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1 | // Copyright Thijs van den Berg, 2008. |
2 | // Copyright John Maddock 2008. | |
3 | // Copyright Paul A. Bristow 2008, 2014. | |
4 | ||
5 | // Use, modification and distribution are subject to the | |
6 | // Boost Software License, Version 1.0. (See accompanying file | |
7 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
8 | ||
9 | // This module implements the Laplace distribution. | |
10 | // Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource. | |
11 | // http://mathworld.wolfram.com/LaplaceDistribution.html | |
12 | // http://en.wikipedia.org/wiki/Laplace_distribution | |
13 | // | |
14 | // Abramowitz and Stegun 1972, p 930 | |
15 | // http://www.math.sfu.ca/~cbm/aands/page_930.htm | |
16 | ||
17 | #ifndef BOOST_STATS_LAPLACE_HPP | |
18 | #define BOOST_STATS_LAPLACE_HPP | |
19 | ||
20 | #include <boost/math/distributions/detail/common_error_handling.hpp> | |
21 | #include <boost/math/distributions/complement.hpp> | |
22 | #include <boost/math/constants/constants.hpp> | |
23 | #include <limits> | |
24 | ||
25 | namespace boost{ namespace math{ | |
26 | ||
1e59de90 | 27 | #ifdef _MSC_VER |
7c673cae FG |
28 | # pragma warning(push) |
29 | # pragma warning(disable:4127) // conditional expression is constant | |
30 | #endif | |
31 | ||
32 | template <class RealType = double, class Policy = policies::policy<> > | |
33 | class laplace_distribution | |
34 | { | |
35 | public: | |
36 | // ---------------------------------- | |
37 | // public Types | |
38 | // ---------------------------------- | |
39 | typedef RealType value_type; | |
40 | typedef Policy policy_type; | |
41 | ||
42 | // ---------------------------------- | |
43 | // Constructor(s) | |
44 | // ---------------------------------- | |
45 | laplace_distribution(RealType l_location = 0, RealType l_scale = 1) | |
46 | : m_location(l_location), m_scale(l_scale) | |
47 | { | |
48 | RealType result; | |
49 | check_parameters("boost::math::laplace_distribution<%1%>::laplace_distribution()", &result); | |
50 | } | |
51 | ||
52 | ||
53 | // ---------------------------------- | |
54 | // Public functions | |
55 | // ---------------------------------- | |
56 | ||
57 | RealType location() const | |
58 | { | |
59 | return m_location; | |
60 | } | |
61 | ||
62 | RealType scale() const | |
63 | { | |
64 | return m_scale; | |
65 | } | |
66 | ||
67 | bool check_parameters(const char* function, RealType* result) const | |
68 | { | |
69 | if(false == detail::check_scale(function, m_scale, result, Policy())) return false; | |
70 | if(false == detail::check_location(function, m_location, result, Policy())) return false; | |
71 | return true; | |
72 | } | |
73 | ||
74 | private: | |
75 | RealType m_location; | |
76 | RealType m_scale; | |
77 | }; // class laplace_distribution | |
78 | ||
79 | // | |
80 | // Convenient type synonym for double. | |
81 | typedef laplace_distribution<double> laplace; | |
82 | ||
1e59de90 TL |
83 | #ifdef __cpp_deduction_guides |
84 | template <class RealType> | |
85 | laplace_distribution(RealType)->laplace_distribution<typename boost::math::tools::promote_args<RealType>::type>; | |
86 | template <class RealType> | |
87 | laplace_distribution(RealType,RealType)->laplace_distribution<typename boost::math::tools::promote_args<RealType>::type>; | |
88 | #endif | |
89 | ||
7c673cae FG |
90 | // |
91 | // Non-member functions. | |
92 | template <class RealType, class Policy> | |
93 | inline const std::pair<RealType, RealType> range(const laplace_distribution<RealType, Policy>&) | |
94 | { | |
95 | if (std::numeric_limits<RealType>::has_infinity) | |
96 | { // Can use infinity. | |
97 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
98 | } | |
99 | else | |
100 | { // Can only use max_value. | |
101 | using boost::math::tools::max_value; | |
102 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. | |
103 | } | |
104 | ||
105 | } | |
106 | ||
107 | template <class RealType, class Policy> | |
108 | inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&) | |
109 | { | |
110 | if (std::numeric_limits<RealType>::has_infinity) | |
111 | { // Can Use infinity. | |
112 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
113 | } | |
114 | else | |
115 | { // Can only use max_value. | |
116 | using boost::math::tools::max_value; | |
117 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. | |
118 | } | |
119 | } | |
120 | ||
121 | template <class RealType, class Policy> | |
122 | inline RealType pdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) | |
123 | { | |
124 | BOOST_MATH_STD_USING // for ADL of std functions | |
125 | ||
126 | // Checking function argument | |
127 | RealType result = 0; | |
128 | const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))"; | |
129 | ||
130 | // Check scale and location. | |
131 | if (false == dist.check_parameters(function, &result)) return result; | |
132 | // Special pdf values. | |
133 | if((boost::math::isinf)(x)) | |
134 | { | |
135 | return 0; // pdf + and - infinity is zero. | |
136 | } | |
137 | if (false == detail::check_x(function, x, &result, Policy())) return result; | |
138 | ||
139 | // General case | |
140 | RealType scale( dist.scale() ); | |
141 | RealType location( dist.location() ); | |
142 | ||
143 | RealType exponent = x - location; | |
144 | if (exponent>0) exponent = -exponent; | |
145 | exponent /= scale; | |
146 | ||
147 | result = exp(exponent); | |
148 | result /= 2 * scale; | |
149 | ||
150 | return result; | |
151 | ||
152 | ||
153 | template <class RealType, class Policy> | |
154 | inline RealType cdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) | |
155 | { | |
156 | BOOST_MATH_STD_USING // For ADL of std functions. | |
157 | ||
158 | RealType result = 0; | |
159 | // Checking function argument. | |
160 | const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)"; | |
161 | // Check scale and location. | |
162 | if (false == dist.check_parameters(function, &result)) return result; | |
163 | ||
164 | // Special cdf values: | |
165 | if((boost::math::isinf)(x)) | |
166 | { | |
167 | if(x < 0) return 0; // -infinity. | |
168 | return 1; // + infinity. | |
169 | } | |
170 | if (false == detail::check_x(function, x, &result, Policy())) return result; | |
171 | ||
172 | // General cdf values | |
173 | RealType scale( dist.scale() ); | |
174 | RealType location( dist.location() ); | |
175 | ||
176 | if (x < location) | |
177 | { | |
178 | result = exp( (x-location)/scale )/2; | |
179 | } | |
180 | else | |
181 | { | |
182 | result = 1 - exp( (location-x)/scale )/2; | |
183 | } | |
184 | return result; | |
185 | } // cdf | |
186 | ||
187 | ||
188 | template <class RealType, class Policy> | |
189 | inline RealType quantile(const laplace_distribution<RealType, Policy>& dist, const RealType& p) | |
190 | { | |
191 | BOOST_MATH_STD_USING // for ADL of std functions. | |
192 | ||
193 | // Checking function argument | |
194 | RealType result = 0; | |
195 | const char* function = "boost::math::quantile(const laplace_distribution<%1%>&, %1%)"; | |
196 | if (false == dist.check_parameters(function, &result)) return result; | |
197 | if(false == detail::check_probability(function, p, &result, Policy())) return result; | |
198 | ||
199 | // Extreme values of p: | |
200 | if(p == 0) | |
201 | { | |
202 | result = policies::raise_overflow_error<RealType>(function, | |
203 | "probability parameter is 0, but must be > 0!", Policy()); | |
204 | return -result; // -std::numeric_limits<RealType>::infinity(); | |
205 | } | |
206 | ||
207 | if(p == 1) | |
208 | { | |
209 | result = policies::raise_overflow_error<RealType>(function, | |
210 | "probability parameter is 1, but must be < 1!", Policy()); | |
211 | return result; // std::numeric_limits<RealType>::infinity(); | |
212 | } | |
213 | // Calculate Quantile | |
214 | RealType scale( dist.scale() ); | |
215 | RealType location( dist.location() ); | |
216 | ||
217 | if (p - 0.5 < 0.0) | |
218 | result = location + scale*log( static_cast<RealType>(p*2) ); | |
219 | else | |
220 | result = location - scale*log( static_cast<RealType>(-p*2 + 2) ); | |
221 | ||
222 | return result; | |
223 | } // quantile | |
224 | ||
225 | ||
226 | template <class RealType, class Policy> | |
227 | inline RealType cdf(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) | |
228 | { | |
229 | // Calculate complement of cdf. | |
230 | BOOST_MATH_STD_USING // for ADL of std functions | |
231 | ||
232 | RealType scale = c.dist.scale(); | |
233 | RealType location = c.dist.location(); | |
234 | RealType x = c.param; | |
235 | RealType result = 0; | |
236 | ||
237 | // Checking function argument. | |
238 | const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; | |
239 | ||
240 | // Check scale and location. | |
241 | //if(false == detail::check_scale(function, scale, result, Policy())) return false; | |
242 | //if(false == detail::check_location(function, location, result, Policy())) return false; | |
243 | if (false == c.dist.check_parameters(function, &result)) return result; | |
244 | ||
245 | // Special cdf values. | |
246 | if((boost::math::isinf)(x)) | |
247 | { | |
248 | if(x < 0) return 1; // cdf complement -infinity is unity. | |
249 | return 0; // cdf complement +infinity is zero. | |
250 | } | |
251 | if(false == detail::check_x(function, x, &result, Policy()))return result; | |
252 | ||
253 | // Cdf interval value. | |
254 | if (-x < -location) | |
255 | { | |
256 | result = exp( (-x+location)/scale )/2; | |
257 | } | |
258 | else | |
259 | { | |
260 | result = 1 - exp( (-location+x)/scale )/2; | |
261 | } | |
262 | return result; | |
263 | } // cdf complement | |
264 | ||
265 | ||
266 | template <class RealType, class Policy> | |
267 | inline RealType quantile(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) | |
268 | { | |
269 | BOOST_MATH_STD_USING // for ADL of std functions. | |
270 | ||
271 | // Calculate quantile. | |
272 | RealType scale = c.dist.scale(); | |
273 | RealType location = c.dist.location(); | |
274 | RealType q = c.param; | |
275 | RealType result = 0; | |
276 | ||
277 | // Checking function argument. | |
278 | const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; | |
279 | if (false == c.dist.check_parameters(function, &result)) return result; | |
280 | ||
281 | // Extreme values. | |
282 | if(q == 0) | |
283 | { | |
284 | return std::numeric_limits<RealType>::infinity(); | |
285 | } | |
286 | if(q == 1) | |
287 | { | |
288 | return -std::numeric_limits<RealType>::infinity(); | |
289 | } | |
290 | if(false == detail::check_probability(function, q, &result, Policy())) return result; | |
291 | ||
292 | if (0.5 - q < 0.0) | |
293 | result = location + scale*log( static_cast<RealType>(-q*2 + 2) ); | |
294 | else | |
295 | result = location - scale*log( static_cast<RealType>(q*2) ); | |
296 | ||
297 | ||
298 | return result; | |
299 | } // quantile | |
300 | ||
301 | template <class RealType, class Policy> | |
302 | inline RealType mean(const laplace_distribution<RealType, Policy>& dist) | |
303 | { | |
304 | return dist.location(); | |
305 | } | |
306 | ||
307 | template <class RealType, class Policy> | |
308 | inline RealType standard_deviation(const laplace_distribution<RealType, Policy>& dist) | |
309 | { | |
310 | return constants::root_two<RealType>() * dist.scale(); | |
311 | } | |
312 | ||
313 | template <class RealType, class Policy> | |
314 | inline RealType mode(const laplace_distribution<RealType, Policy>& dist) | |
315 | { | |
316 | return dist.location(); | |
317 | } | |
318 | ||
319 | template <class RealType, class Policy> | |
320 | inline RealType median(const laplace_distribution<RealType, Policy>& dist) | |
321 | { | |
322 | return dist.location(); | |
323 | } | |
324 | ||
325 | template <class RealType, class Policy> | |
326 | inline RealType skewness(const laplace_distribution<RealType, Policy>& /*dist*/) | |
327 | { | |
328 | return 0; | |
329 | } | |
330 | ||
331 | template <class RealType, class Policy> | |
332 | inline RealType kurtosis(const laplace_distribution<RealType, Policy>& /*dist*/) | |
333 | { | |
334 | return 6; | |
335 | } | |
336 | ||
337 | template <class RealType, class Policy> | |
338 | inline RealType kurtosis_excess(const laplace_distribution<RealType, Policy>& /*dist*/) | |
339 | { | |
340 | return 3; | |
341 | } | |
342 | ||
f67539c2 TL |
343 | template <class RealType, class Policy> |
344 | inline RealType entropy(const laplace_distribution<RealType, Policy> & dist) | |
345 | { | |
346 | using std::log; | |
347 | return log(2*dist.scale()*constants::e<RealType>()); | |
348 | } | |
349 | ||
1e59de90 | 350 | #ifdef _MSC_VER |
7c673cae FG |
351 | # pragma warning(pop) |
352 | #endif | |
353 | ||
354 | } // namespace math | |
355 | } // namespace boost | |
356 | ||
357 | // This include must be at the end, *after* the accessors | |
358 | // for this distribution have been defined, in order to | |
359 | // keep compilers that support two-phase lookup happy. | |
360 | #include <boost/math/distributions/detail/derived_accessors.hpp> | |
361 | ||
362 | #endif // BOOST_STATS_LAPLACE_HPP | |
363 | ||
364 |