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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 | ||
27 | #ifdef BOOST_MSVC | |
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 | ||
83 | // | |
84 | // Non-member functions. | |
85 | template <class RealType, class Policy> | |
86 | inline const std::pair<RealType, RealType> range(const laplace_distribution<RealType, Policy>&) | |
87 | { | |
88 | if (std::numeric_limits<RealType>::has_infinity) | |
89 | { // Can use infinity. | |
90 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
91 | } | |
92 | else | |
93 | { // Can only use max_value. | |
94 | using boost::math::tools::max_value; | |
95 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. | |
96 | } | |
97 | ||
98 | } | |
99 | ||
100 | template <class RealType, class Policy> | |
101 | inline const std::pair<RealType, RealType> support(const laplace_distribution<RealType, Policy>&) | |
102 | { | |
103 | if (std::numeric_limits<RealType>::has_infinity) | |
104 | { // Can Use infinity. | |
105 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
106 | } | |
107 | else | |
108 | { // Can only use max_value. | |
109 | using boost::math::tools::max_value; | |
110 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. | |
111 | } | |
112 | } | |
113 | ||
114 | template <class RealType, class Policy> | |
115 | inline RealType pdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) | |
116 | { | |
117 | BOOST_MATH_STD_USING // for ADL of std functions | |
118 | ||
119 | // Checking function argument | |
120 | RealType result = 0; | |
121 | const char* function = "boost::math::pdf(const laplace_distribution<%1%>&, %1%))"; | |
122 | ||
123 | // Check scale and location. | |
124 | if (false == dist.check_parameters(function, &result)) return result; | |
125 | // Special pdf values. | |
126 | if((boost::math::isinf)(x)) | |
127 | { | |
128 | return 0; // pdf + and - infinity is zero. | |
129 | } | |
130 | if (false == detail::check_x(function, x, &result, Policy())) return result; | |
131 | ||
132 | // General case | |
133 | RealType scale( dist.scale() ); | |
134 | RealType location( dist.location() ); | |
135 | ||
136 | RealType exponent = x - location; | |
137 | if (exponent>0) exponent = -exponent; | |
138 | exponent /= scale; | |
139 | ||
140 | result = exp(exponent); | |
141 | result /= 2 * scale; | |
142 | ||
143 | return result; | |
144 | ||
145 | ||
146 | template <class RealType, class Policy> | |
147 | inline RealType cdf(const laplace_distribution<RealType, Policy>& dist, const RealType& x) | |
148 | { | |
149 | BOOST_MATH_STD_USING // For ADL of std functions. | |
150 | ||
151 | RealType result = 0; | |
152 | // Checking function argument. | |
153 | const char* function = "boost::math::cdf(const laplace_distribution<%1%>&, %1%)"; | |
154 | // Check scale and location. | |
155 | if (false == dist.check_parameters(function, &result)) return result; | |
156 | ||
157 | // Special cdf values: | |
158 | if((boost::math::isinf)(x)) | |
159 | { | |
160 | if(x < 0) return 0; // -infinity. | |
161 | return 1; // + infinity. | |
162 | } | |
163 | if (false == detail::check_x(function, x, &result, Policy())) return result; | |
164 | ||
165 | // General cdf values | |
166 | RealType scale( dist.scale() ); | |
167 | RealType location( dist.location() ); | |
168 | ||
169 | if (x < location) | |
170 | { | |
171 | result = exp( (x-location)/scale )/2; | |
172 | } | |
173 | else | |
174 | { | |
175 | result = 1 - exp( (location-x)/scale )/2; | |
176 | } | |
177 | return result; | |
178 | } // cdf | |
179 | ||
180 | ||
181 | template <class RealType, class Policy> | |
182 | inline RealType quantile(const laplace_distribution<RealType, Policy>& dist, const RealType& p) | |
183 | { | |
184 | BOOST_MATH_STD_USING // for ADL of std functions. | |
185 | ||
186 | // Checking function argument | |
187 | RealType result = 0; | |
188 | const char* function = "boost::math::quantile(const laplace_distribution<%1%>&, %1%)"; | |
189 | if (false == dist.check_parameters(function, &result)) return result; | |
190 | if(false == detail::check_probability(function, p, &result, Policy())) return result; | |
191 | ||
192 | // Extreme values of p: | |
193 | if(p == 0) | |
194 | { | |
195 | result = policies::raise_overflow_error<RealType>(function, | |
196 | "probability parameter is 0, but must be > 0!", Policy()); | |
197 | return -result; // -std::numeric_limits<RealType>::infinity(); | |
198 | } | |
199 | ||
200 | if(p == 1) | |
201 | { | |
202 | result = policies::raise_overflow_error<RealType>(function, | |
203 | "probability parameter is 1, but must be < 1!", Policy()); | |
204 | return result; // std::numeric_limits<RealType>::infinity(); | |
205 | } | |
206 | // Calculate Quantile | |
207 | RealType scale( dist.scale() ); | |
208 | RealType location( dist.location() ); | |
209 | ||
210 | if (p - 0.5 < 0.0) | |
211 | result = location + scale*log( static_cast<RealType>(p*2) ); | |
212 | else | |
213 | result = location - scale*log( static_cast<RealType>(-p*2 + 2) ); | |
214 | ||
215 | return result; | |
216 | } // quantile | |
217 | ||
218 | ||
219 | template <class RealType, class Policy> | |
220 | inline RealType cdf(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) | |
221 | { | |
222 | // Calculate complement of cdf. | |
223 | BOOST_MATH_STD_USING // for ADL of std functions | |
224 | ||
225 | RealType scale = c.dist.scale(); | |
226 | RealType location = c.dist.location(); | |
227 | RealType x = c.param; | |
228 | RealType result = 0; | |
229 | ||
230 | // Checking function argument. | |
231 | const char* function = "boost::math::cdf(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; | |
232 | ||
233 | // Check scale and location. | |
234 | //if(false == detail::check_scale(function, scale, result, Policy())) return false; | |
235 | //if(false == detail::check_location(function, location, result, Policy())) return false; | |
236 | if (false == c.dist.check_parameters(function, &result)) return result; | |
237 | ||
238 | // Special cdf values. | |
239 | if((boost::math::isinf)(x)) | |
240 | { | |
241 | if(x < 0) return 1; // cdf complement -infinity is unity. | |
242 | return 0; // cdf complement +infinity is zero. | |
243 | } | |
244 | if(false == detail::check_x(function, x, &result, Policy()))return result; | |
245 | ||
246 | // Cdf interval value. | |
247 | if (-x < -location) | |
248 | { | |
249 | result = exp( (-x+location)/scale )/2; | |
250 | } | |
251 | else | |
252 | { | |
253 | result = 1 - exp( (-location+x)/scale )/2; | |
254 | } | |
255 | return result; | |
256 | } // cdf complement | |
257 | ||
258 | ||
259 | template <class RealType, class Policy> | |
260 | inline RealType quantile(const complemented2_type<laplace_distribution<RealType, Policy>, RealType>& c) | |
261 | { | |
262 | BOOST_MATH_STD_USING // for ADL of std functions. | |
263 | ||
264 | // Calculate quantile. | |
265 | RealType scale = c.dist.scale(); | |
266 | RealType location = c.dist.location(); | |
267 | RealType q = c.param; | |
268 | RealType result = 0; | |
269 | ||
270 | // Checking function argument. | |
271 | const char* function = "quantile(const complemented2_type<laplace_distribution<%1%>, %1%>&)"; | |
272 | if (false == c.dist.check_parameters(function, &result)) return result; | |
273 | ||
274 | // Extreme values. | |
275 | if(q == 0) | |
276 | { | |
277 | return std::numeric_limits<RealType>::infinity(); | |
278 | } | |
279 | if(q == 1) | |
280 | { | |
281 | return -std::numeric_limits<RealType>::infinity(); | |
282 | } | |
283 | if(false == detail::check_probability(function, q, &result, Policy())) return result; | |
284 | ||
285 | if (0.5 - q < 0.0) | |
286 | result = location + scale*log( static_cast<RealType>(-q*2 + 2) ); | |
287 | else | |
288 | result = location - scale*log( static_cast<RealType>(q*2) ); | |
289 | ||
290 | ||
291 | return result; | |
292 | } // quantile | |
293 | ||
294 | template <class RealType, class Policy> | |
295 | inline RealType mean(const laplace_distribution<RealType, Policy>& dist) | |
296 | { | |
297 | return dist.location(); | |
298 | } | |
299 | ||
300 | template <class RealType, class Policy> | |
301 | inline RealType standard_deviation(const laplace_distribution<RealType, Policy>& dist) | |
302 | { | |
303 | return constants::root_two<RealType>() * dist.scale(); | |
304 | } | |
305 | ||
306 | template <class RealType, class Policy> | |
307 | inline RealType mode(const laplace_distribution<RealType, Policy>& dist) | |
308 | { | |
309 | return dist.location(); | |
310 | } | |
311 | ||
312 | template <class RealType, class Policy> | |
313 | inline RealType median(const laplace_distribution<RealType, Policy>& dist) | |
314 | { | |
315 | return dist.location(); | |
316 | } | |
317 | ||
318 | template <class RealType, class Policy> | |
319 | inline RealType skewness(const laplace_distribution<RealType, Policy>& /*dist*/) | |
320 | { | |
321 | return 0; | |
322 | } | |
323 | ||
324 | template <class RealType, class Policy> | |
325 | inline RealType kurtosis(const laplace_distribution<RealType, Policy>& /*dist*/) | |
326 | { | |
327 | return 6; | |
328 | } | |
329 | ||
330 | template <class RealType, class Policy> | |
331 | inline RealType kurtosis_excess(const laplace_distribution<RealType, Policy>& /*dist*/) | |
332 | { | |
333 | return 3; | |
334 | } | |
335 | ||
336 | #ifdef BOOST_MSVC | |
337 | # pragma warning(pop) | |
338 | #endif | |
339 | ||
340 | } // namespace math | |
341 | } // namespace boost | |
342 | ||
343 | // This include must be at the end, *after* the accessors | |
344 | // for this distribution have been defined, in order to | |
345 | // keep compilers that support two-phase lookup happy. | |
346 | #include <boost/math/distributions/detail/derived_accessors.hpp> | |
347 | ||
348 | #endif // BOOST_STATS_LAPLACE_HPP | |
349 | ||
350 |