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#include <type_traits>
25
26namespace boost{ namespace math{
27
28template <class RealType = double, class Policy = policies::policy<> >
29class normal_distribution
30{
31public:
32 using value_type = RealType;
33 using policy_type = Policy;
34
35 explicit normal_distribution(RealType l_mean = 0, RealType sd = 1)
36 : m_mean(l_mean), m_sd(sd)
37 { // Default is a 'standard' normal distribution N01.
38 static const char* function = "boost::math::normal_distribution<%1%>::normal_distribution";
39
40 RealType result;
41 detail::check_scale(function, sd, &result, Policy());
42 detail::check_location(function, l_mean, &result, Policy());
43 }
44
45 RealType mean()const
46 { // alias for location.
47 return m_mean;
48 }
49
50 RealType standard_deviation()const
51 { // alias for scale.
52 return m_sd;
53 }
54
55 // Synonyms, provided to allow generic use of find_location and find_scale.
56 RealType location()const
57 { // location.
58 return m_mean;
59 }
60 RealType scale()const
61 { // scale.
62 return m_sd;
63 }
64
65private:
66 //
67 // Data members:
68 //
69 RealType m_mean; // distribution mean or location.
70 RealType m_sd; // distribution standard deviation or scale.
71}; // class normal_distribution
72
73using normal = normal_distribution<double>;
74
75//
76// Deduction guides, note we don't check the
77// value of __cpp_deduction_guides, just assume
78// they work as advertised, even if this is pre-final C++17.
79//
80#ifdef __cpp_deduction_guides
81
82template <class RealType>
83normal_distribution(RealType, RealType)->normal_distribution<typename boost::math::tools::promote_args<RealType>::type>;
84template <class RealType>
85normal_distribution(RealType)->normal_distribution<typename boost::math::tools::promote_args<RealType>::type>;
86
87#endif
88
89#ifdef _MSC_VER
90#pragma warning(push)
91#pragma warning(disable:4127)
92#endif
93
94template <class RealType, class Policy>
95inline std::pair<RealType, RealType> range(const normal_distribution<RealType, Policy>& /*dist*/)
96{ // Range of permissible values for random variable x.
97 if (std::numeric_limits<RealType>::has_infinity)
98 {
99 return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
100 }
101 else
102 { // Can only use max_value.
103 using boost::math::tools::max_value;
104 return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
105 }
106}
107
108template <class RealType, class Policy>
109inline std::pair<RealType, RealType> support(const normal_distribution<RealType, Policy>& /*dist*/)
110{ // This is range values for random variable x where cdf rises from 0 to 1, and outside it, the pdf is zero.
111 if (std::numeric_limits<RealType>::has_infinity)
112 {
113 return std::pair<RealType, RealType>(-std::numeric_limits<RealType>::infinity(), std::numeric_limits<RealType>::infinity()); // - to + infinity.
114 }
115 else
116 { // Can only use max_value.
117 using boost::math::tools::max_value;
118 return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max value.
119 }
120}
121
122#ifdef _MSC_VER
123#pragma warning(pop)
124#endif
125
126template <class RealType, class Policy>
127inline RealType pdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
128{
129 BOOST_MATH_STD_USING // for ADL of std functions
130
131 RealType sd = dist.standard_deviation();
132 RealType mean = dist.mean();
133
134 static const char* function = "boost::math::pdf(const normal_distribution<%1%>&, %1%)";
135
136 RealType result = 0;
137 if(false == detail::check_scale(function, sd, &result, Policy()))
138 {
139 return result;
140 }
141 if(false == detail::check_location(function, mean, &result, Policy()))
142 {
143 return result;
144 }
145 if((boost::math::isinf)(x))
146 {
147 return 0; // pdf + and - infinity is zero.
148 }
149 if(false == detail::check_x(function, x, &result, Policy()))
150 {
151 return result;
152 }
153
154 RealType exponent = x - mean;
155 exponent *= -exponent;
156 exponent /= 2 * sd * sd;
157
158 result = exp(exponent);
159 result /= sd * sqrt(2 * constants::pi<RealType>());
160
161 return result;
162} // pdf
163
164template <class RealType, class Policy>
165inline RealType logpdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
166{
167 BOOST_MATH_STD_USING // for ADL of std functions
168
169 const RealType sd = dist.standard_deviation();
170 const RealType mean = dist.mean();
171
172 static const char* function = "boost::math::logpdf(const normal_distribution<%1%>&, %1%)";
173
174 RealType result = -std::numeric_limits<RealType>::infinity();
175 if(false == detail::check_scale(function, sd, &result, Policy()))
176 {
177 return result;
178 }
179 if(false == detail::check_location(function, mean, &result, Policy()))
180 {
181 return result;
182 }
183 if((boost::math::isinf)(x))
184 {
185 return result; // pdf + and - infinity is zero so logpdf is -inf
186 }
187 if(false == detail::check_x(function, x, &result, Policy()))
188 {
189 return result;
190 }
191
192 const RealType pi = boost::math::constants::pi<RealType>();
193 const RealType half = boost::math::constants::half<RealType>();
194
195 result = -log(sd) - half*log(2*pi) - (x-mean)*(x-mean)/(2*sd*sd);
196
197 return result;
198}
199
200template <class RealType, class Policy>
201inline RealType cdf(const normal_distribution<RealType, Policy>& dist, const RealType& x)
202{
203 BOOST_MATH_STD_USING // for ADL of std functions
204
205 RealType sd = dist.standard_deviation();
206 RealType mean = dist.mean();
207 static const char* function = "boost::math::cdf(const normal_distribution<%1%>&, %1%)";
208 RealType result = 0;
209 if(false == detail::check_scale(function, sd, &result, Policy()))
210 {
211 return result;
212 }
213 if(false == detail::check_location(function, mean, &result, Policy()))
214 {
215 return result;
216 }
217 if((boost::math::isinf)(x))
218 {
219 if(x < 0) return 0; // -infinity
220 return 1; // + infinity
221 }
222 if(false == detail::check_x(function, x, &result, Policy()))
223 {
224 return result;
225 }
226 RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
227 result = boost::math::erfc(-diff, Policy()) / 2;
228 return result;
229} // cdf
230
231template <class RealType, class Policy>
232inline RealType quantile(const normal_distribution<RealType, Policy>& dist, const RealType& p)
233{
234 BOOST_MATH_STD_USING // for ADL of std functions
235
236 RealType sd = dist.standard_deviation();
237 RealType mean = dist.mean();
238 static const char* function = "boost::math::quantile(const normal_distribution<%1%>&, %1%)";
239
240 RealType result = 0;
241 if(false == detail::check_scale(function, sd, &result, Policy()))
242 return result;
243 if(false == detail::check_location(function, mean, &result, Policy()))
244 return result;
245 if(false == detail::check_probability(function, p, &result, Policy()))
246 return result;
247
248 result= boost::math::erfc_inv(2 * p, Policy());
249 result = -result;
250 result *= sd * constants::root_two<RealType>();
251 result += mean;
252 return result;
253} // quantile
254
255template <class RealType, class Policy>
256inline RealType cdf(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 RealType x = c.param;
263 static const char* function = "boost::math::cdf(const complement(normal_distribution<%1%>&), %1%)";
264
265 RealType result = 0;
266 if(false == detail::check_scale(function, sd, &result, Policy()))
267 return result;
268 if(false == detail::check_location(function, mean, &result, Policy()))
269 return result;
270 if((boost::math::isinf)(x))
271 {
272 if(x < 0) return 1; // cdf complement -infinity is unity.
273 return 0; // cdf complement +infinity is zero
274 }
275 if(false == detail::check_x(function, x, &result, Policy()))
276 return result;
277
278 RealType diff = (x - mean) / (sd * constants::root_two<RealType>());
279 result = boost::math::erfc(diff, Policy()) / 2;
280 return result;
281} // cdf complement
282
283template <class RealType, class Policy>
284inline RealType quantile(const complemented2_type<normal_distribution<RealType, Policy>, RealType>& c)
285{
286 BOOST_MATH_STD_USING // for ADL of std functions
287
288 RealType sd = c.dist.standard_deviation();
289 RealType mean = c.dist.mean();
290 static const char* function = "boost::math::quantile(const complement(normal_distribution<%1%>&), %1%)";
291 RealType result = 0;
292 if(false == detail::check_scale(function, sd, &result, Policy()))
293 return result;
294 if(false == detail::check_location(function, mean, &result, Policy()))
295 return result;
296 RealType q = c.param;
297 if(false == detail::check_probability(function, q, &result, Policy()))
298 return result;
299 result = boost::math::erfc_inv(2 * q, Policy());
300 result *= sd * constants::root_two<RealType>();
301 result += mean;
302 return result;
303} // quantile
304
305template <class RealType, class Policy>
306inline RealType mean(const normal_distribution<RealType, Policy>& dist)
307{
308 return dist.mean();
309}
310
311template <class RealType, class Policy>
312inline RealType standard_deviation(const normal_distribution<RealType, Policy>& dist)
313{
314 return dist.standard_deviation();
315}
316
317template <class RealType, class Policy>
318inline RealType mode(const normal_distribution<RealType, Policy>& dist)
319{
320 return dist.mean();
321}
322
323template <class RealType, class Policy>
324inline RealType median(const normal_distribution<RealType, Policy>& dist)
325{
326 return dist.mean();
327}
328
329template <class RealType, class Policy>
330inline RealType skewness(const normal_distribution<RealType, Policy>& /*dist*/)
331{
332 return 0;
333}
334
335template <class RealType, class Policy>
336inline RealType kurtosis(const normal_distribution<RealType, Policy>& /*dist*/)
337{
338 return 3;
339}
340
341template <class RealType, class Policy>
342inline RealType kurtosis_excess(const normal_distribution<RealType, Policy>& /*dist*/)
343{
344 return 0;
345}
346
347template <class RealType, class Policy>
348inline RealType entropy(const normal_distribution<RealType, Policy> & dist)
349{
350 using std::log;
351 RealType arg = constants::two_pi<RealType>()*constants::e<RealType>()*dist.standard_deviation()*dist.standard_deviation();
352 return log(arg)/2;
353}
354
355} // namespace math
356} // namespace boost
357
358// This include must be at the end, *after* the accessors
359// for this distribution have been defined, in order to
360// keep compilers that support two-phase lookup happy.
361#include <boost/math/distributions/detail/derived_accessors.hpp>
362
363#endif // BOOST_STATS_NORMAL_HPP
364
365
366

source code of include/boost/math/distributions/normal.hpp