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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_LOGNORMAL_HPP | |
7 | #define BOOST_STATS_LOGNORMAL_HPP | |
8 | ||
9 | // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm | |
10 | // http://mathworld.wolfram.com/LogNormalDistribution.html | |
11 | // http://en.wikipedia.org/wiki/Lognormal_distribution | |
12 | ||
13 | #include <boost/math/distributions/fwd.hpp> | |
14 | #include <boost/math/distributions/normal.hpp> | |
15 | #include <boost/math/special_functions/expm1.hpp> | |
16 | #include <boost/math/distributions/detail/common_error_handling.hpp> | |
17 | ||
18 | #include <utility> | |
19 | ||
20 | namespace boost{ namespace math | |
21 | { | |
22 | namespace detail | |
23 | { | |
24 | ||
25 | template <class RealType, class Policy> | |
26 | inline bool check_lognormal_x( | |
27 | const char* function, | |
28 | RealType const& x, | |
29 | RealType* result, const Policy& pol) | |
30 | { | |
31 | if((x < 0) || !(boost::math::isfinite)(x)) | |
32 | { | |
33 | *result = policies::raise_domain_error<RealType>( | |
34 | function, | |
35 | "Random variate is %1% but must be >= 0 !", x, pol); | |
36 | return false; | |
37 | } | |
38 | return true; | |
39 | } | |
40 | ||
41 | } // namespace detail | |
42 | ||
43 | ||
44 | template <class RealType = double, class Policy = policies::policy<> > | |
45 | class lognormal_distribution | |
46 | { | |
47 | public: | |
48 | typedef RealType value_type; | |
49 | typedef Policy policy_type; | |
50 | ||
51 | lognormal_distribution(RealType l_location = 0, RealType l_scale = 1) | |
52 | : m_location(l_location), m_scale(l_scale) | |
53 | { | |
54 | RealType result; | |
55 | detail::check_scale("boost::math::lognormal_distribution<%1%>::lognormal_distribution", l_scale, &result, Policy()); | |
56 | detail::check_location("boost::math::lognormal_distribution<%1%>::lognormal_distribution", l_location, &result, Policy()); | |
57 | } | |
58 | ||
59 | RealType location()const | |
60 | { | |
61 | return m_location; | |
62 | } | |
63 | ||
64 | RealType scale()const | |
65 | { | |
66 | return m_scale; | |
67 | } | |
68 | private: | |
69 | // | |
70 | // Data members: | |
71 | // | |
72 | RealType m_location; // distribution location. | |
73 | RealType m_scale; // distribution scale. | |
74 | }; | |
75 | ||
76 | typedef lognormal_distribution<double> lognormal; | |
77 | ||
78 | template <class RealType, class Policy> | |
79 | inline const std::pair<RealType, RealType> range(const lognormal_distribution<RealType, Policy>& /*dist*/) | |
80 | { // Range of permissible values for random variable x is >0 to +infinity. | |
81 | using boost::math::tools::max_value; | |
82 | return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); | |
83 | } | |
84 | ||
85 | template <class RealType, class Policy> | |
86 | inline const std::pair<RealType, RealType> support(const lognormal_distribution<RealType, Policy>& /*dist*/) | |
87 | { // Range of supported values for random variable x. | |
88 | // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. | |
89 | using boost::math::tools::max_value; | |
90 | return std::pair<RealType, RealType>(static_cast<RealType>(0), max_value<RealType>()); | |
91 | } | |
92 | ||
93 | template <class RealType, class Policy> | |
94 | RealType pdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x) | |
95 | { | |
96 | BOOST_MATH_STD_USING // for ADL of std functions | |
97 | ||
98 | RealType mu = dist.location(); | |
99 | RealType sigma = dist.scale(); | |
100 | ||
101 | static const char* function = "boost::math::pdf(const lognormal_distribution<%1%>&, %1%)"; | |
102 | ||
103 | RealType result = 0; | |
104 | if(0 == detail::check_scale(function, sigma, &result, Policy())) | |
105 | return result; | |
106 | if(0 == detail::check_location(function, mu, &result, Policy())) | |
107 | return result; | |
108 | if(0 == detail::check_lognormal_x(function, x, &result, Policy())) | |
109 | return result; | |
110 | ||
111 | if(x == 0) | |
112 | return 0; | |
113 | ||
114 | RealType exponent = log(x) - mu; | |
115 | exponent *= -exponent; | |
116 | exponent /= 2 * sigma * sigma; | |
117 | ||
118 | result = exp(exponent); | |
119 | result /= sigma * sqrt(2 * constants::pi<RealType>()) * x; | |
120 | ||
121 | return result; | |
122 | } | |
123 | ||
124 | template <class RealType, class Policy> | |
125 | inline RealType cdf(const lognormal_distribution<RealType, Policy>& dist, const RealType& x) | |
126 | { | |
127 | BOOST_MATH_STD_USING // for ADL of std functions | |
128 | ||
129 | static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)"; | |
130 | ||
131 | RealType result = 0; | |
132 | if(0 == detail::check_scale(function, dist.scale(), &result, Policy())) | |
133 | return result; | |
134 | if(0 == detail::check_location(function, dist.location(), &result, Policy())) | |
135 | return result; | |
136 | if(0 == detail::check_lognormal_x(function, x, &result, Policy())) | |
137 | return result; | |
138 | ||
139 | if(x == 0) | |
140 | return 0; | |
141 | ||
142 | normal_distribution<RealType, Policy> norm(dist.location(), dist.scale()); | |
143 | return cdf(norm, log(x)); | |
144 | } | |
145 | ||
146 | template <class RealType, class Policy> | |
147 | inline RealType quantile(const lognormal_distribution<RealType, Policy>& dist, const RealType& p) | |
148 | { | |
149 | BOOST_MATH_STD_USING // for ADL of std functions | |
150 | ||
151 | static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)"; | |
152 | ||
153 | RealType result = 0; | |
154 | if(0 == detail::check_scale(function, dist.scale(), &result, Policy())) | |
155 | return result; | |
156 | if(0 == detail::check_location(function, dist.location(), &result, Policy())) | |
157 | return result; | |
158 | if(0 == detail::check_probability(function, p, &result, Policy())) | |
159 | return result; | |
160 | ||
161 | if(p == 0) | |
162 | return 0; | |
163 | if(p == 1) | |
164 | return policies::raise_overflow_error<RealType>(function, 0, Policy()); | |
165 | ||
166 | normal_distribution<RealType, Policy> norm(dist.location(), dist.scale()); | |
167 | return exp(quantile(norm, p)); | |
168 | } | |
169 | ||
170 | template <class RealType, class Policy> | |
171 | inline RealType cdf(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c) | |
172 | { | |
173 | BOOST_MATH_STD_USING // for ADL of std functions | |
174 | ||
175 | static const char* function = "boost::math::cdf(const lognormal_distribution<%1%>&, %1%)"; | |
176 | ||
177 | RealType result = 0; | |
178 | if(0 == detail::check_scale(function, c.dist.scale(), &result, Policy())) | |
179 | return result; | |
180 | if(0 == detail::check_location(function, c.dist.location(), &result, Policy())) | |
181 | return result; | |
182 | if(0 == detail::check_lognormal_x(function, c.param, &result, Policy())) | |
183 | return result; | |
184 | ||
185 | if(c.param == 0) | |
186 | return 1; | |
187 | ||
188 | normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale()); | |
189 | return cdf(complement(norm, log(c.param))); | |
190 | } | |
191 | ||
192 | template <class RealType, class Policy> | |
193 | inline RealType quantile(const complemented2_type<lognormal_distribution<RealType, Policy>, RealType>& c) | |
194 | { | |
195 | BOOST_MATH_STD_USING // for ADL of std functions | |
196 | ||
197 | static const char* function = "boost::math::quantile(const lognormal_distribution<%1%>&, %1%)"; | |
198 | ||
199 | RealType result = 0; | |
200 | if(0 == detail::check_scale(function, c.dist.scale(), &result, Policy())) | |
201 | return result; | |
202 | if(0 == detail::check_location(function, c.dist.location(), &result, Policy())) | |
203 | return result; | |
204 | if(0 == detail::check_probability(function, c.param, &result, Policy())) | |
205 | return result; | |
206 | ||
207 | if(c.param == 1) | |
208 | return 0; | |
209 | if(c.param == 0) | |
210 | return policies::raise_overflow_error<RealType>(function, 0, Policy()); | |
211 | ||
212 | normal_distribution<RealType, Policy> norm(c.dist.location(), c.dist.scale()); | |
213 | return exp(quantile(complement(norm, c.param))); | |
214 | } | |
215 | ||
216 | template <class RealType, class Policy> | |
217 | inline RealType mean(const lognormal_distribution<RealType, Policy>& dist) | |
218 | { | |
219 | BOOST_MATH_STD_USING // for ADL of std functions | |
220 | ||
221 | RealType mu = dist.location(); | |
222 | RealType sigma = dist.scale(); | |
223 | ||
224 | RealType result = 0; | |
225 | if(0 == detail::check_scale("boost::math::mean(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
226 | return result; | |
227 | if(0 == detail::check_location("boost::math::mean(const lognormal_distribution<%1%>&)", mu, &result, Policy())) | |
228 | return result; | |
229 | ||
230 | return exp(mu + sigma * sigma / 2); | |
231 | } | |
232 | ||
233 | template <class RealType, class Policy> | |
234 | inline RealType variance(const lognormal_distribution<RealType, Policy>& dist) | |
235 | { | |
236 | BOOST_MATH_STD_USING // for ADL of std functions | |
237 | ||
238 | RealType mu = dist.location(); | |
239 | RealType sigma = dist.scale(); | |
240 | ||
241 | RealType result = 0; | |
242 | if(0 == detail::check_scale("boost::math::variance(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
243 | return result; | |
244 | if(0 == detail::check_location("boost::math::variance(const lognormal_distribution<%1%>&)", mu, &result, Policy())) | |
245 | return result; | |
246 | ||
247 | return boost::math::expm1(sigma * sigma, Policy()) * exp(2 * mu + sigma * sigma); | |
248 | } | |
249 | ||
250 | template <class RealType, class Policy> | |
251 | inline RealType mode(const lognormal_distribution<RealType, Policy>& dist) | |
252 | { | |
253 | BOOST_MATH_STD_USING // for ADL of std functions | |
254 | ||
255 | RealType mu = dist.location(); | |
256 | RealType sigma = dist.scale(); | |
257 | ||
258 | RealType result = 0; | |
259 | if(0 == detail::check_scale("boost::math::mode(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
260 | return result; | |
261 | if(0 == detail::check_location("boost::math::mode(const lognormal_distribution<%1%>&)", mu, &result, Policy())) | |
262 | return result; | |
263 | ||
264 | return exp(mu - sigma * sigma); | |
265 | } | |
266 | ||
267 | template <class RealType, class Policy> | |
268 | inline RealType median(const lognormal_distribution<RealType, Policy>& dist) | |
269 | { | |
270 | BOOST_MATH_STD_USING // for ADL of std functions | |
271 | RealType mu = dist.location(); | |
272 | return exp(mu); // e^mu | |
273 | } | |
274 | ||
275 | template <class RealType, class Policy> | |
276 | inline RealType skewness(const lognormal_distribution<RealType, Policy>& dist) | |
277 | { | |
278 | BOOST_MATH_STD_USING // for ADL of std functions | |
279 | ||
280 | //RealType mu = dist.location(); | |
281 | RealType sigma = dist.scale(); | |
282 | ||
283 | RealType ss = sigma * sigma; | |
284 | RealType ess = exp(ss); | |
285 | ||
286 | RealType result = 0; | |
287 | if(0 == detail::check_scale("boost::math::skewness(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
288 | return result; | |
289 | if(0 == detail::check_location("boost::math::skewness(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) | |
290 | return result; | |
291 | ||
292 | return (ess + 2) * sqrt(boost::math::expm1(ss, Policy())); | |
293 | } | |
294 | ||
295 | template <class RealType, class Policy> | |
296 | inline RealType kurtosis(const lognormal_distribution<RealType, Policy>& dist) | |
297 | { | |
298 | BOOST_MATH_STD_USING // for ADL of std functions | |
299 | ||
300 | //RealType mu = dist.location(); | |
301 | RealType sigma = dist.scale(); | |
302 | RealType ss = sigma * sigma; | |
303 | ||
304 | RealType result = 0; | |
305 | if(0 == detail::check_scale("boost::math::kurtosis(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
306 | return result; | |
307 | if(0 == detail::check_location("boost::math::kurtosis(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) | |
308 | return result; | |
309 | ||
310 | return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 3; | |
311 | } | |
312 | ||
313 | template <class RealType, class Policy> | |
314 | inline RealType kurtosis_excess(const lognormal_distribution<RealType, Policy>& dist) | |
315 | { | |
316 | BOOST_MATH_STD_USING // for ADL of std functions | |
317 | ||
318 | // RealType mu = dist.location(); | |
319 | RealType sigma = dist.scale(); | |
320 | RealType ss = sigma * sigma; | |
321 | ||
322 | RealType result = 0; | |
323 | if(0 == detail::check_scale("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", sigma, &result, Policy())) | |
324 | return result; | |
325 | if(0 == detail::check_location("boost::math::kurtosis_excess(const lognormal_distribution<%1%>&)", dist.location(), &result, Policy())) | |
326 | return result; | |
327 | ||
328 | return exp(4 * ss) + 2 * exp(3 * ss) + 3 * exp(2 * ss) - 6; | |
329 | } | |
330 | ||
331 | } // namespace math | |
332 | } // namespace boost | |
333 | ||
334 | // This include must be at the end, *after* the accessors | |
335 | // for this distribution have been defined, in order to | |
336 | // keep compilers that support two-phase lookup happy. | |
337 | #include <boost/math/distributions/detail/derived_accessors.hpp> | |
338 | ||
339 | #endif // BOOST_STATS_STUDENTS_T_HPP | |
340 | ||
341 |