1 // Copyright 2008 Gautam Sewani
2 //
3 // Use, modification and distribution are subject to the
4 // Boost Software License, Version 1.0.
5 // (See accompanying file LICENSE_1_0.txt
6 // or copy at http://www.boost.org/LICENSE_1_0.txt)
7 
8 #ifndef BOOST_MATH_DISTRIBUTIONS_LOGISTIC
9 #define BOOST_MATH_DISTRIBUTIONS_LOGISTIC
10 
11 #include <boost/math/distributions/fwd.hpp>
12 #include <boost/math/distributions/detail/common_error_handling.hpp>
13 #include <boost/math/distributions/complement.hpp>
14 #include <boost/math/special_functions/log1p.hpp>
15 #include <boost/math/constants/constants.hpp>
16 #include <utility>
17 
18 namespace boost { namespace math {
19 
20     template <class RealType = double, class Policy = policies::policy<> >
21     class logistic_distribution
22     {
23     public:
24       typedef RealType value_type;
25       typedef Policy policy_type;
26 
logistic_distribution(RealType l_location=0,RealType l_scale=1)27       logistic_distribution(RealType l_location=0, RealType l_scale=1) // Constructor.
28         : m_location(l_location), m_scale(l_scale)
29       {
30         static const char* function = "boost::math::logistic_distribution<%1%>::logistic_distribution";
31 
32         RealType result;
33         detail::check_scale(function, l_scale, &result, Policy());
34         detail::check_location(function, l_location, &result, Policy());
35       }
36       // Accessor functions.
scale() const37       RealType scale()const
38       {
39         return m_scale;
40       }
41 
location() const42       RealType location()const
43       {
44         return m_location;
45       }
46     private:
47       // Data members:
48       RealType m_location;  // distribution location aka mu.
49       RealType m_scale;  // distribution scale aka s.
50     }; // class logistic_distribution
51 
52 
53     typedef logistic_distribution<double> logistic;
54 
55     template <class RealType, class Policy>
range(const logistic_distribution<RealType,Policy> &)56     inline const std::pair<RealType, RealType> range(const logistic_distribution<RealType, Policy>& /* dist */)
57     { // Range of permissible values for random variable x.
58       using boost::math::tools::max_value;
59       return std::pair<RealType, RealType>(
60          std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(),
61          std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>());
62     }
63 
64     template <class RealType, class Policy>
support(const logistic_distribution<RealType,Policy> &)65     inline const std::pair<RealType, RealType> support(const logistic_distribution<RealType, Policy>& /* dist */)
66     { // Range of supported values for random variable x.
67       // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
68       using boost::math::tools::max_value;
69       return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity
70     }
71 
72     template <class RealType, class Policy>
pdf(const logistic_distribution<RealType,Policy> & dist,const RealType & x)73     inline RealType pdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x)
74     {
75        static const char* function = "boost::math::pdf(const logistic_distribution<%1%>&, %1%)";
76        RealType scale = dist.scale();
77        RealType location = dist.location();
78        RealType result = 0;
79 
80        if(false == detail::check_scale(function, scale , &result, Policy()))
81        {
82           return result;
83        }
84        if(false == detail::check_location(function, location, &result, Policy()))
85        {
86           return result;
87        }
88 
89        if((boost::math::isinf)(x))
90        {
91           return 0; // pdf + and - infinity is zero.
92        }
93 
94        if(false == detail::check_x(function, x, &result, Policy()))
95        {
96           return result;
97        }
98 
99        BOOST_MATH_STD_USING
100        RealType exp_term = (location - x) / scale;
101        if(fabs(exp_term) > tools::log_max_value<RealType>())
102           return 0;
103        exp_term = exp(exp_term);
104        if((exp_term * scale > 1) && (exp_term > tools::max_value<RealType>() / (scale * exp_term)))
105           return 1 / (scale * exp_term);
106        return (exp_term) / (scale * (1 + exp_term) * (1 + exp_term));
107     }
108 
109     template <class RealType, class Policy>
cdf(const logistic_distribution<RealType,Policy> & dist,const RealType & x)110     inline RealType cdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x)
111     {
112        RealType scale = dist.scale();
113        RealType location = dist.location();
114        RealType result = 0; // of checks.
115        static const char* function = "boost::math::cdf(const logistic_distribution<%1%>&, %1%)";
116        if(false == detail::check_scale(function, scale, &result, Policy()))
117        {
118           return result;
119        }
120        if(false == detail::check_location(function, location, &result, Policy()))
121        {
122           return result;
123        }
124 
125        if((boost::math::isinf)(x))
126        {
127           if(x < 0) return 0; // -infinity
128           return 1; // + infinity
129        }
130 
131        if(false == detail::check_x(function, x, &result, Policy()))
132        {
133           return result;
134        }
135        BOOST_MATH_STD_USING
136        RealType power = (location - x) / scale;
137        if(power > tools::log_max_value<RealType>())
138           return 0;
139        if(power < -tools::log_max_value<RealType>())
140           return 1;
141        return 1 / (1 + exp(power));
142     }
143 
144     template <class RealType, class Policy>
quantile(const logistic_distribution<RealType,Policy> & dist,const RealType & p)145     inline RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p)
146     {
147        BOOST_MATH_STD_USING
148        RealType location = dist.location();
149        RealType scale = dist.scale();
150 
151        static const char* function = "boost::math::quantile(const logistic_distribution<%1%>&, %1%)";
152 
153        RealType result = 0;
154        if(false == detail::check_scale(function, scale, &result, Policy()))
155           return result;
156        if(false == detail::check_location(function, location, &result, Policy()))
157           return result;
158        if(false == detail::check_probability(function, p, &result, Policy()))
159           return result;
160 
161        if(p == 0)
162        {
163           return -policies::raise_overflow_error<RealType>(function,"probability argument is 0, must be >0 and <1",Policy());
164        }
165        if(p == 1)
166        {
167           return policies::raise_overflow_error<RealType>(function,"probability argument is 1, must be >0 and <1",Policy());
168        }
169        //Expressions to try
170        //return location+scale*log(p/(1-p));
171        //return location+scale*log1p((2*p-1)/(1-p));
172 
173        //return location - scale*log( (1-p)/p);
174        //return location - scale*log1p((1-2*p)/p);
175 
176        //return -scale*log(1/p-1) + location;
177        return location - scale * log((1 - p) / p);
178      } // RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p)
179 
180     template <class RealType, class Policy>
cdf(const complemented2_type<logistic_distribution<RealType,Policy>,RealType> & c)181     inline RealType cdf(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c)
182     {
183        BOOST_MATH_STD_USING
184        RealType location = c.dist.location();
185        RealType scale = c.dist.scale();
186        RealType x = c.param;
187        static const char* function = "boost::math::cdf(const complement(logistic_distribution<%1%>&), %1%)";
188 
189        RealType result = 0;
190        if(false == detail::check_scale(function, scale, &result, Policy()))
191        {
192           return result;
193        }
194        if(false == detail::check_location(function, location, &result, Policy()))
195        {
196           return result;
197        }
198        if((boost::math::isinf)(x))
199        {
200           if(x < 0) return 1; // cdf complement -infinity is unity.
201           return 0; // cdf complement +infinity is zero.
202        }
203        if(false == detail::check_x(function, x, &result, Policy()))
204        {
205           return result;
206        }
207        RealType power = (x - location) / scale;
208        if(power > tools::log_max_value<RealType>())
209           return 0;
210        if(power < -tools::log_max_value<RealType>())
211           return 1;
212        return 1 / (1 + exp(power));
213     }
214 
215     template <class RealType, class Policy>
quantile(const complemented2_type<logistic_distribution<RealType,Policy>,RealType> & c)216     inline RealType quantile(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c)
217     {
218        BOOST_MATH_STD_USING
219        RealType scale = c.dist.scale();
220        RealType location = c.dist.location();
221        static const char* function = "boost::math::quantile(const complement(logistic_distribution<%1%>&), %1%)";
222        RealType result = 0;
223        if(false == detail::check_scale(function, scale, &result, Policy()))
224           return result;
225        if(false == detail::check_location(function, location, &result, Policy()))
226           return result;
227        RealType q = c.param;
228        if(false == detail::check_probability(function, q, &result, Policy()))
229           return result;
230        using boost::math::tools::max_value;
231 
232        if(q == 1)
233        {
234           return -policies::raise_overflow_error<RealType>(function,"probability argument is 1, but must be >0 and <1",Policy());
235        }
236        if(q == 0)
237        {
238           return policies::raise_overflow_error<RealType>(function,"probability argument is 0, but must be >0 and <1",Policy());
239        }
240        //Expressions to try
241        //return location+scale*log((1-q)/q);
242        return location + scale * log((1 - q) / q);
243 
244        //return location-scale*log(q/(1-q));
245        //return location-scale*log1p((2*q-1)/(1-q));
246 
247        //return location+scale*log(1/q-1);
248        //return location+scale*log1p(1/q-2);
249     }
250 
251     template <class RealType, class Policy>
mean(const logistic_distribution<RealType,Policy> & dist)252     inline RealType mean(const logistic_distribution<RealType, Policy>& dist)
253     {
254       return dist.location();
255     } // RealType mean(const logistic_distribution<RealType, Policy>& dist)
256 
257     template <class RealType, class Policy>
variance(const logistic_distribution<RealType,Policy> & dist)258     inline RealType variance(const logistic_distribution<RealType, Policy>& dist)
259     {
260       BOOST_MATH_STD_USING
261       RealType scale = dist.scale();
262       return boost::math::constants::pi<RealType>()*boost::math::constants::pi<RealType>()*scale*scale/3;
263     } // RealType variance(const logistic_distribution<RealType, Policy>& dist)
264 
265     template <class RealType, class Policy>
mode(const logistic_distribution<RealType,Policy> & dist)266     inline RealType mode(const logistic_distribution<RealType, Policy>& dist)
267     {
268       return dist.location();
269     }
270 
271     template <class RealType, class Policy>
median(const logistic_distribution<RealType,Policy> & dist)272     inline RealType median(const logistic_distribution<RealType, Policy>& dist)
273     {
274       return dist.location();
275     }
276     template <class RealType, class Policy>
skewness(const logistic_distribution<RealType,Policy> &)277     inline RealType skewness(const logistic_distribution<RealType, Policy>& /*dist*/)
278     {
279       return 0;
280     } // RealType skewness(const logistic_distribution<RealType, Policy>& dist)
281 
282     template <class RealType, class Policy>
kurtosis_excess(const logistic_distribution<RealType,Policy> &)283     inline RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& /*dist*/)
284     {
285       return static_cast<RealType>(6)/5;
286     } // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist)
287 
288     template <class RealType, class Policy>
kurtosis(const logistic_distribution<RealType,Policy> & dist)289     inline RealType kurtosis(const logistic_distribution<RealType, Policy>& dist)
290     {
291       return kurtosis_excess(dist) + 3;
292     } // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist)
293 
294     template <class RealType, class Policy>
entropy(const logistic_distribution<RealType,Policy> & dist)295     inline RealType entropy(const logistic_distribution<RealType, Policy>& dist)
296     {
297        using std::log;
298        return 2 + log(dist.scale());
299     }
300   }}
301 
302 
303 // Must come at the end:
304 #include <boost/math/distributions/detail/derived_accessors.hpp>
305 
306 #endif // BOOST_MATH_DISTRIBUTIONS_LOGISTIC
307