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,
hypergeometric_distribution(unsigned r,unsigned n,unsigned N)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
defective() const42
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 {
range(const hypergeometric_distribution<RealType,Policy> & dist)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
support(const hypergeometric_distribution<RealType,Policy> & d)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;
pdf(const hypergeometric_distribution<RealType,Policy> & dist,const unsigned & 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;
pdf(const hypergeometric_distribution<RealType,Policy> & dist,const U & x)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 {
cdf(const hypergeometric_distribution<RealType,Policy> & dist,const unsigned & x)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;
cdf(const hypergeometric_distribution<RealType,Policy> & dist,const U & x)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;
cdf(const complemented2_type<hypergeometric_distribution<RealType,Policy>,unsigned> & c)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
cdf(const complemented2_type<hypergeometric_distribution<RealType,Policy>,U> & c)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
quantile(const complemented2_type<hypergeometric_distribution<RealType,Policy>,RealType> & c)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)
mean(const hypergeometric_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
mode(const hypergeometric_distribution<RealType,Policy> & dist)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 {
kurtosis_excess(const hypergeometric_distribution<RealType,Policy> & dist)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();
kurtosis(const hypergeometric_distribution<RealType,Policy> & dist)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
342