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1 | // Copyright John Maddock 2006, 2007. |
2 | // Copyright Paul A. Bristow 2006, 2007. | |
3 | ||
4 | // Use, modification and distribution are subject to the | |
5 | // Boost Software License, Version 1.0. (See accompanying file | |
6 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
7 | ||
8 | #ifndef BOOST_STATS_NORMAL_HPP | |
9 | #define BOOST_STATS_NORMAL_HPP | |
10 | ||
11 | // http://en.wikipedia.org/wiki/Normal_distribution | |
12 | // http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm | |
13 | // Also: | |
14 | // Weisstein, Eric W. "Normal Distribution." | |
15 | // From MathWorld--A Wolfram Web Resource. | |
16 | // http://mathworld.wolfram.com/NormalDistribution.html | |
17 | ||
18 | #include <boost/math/distributions/fwd.hpp> | |
19 | #include <boost/math/special_functions/erf.hpp> // for erf/erfc. | |
20 | #include <boost/math/distributions/complement.hpp> | |
21 | #include <boost/math/distributions/detail/common_error_handling.hpp> | |
22 | ||
23 | #include <utility> | |
24 | ||
25 | namespace boost{ namespace math{ | |
26 | ||
27 | template <class RealType = double, class Policy = policies::policy<> > | |
28 | class normal_distribution | |
29 | { | |
30 | public: | |
31 | typedef RealType value_type; | |
32 | typedef Policy policy_type; | |
33 | ||
34 | normal_distribution(RealType l_mean = 0, RealType sd = 1) | |
35 | : m_mean(l_mean), m_sd(sd) | |
36 | { // Default is a 'standard' normal distribution N01. | |
37 | static const char* function = "boost::math::normal_distribution<%1%>::normal_distribution"; | |
38 | ||
39 | RealType result; | |
40 | detail::check_scale(function, sd, &result, Policy()); | |
41 | detail::check_location(function, l_mean, &result, Policy()); | |
42 | } | |
43 | ||
44 | RealType mean()const | |
45 | { // alias for location. | |
46 | return m_mean; | |
47 | } | |
48 | ||
49 | RealType standard_deviation()const | |
50 | { // alias for scale. | |
51 | return m_sd; | |
52 | } | |
53 | ||
54 | // Synonyms, provided to allow generic use of find_location and find_scale. | |
55 | RealType location()const | |
56 | { // location. | |
57 | return m_mean; | |
58 | } | |
59 | RealType scale()const | |
60 | { // scale. | |
61 | return m_sd; | |
62 | } | |
63 | ||
64 | private: | |
65 | // | |
66 | // Data members: | |
67 | // | |
68 | RealType m_mean; // distribution mean or location. | |
69 | RealType m_sd; // distribution standard deviation or scale. | |
70 | }; // class normal_distribution | |
71 | ||
72 | typedef normal_distribution<double> normal; | |
73 | ||
74 | #ifdef BOOST_MSVC | |
75 | #pragma warning(push) | |
76 | #pragma warning(disable:4127) | |
77 | #endif | |
78 | ||
79 | template <class RealType, class Policy> | |
80 | inline const std::pair<RealType, RealType> range(const normal_distribution<RealType, Policy>& /*dist*/) | |
81 | { // Range of permissible values for random variable x. | |
82 | if (std::numeric_limits<RealType>::has_infinity) | |
83 | { | |
84 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
85 | } | |
86 | else | |
87 | { // Can only use max_value. | |
88 | using boost::math::tools::max_value; | |
89 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. | |
90 | } | |
91 | } | |
92 | ||
93 | template <class RealType, class Policy> | |
94 | inline const std::pair<RealType, RealType> support(const normal_distribution<RealType, Policy>& /*dist*/) | |
95 | { // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero. | |
96 | if (std::numeric_limits<RealType>::has_infinity) | |
97 | { | |
98 | return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity. | |
99 | } | |
100 | else | |
101 | { // Can only use max_value. | |
102 | using boost::math::tools::max_value; | |
103 | return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value. | |
104 | } | |
105 | } | |
106 | ||
107 | #ifdef BOOST_MSVC | |
108 | #pragma warning(pop) | |
109 | #endif | |
110 | ||
111 | template <class RealType, class Policy> | |
112 | inline RealType pdf(const normal_distribution<RealType, Policy>& dist, const RealType& x) | |
113 | { | |
114 | BOOST_MATH_STD_USING // for ADL of std functions | |
115 | ||
116 | RealType sd = dist.standard_deviation(); | |
117 | RealType mean = dist.mean(); | |
118 | ||
119 | static const char* function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)"; | |
120 | ||
121 | RealType result = 0; | |
122 | if(false == detail::check_scale(function, sd, &result, Policy())) | |
123 | { | |
124 | return result; | |
125 | } | |
126 | if(false == detail::check_location(function, mean, &result, Policy())) | |
127 | { | |
128 | return result; | |
129 | } | |
130 | if((boost::math::isinf)(x)) | |
131 | { | |
132 | return 0; // pdf + and - infinity is zero. | |
133 | } | |
134 | // Below produces MSVC 4127 warnings, so the above used instead. | |
135 | //if(std::numeric_limits<RealType>::has_infinity && abs(x) == std::numeric_limits<RealType>::infinity()) | |
136 | //{ // pdf + and - infinity is zero. | |
137 | // return 0; | |
138 | //} | |
139 | if(false == detail::check_x(function, x, &result, Policy())) | |
140 | { | |
141 | return result; | |
142 | } | |
143 | ||
144 | RealType exponent = x - mean; | |
145 | exponent *= -exponent; | |
146 | exponent /= 2 * sd * sd; | |
147 | ||
148 | result = exp(exponent); | |
149 | result /= sd * sqrt(2 * constants::pi<RealType>()); | |
150 | ||
151 | return result; | |
152 | ||
153 | ||
154 | template <class RealType, class Policy> | |
155 | inline RealType cdf(const normal_distribution<RealType, Policy>& dist, const RealType& x) | |
156 | { | |
157 | BOOST_MATH_STD_USING // for ADL of std functions | |
158 | ||
159 | RealType sd = dist.standard_deviation(); | |
160 | RealType mean = dist.mean(); | |
161 | static const char* function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)"; | |
162 | RealType result = 0; | |
163 | if(false == detail::check_scale(function, sd, &result, Policy())) | |
164 | { | |
165 | return result; | |
166 | } | |
167 | if(false == detail::check_location(function, mean, &result, Policy())) | |
168 | { | |
169 | return result; | |
170 | } | |
171 | if((boost::math::isinf)(x)) | |
172 | { | |
173 | if(x < 0) return 0; // -infinity | |
174 | return 1; // + infinity | |
175 | } | |
176 | // These produce MSVC 4127 warnings, so the above used instead. | |
177 | //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) | |
178 | //{ // cdf +infinity is unity. | |
179 | // return 1; | |
180 | //} | |
181 | //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) | |
182 | //{ // cdf -infinity is zero. | |
183 | // return 0; | |
184 | //} | |
185 | if(false == detail::check_x(function, x, &result, Policy())) | |
186 | { | |
187 | return result; | |
188 | } | |
189 | RealType diff = (x - mean) / (sd * constants::root_two<RealType>()); | |
190 | result = boost::math::erfc(-diff, Policy()) / 2; | |
191 | return result; | |
192 | } // cdf | |
193 | ||
194 | template <class RealType, class Policy> | |
195 | inline RealType quantile(const normal_distribution<RealType, Policy>& dist, const RealType& p) | |
196 | { | |
197 | BOOST_MATH_STD_USING // for ADL of std functions | |
198 | ||
199 | RealType sd = dist.standard_deviation(); | |
200 | RealType mean = dist.mean(); | |
201 | static const char* function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)"; | |
202 | ||
203 | RealType result = 0; | |
204 | if(false == detail::check_scale(function, sd, &result, Policy())) | |
205 | return result; | |
206 | if(false == detail::check_location(function, mean, &result, Policy())) | |
207 | return result; | |
208 | if(false == detail::check_probability(function, p, &result, Policy())) | |
209 | return result; | |
210 | ||
211 | result= boost::math::erfc_inv(2 * p, Policy()); | |
212 | result = -result; | |
213 | result *= sd * constants::root_two<RealType>(); | |
214 | result += mean; | |
215 | return result; | |
216 | } // quantile | |
217 | ||
218 | template <class RealType, class Policy> | |
219 | inline RealType cdf(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c) | |
220 | { | |
221 | BOOST_MATH_STD_USING // for ADL of std functions | |
222 | ||
223 | RealType sd = c.dist.standard_deviation(); | |
224 | RealType mean = c.dist.mean(); | |
225 | RealType x = c.param; | |
226 | static const char* function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)"; | |
227 | ||
228 | RealType result = 0; | |
229 | if(false == detail::check_scale(function, sd, &result, Policy())) | |
230 | return result; | |
231 | if(false == detail::check_location(function, mean, &result, Policy())) | |
232 | return result; | |
233 | if((boost::math::isinf)(x)) | |
234 | { | |
235 | if(x < 0) return 1; // cdf complement -infinity is unity. | |
236 | return 0; // cdf complement +infinity is zero | |
237 | } | |
238 | // These produce MSVC 4127 warnings, so the above used instead. | |
239 | //if(std::numeric_limits<RealType>::has_infinity && x == std::numeric_limits<RealType>::infinity()) | |
240 | //{ // cdf complement +infinity is zero. | |
241 | // return 0; | |
242 | //} | |
243 | //if(std::numeric_limits<RealType>::has_infinity && x == -std::numeric_limits<RealType>::infinity()) | |
244 | //{ // cdf complement -infinity is unity. | |
245 | // return 1; | |
246 | //} | |
247 | if(false == detail::check_x(function, x, &result, Policy())) | |
248 | return result; | |
249 | ||
250 | RealType diff = (x - mean) / (sd * constants::root_two<RealType>()); | |
251 | result = boost::math::erfc(diff, Policy()) / 2; | |
252 | return result; | |
253 | } // cdf complement | |
254 | ||
255 | template <class RealType, class Policy> | |
256 | inline RealType quantile(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c) | |
257 | { | |
258 | BOOST_MATH_STD_USING // for ADL of std functions | |
259 | ||
260 | RealType sd = c.dist.standard_deviation(); | |
261 | RealType mean = c.dist.mean(); | |
262 | static const char* function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)"; | |
263 | RealType result = 0; | |
264 | if(false == detail::check_scale(function, sd, &result, Policy())) | |
265 | return result; | |
266 | if(false == detail::check_location(function, mean, &result, Policy())) | |
267 | return result; | |
268 | RealType q = c.param; | |
269 | if(false == detail::check_probability(function, q, &result, Policy())) | |
270 | return result; | |
271 | result = boost::math::erfc_inv(2 * q, Policy()); | |
272 | result *= sd * constants::root_two<RealType>(); | |
273 | result += mean; | |
274 | return result; | |
275 | } // quantile | |
276 | ||
277 | template <class RealType, class Policy> | |
278 | inline RealType mean(const normal_distribution<RealType, Policy>& dist) | |
279 | { | |
280 | return dist.mean(); | |
281 | } | |
282 | ||
283 | template <class RealType, class Policy> | |
284 | inline RealType standard_deviation(const normal_distribution<RealType, Policy>& dist) | |
285 | { | |
286 | return dist.standard_deviation(); | |
287 | } | |
288 | ||
289 | template <class RealType, class Policy> | |
290 | inline RealType mode(const normal_distribution<RealType, Policy>& dist) | |
291 | { | |
292 | return dist.mean(); | |
293 | } | |
294 | ||
295 | template <class RealType, class Policy> | |
296 | inline RealType median(const normal_distribution<RealType, Policy>& dist) | |
297 | { | |
298 | return dist.mean(); | |
299 | } | |
300 | ||
301 | template <class RealType, class Policy> | |
302 | inline RealType skewness(const normal_distribution<RealType, Policy>& /*dist*/) | |
303 | { | |
304 | return 0; | |
305 | } | |
306 | ||
307 | template <class RealType, class Policy> | |
308 | inline RealType kurtosis(const normal_distribution<RealType, Policy>& /*dist*/) | |
309 | { | |
310 | return 3; | |
311 | } | |
312 | ||
313 | template <class RealType, class Policy> | |
314 | inline RealType kurtosis_excess(const normal_distribution<RealType, Policy>& /*dist*/) | |
315 | { | |
316 | return 0; | |
317 | } | |
318 | ||
f67539c2 TL |
319 | template <class RealType, class Policy> |
320 | inline RealType entropy(const normal_distribution<RealType, Policy> & dist) | |
321 | { | |
322 | using std::log; | |
323 | RealType arg = constants::two_pi<RealType>()*constants::e<RealType>()*dist.standard_deviation()*dist.standard_deviation(); | |
324 | return log(arg)/2; | |
325 | } | |
326 | ||
7c673cae FG |
327 | } // namespace math |
328 | } // namespace boost | |
329 | ||
330 | // This include must be at the end, *after* the accessors | |
331 | // for this distribution have been defined, in order to | |
332 | // keep compilers that support two-phase lookup happy. | |
333 | #include <boost/math/distributions/detail/derived_accessors.hpp> | |
334 | ||
335 | #endif // BOOST_STATS_NORMAL_HPP | |
336 | ||
337 |