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_EXPONENTIAL_HPP
7#define BOOST_STATS_EXPONENTIAL_HPP
8
9#include <boost/math/distributions/fwd.hpp>
10#include <boost/math/constants/constants.hpp>
11#include <boost/math/special_functions/log1p.hpp>
12#include <boost/math/special_functions/expm1.hpp>
13#include <boost/math/distributions/complement.hpp>
14#include <boost/math/distributions/detail/common_error_handling.hpp>
15
16#ifdef _MSC_VER
17# pragma warning(push)
18# pragma warning(disable: 4127) // conditional expression is constant
19# pragma warning(disable: 4702) // unreachable code (return after domain_error throw).
20#endif
21
22#include <utility>
23#include <cmath>
24
25namespace boost{ namespace math{
26
27namespace detail{
28//
29// Error check:
30//
31template <class RealType, class Policy>
32inline bool verify_lambda(const char* function, RealType l, RealType* presult, const Policy& pol)
33{
34 if((l <= 0) || !(boost::math::isfinite)(l))
35 {
36 *presult = policies::raise_domain_error<RealType>(
37 function,
38 "The scale parameter \"lambda\" must be > 0, but was: %1%.", l, pol);
39 return false;
40 }
41 return true;
42}
43
44template <class RealType, class Policy>
45inline bool verify_exp_x(const char* function, RealType x, RealType* presult, const Policy& pol)
46{
47 if((x < 0) || (boost::math::isnan)(x))
48 {
49 *presult = policies::raise_domain_error<RealType>(
50 function,
51 "The random variable must be >= 0, but was: %1%.", x, pol);
52 return false;
53 }
54 return true;
55}
56
57} // namespace detail
58
59template <class RealType = double, class Policy = policies::policy<> >
60class exponential_distribution
61{
62public:
63 using value_type = RealType;
64 using policy_type = Policy;
65
66 explicit exponential_distribution(RealType l_lambda = 1)
67 : m_lambda(l_lambda)
68 {
69 RealType err;
70 detail::verify_lambda("boost::math::exponential_distribution<%1%>::exponential_distribution", l_lambda, &err, Policy());
71 } // exponential_distribution
72
73 RealType lambda()const { return m_lambda; }
74
75private:
76 RealType m_lambda;
77};
78
79using exponential = exponential_distribution<double>;
80
81#ifdef __cpp_deduction_guides
82template <class RealType>
83exponential_distribution(RealType)->exponential_distribution<typename boost::math::tools::promote_args<RealType>::type>;
84#endif
85
86template <class RealType, class Policy>
87inline std::pair<RealType, RealType> range(const exponential_distribution<RealType, Policy>& /*dist*/)
88{ // Range of permissible values for random variable x.
89 if (std::numeric_limits<RealType>::has_infinity)
90 {
91 return std::pair<RealType, RealType>(static_cast<RealType>(0), std::numeric_limits<RealType>::infinity()); // 0 to + infinity.
92 }
93 else
94 {
95 using boost::math::tools::max_value;
96 return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); // 0 to + max
97 }
98}
99
100template <class RealType, class Policy>
101inline std::pair<RealType, RealType> support(const exponential_distribution<RealType, Policy>& /*dist*/)
102{ // Range of supported values for random variable x.
103 // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
104 using boost::math::tools::max_value;
105 using boost::math::tools::min_value;
106 return std::pair<RealType, RealType>(min_value<RealType>(), max_value<RealType>());
107 // min_value<RealType>() to avoid a discontinuity at x = 0.
108}
109
110template <class RealType, class Policy>
111inline RealType pdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
112{
113 BOOST_MATH_STD_USING // for ADL of std functions
114
115 static const char* function = "boost::math::pdf(const exponential_distribution<%1%>&, %1%)";
116
117 RealType lambda = dist.lambda();
118 RealType result = 0;
119 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
120 return result;
121 if(0 == detail::verify_exp_x(function, x, &result, Policy()))
122 return result;
123 // Workaround for VC11/12 bug:
124 if ((boost::math::isinf)(x))
125 return 0;
126 result = lambda * exp(-lambda * x);
127 return result;
128} // pdf
129
130template <class RealType, class Policy>
131inline RealType logpdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
132{
133 BOOST_MATH_STD_USING // for ADL of std functions
134
135 static const char* function = "boost::math::logpdf(const exponential_distribution<%1%>&, %1%)";
136
137 RealType lambda = dist.lambda();
138 RealType result = -std::numeric_limits<RealType>::infinity();
139 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
140 return result;
141 if(0 == detail::verify_exp_x(function, x, &result, Policy()))
142 return result;
143
144 result = log(lambda) - lambda * x;
145 return result;
146} // logpdf
147
148template <class RealType, class Policy>
149inline RealType cdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
150{
151 BOOST_MATH_STD_USING // for ADL of std functions
152
153 static const char* function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)";
154
155 RealType result = 0;
156 RealType lambda = dist.lambda();
157 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
158 return result;
159 if(0 == detail::verify_exp_x(function, x, &result, Policy()))
160 return result;
161 result = -boost::math::expm1(-x * lambda, Policy());
162
163 return result;
164} // cdf
165
166template <class RealType, class Policy>
167inline RealType logcdf(const exponential_distribution<RealType, Policy>& dist, const RealType& x)
168{
169 BOOST_MATH_STD_USING // for ADL of std functions
170
171 static const char* function = "boost::math::logcdf(const exponential_distribution<%1%>&, %1%)";
172
173 RealType result = 0;
174 RealType lambda = dist.lambda();
175 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
176 return result;
177 if(0 == detail::verify_exp_x(function, x, &result, Policy()))
178 return result;
179 result = boost::math::log1p(-exp(-x * lambda), Policy());
180
181 return result;
182} // cdf
183
184template <class RealType, class Policy>
185inline RealType quantile(const exponential_distribution<RealType, Policy>& dist, const RealType& p)
186{
187 BOOST_MATH_STD_USING // for ADL of std functions
188
189 static const char* function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)";
190
191 RealType result = 0;
192 RealType lambda = dist.lambda();
193 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
194 return result;
195 if(0 == detail::check_probability(function, p, &result, Policy()))
196 return result;
197
198 if(p == 0)
199 return 0;
200 if(p == 1)
201 return policies::raise_overflow_error<RealType>(function, 0, Policy());
202
203 result = -boost::math::log1p(-p, Policy()) / lambda;
204 return result;
205} // quantile
206
207template <class RealType, class Policy>
208inline RealType cdf(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
209{
210 BOOST_MATH_STD_USING // for ADL of std functions
211
212 static const char* function = "boost::math::cdf(const exponential_distribution<%1%>&, %1%)";
213
214 RealType result = 0;
215 RealType lambda = c.dist.lambda();
216 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
217 return result;
218 if(0 == detail::verify_exp_x(function, c.param, &result, Policy()))
219 return result;
220 // Workaround for VC11/12 bug:
221 if (c.param >= tools::max_value<RealType>())
222 return 0;
223 result = exp(-c.param * lambda);
224
225 return result;
226}
227
228template <class RealType, class Policy>
229inline RealType logcdf(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
230{
231 BOOST_MATH_STD_USING // for ADL of std functions
232
233 static const char* function = "boost::math::logcdf(const exponential_distribution<%1%>&, %1%)";
234
235 RealType result = 0;
236 RealType lambda = c.dist.lambda();
237 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
238 return result;
239 if(0 == detail::verify_exp_x(function, c.param, &result, Policy()))
240 return result;
241 // Workaround for VC11/12 bug:
242 if (c.param >= tools::max_value<RealType>())
243 return 0;
244 result = -c.param * lambda;
245
246 return result;
247}
248
249template <class RealType, class Policy>
250inline RealType quantile(const complemented2_type<exponential_distribution<RealType, Policy>, RealType>& c)
251{
252 BOOST_MATH_STD_USING // for ADL of std functions
253
254 static const char* function = "boost::math::quantile(const exponential_distribution<%1%>&, %1%)";
255
256 RealType result = 0;
257 RealType lambda = c.dist.lambda();
258 if(0 == detail::verify_lambda(function, lambda, &result, Policy()))
259 return result;
260
261 RealType q = c.param;
262 if(0 == detail::check_probability(function, q, &result, Policy()))
263 return result;
264
265 if(q == 1)
266 return 0;
267 if(q == 0)
268 return policies::raise_overflow_error<RealType>(function, 0, Policy());
269
270 result = -log(q) / lambda;
271 return result;
272}
273
274template <class RealType, class Policy>
275inline RealType mean(const exponential_distribution<RealType, Policy>& dist)
276{
277 RealType result = 0;
278 RealType lambda = dist.lambda();
279 if(0 == detail::verify_lambda("boost::math::mean(const exponential_distribution<%1%>&)", lambda, &result, Policy()))
280 return result;
281 return 1 / lambda;
282}
283
284template <class RealType, class Policy>
285inline RealType standard_deviation(const exponential_distribution<RealType, Policy>& dist)
286{
287 RealType result = 0;
288 RealType lambda = dist.lambda();
289 if(0 == detail::verify_lambda("boost::math::standard_deviation(const exponential_distribution<%1%>&)", lambda, &result, Policy()))
290 return result;
291 return 1 / lambda;
292}
293
294template <class RealType, class Policy>
295inline RealType mode(const exponential_distribution<RealType, Policy>& /*dist*/)
296{
297 return 0;
298}
299
300template <class RealType, class Policy>
301inline RealType median(const exponential_distribution<RealType, Policy>& dist)
302{
303 using boost::math::constants::ln_two;
304 return ln_two<RealType>() / dist.lambda(); // ln(2) / lambda
305}
306
307template <class RealType, class Policy>
308inline RealType skewness(const exponential_distribution<RealType, Policy>& /*dist*/)
309{
310 return 2;
311}
312
313template <class RealType, class Policy>
314inline RealType kurtosis(const exponential_distribution<RealType, Policy>& /*dist*/)
315{
316 return 9;
317}
318
319template <class RealType, class Policy>
320inline RealType kurtosis_excess(const exponential_distribution<RealType, Policy>& /*dist*/)
321{
322 return 6;
323}
324
325template <class RealType, class Policy>
326inline RealType entropy(const exponential_distribution<RealType, Policy>& dist)
327{
328 using std::log;
329 return 1 - log(dist.lambda());
330}
331
332} // namespace math
333} // namespace boost
334
335#ifdef _MSC_VER
336# pragma warning(pop)
337#endif
338
339// This include must be at the end, *after* the accessors
340// for this distribution have been defined, in order to
341// keep compilers that support two-phase lookup happy.
342#include <boost/math/distributions/detail/derived_accessors.hpp>
343
344#endif // BOOST_STATS_EXPONENTIAL_HPP
345

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