static const char* function = "boost::math::variance(const weibull_distribution<%1%>)";
269
270 RealType result = 0;
271 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
272 {
273 return result;
274 }
275 result = boost::math::tgamma(1 + 1 / shape, Policy());
276 result *= -result;
277 result += boost::math::tgamma(1 + 2 / shape, Policy());
278 result *= scale * scale;
279 return result;
280 }
281
282 template <class RealType, class Policy>
mode(const weibull_distribution<RealType,Policy> & dist)283 inline RealType mode(const weibull_distribution<RealType, Policy>& dist)
284 {
285 BOOST_MATH_STD_USING // for ADL of std function pow.
286
287 static const char* function = "boost::math::mode(const weibull_distribution<%1%>)";
288
289 RealType shape = dist.shape();
290 RealType scale = dist.scale();
291
292 RealType result = 0;
293 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
294 {
295 return result;
296 }
297 if(shape <= 1)
298 return 0;
299 result = scale * pow((shape - 1) / shape, 1 / shape);
300 return result;
301 }
302
303 template <class RealType, class Policy>
median(const weibull_distribution<RealType,Policy> & dist)304 inline RealType median(const weibull_distribution<RealType, Policy>& dist)
305 {
306 BOOST_MATH_STD_USING // for ADL of std function pow.
307
308 static const char* function = "boost::math::median(const weibull_distribution<%1%>)";
309
310 RealType shape = dist.shape(); // Wikipedia k
311 RealType scale = dist.scale(); // Wikipedia lambda
312
313 RealType result = 0;
314 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
315 {
316 return result;
317 }
318 using boost::math::constants::ln_two;
319 result = scale * pow(ln_two<RealType>(), 1 / shape);
320 return result;
321 }
322
323 template <class RealType, class Policy>
skewness(const weibull_distribution<RealType,Policy> & dist)324 inline RealType skewness(const weibull_distribution<RealType, Policy>& dist)
325 {
326 BOOST_MATH_STD_USING // for ADL of std functions
327
328 static const char* function = "boost::math::skewness(const weibull_distribution<%1%>)";
329
330 RealType shape = dist.shape();
331 RealType scale = dist.scale();
332
333 RealType result = 0;
334 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
335 {
336 return result;
337 }
338 RealType g1, g2, g3, d;
339
340 g1 = boost::math::tgamma(1 + 1 / shape, Policy());
341 g2 = boost::math::tgamma(1 + 2 / shape, Policy());
342 g3 = boost::math::tgamma(1 + 3 / shape, Policy());
343 d = pow(g2 - g1 * g1, RealType(1.5));
344
345 result = (2 * g1 * g1 * g1 - 3 * g1 * g2 + g3) / d;
346 return result;
347 }
348
349 template <class RealType, class Policy>
kurtosis_excess(const weibull_distribution<RealType,Policy> & dist)350 inline RealType kurtosis_excess(const weibull_distribution<RealType, Policy>& dist)
351 {
352 BOOST_MATH_STD_USING // for ADL of std functions
353
354 static const char* function = "boost::math::kurtosis_excess(const weibull_distribution<%1%>)";
355
356 RealType shape = dist.shape();
357 RealType scale = dist.scale();
358
359 RealType result = 0;
360 if(false == detail::check_weibull(function, scale, shape, &result, Policy()))
361 return result;
362
363 RealType g1, g2, g3, g4, d, g1_2, g1_4;
364
365 g1 = boost::math::tgamma(1 + 1 / shape, Policy());
366 g2 = boost::math::tgamma(1 + 2 / shape, Policy());
367 g3 = boost::math::tgamma(1 + 3 / shape, Policy());
368 g4 = boost::math::tgamma(1 + 4 / shape, Policy());
369 g1_2 = g1 * g1;
370 g1_4 = g1_2 * g1_2;
371 d = g2 - g1_2;
372 d *= d;
373
374 result = -6 * g1_4 + 12 * g1_2 * g2 - 3 * g2 * g2 - 4 * g1 * g3 + g4;
375 result /= d;
376 return result;
377 }
378
379 template <class RealType, class Policy>
kurtosis(const weibull_distribution<RealType,Policy> & dist)380 inline RealType kurtosis(const weibull_distribution<RealType, Policy>& dist)
381 {
382 return kurtosis_excess(dist) + 3;
383 }
384
385 } // namespace math
386 } // namespace boost
387
388 // This include must be at the end, *after* the accessors
389 // for this distribution have been defined, in order to
390 // keep compilers that support two-phase lookup happy.
391 #include <boost/math/distributions/detail/derived_accessors.hpp>
392
393 #endif // BOOST_STATS_WEIBULL_HPP
394
395
396