// Copyright 2008 Gautam Sewani | |
// | |
// Use, modification and distribution are subject to the | |
// Boost Software License, Version 1.0. | |
// (See accompanying file LICENSE_1_0.txt | |
// or copy at http://www.boost.org/LICENSE_1_0.txt) | |
#include <boost/math/distributions/fwd.hpp> | |
#include <boost/math/distributions/detail/common_error_handling.hpp> | |
#include <boost/math/distributions/complement.hpp> | |
#include <boost/math/special_functions/log1p.hpp> | |
#include <boost/math/constants/constants.hpp> | |
#include <utility> | |
namespace boost { namespace math { | |
template <class RealType = double, class Policy = policies::policy<> > | |
class logistic_distribution | |
{ | |
public: | |
typedef RealType value_type; | |
typedef Policy policy_type; | |
logistic_distribution(RealType location=0, RealType scale=1) // Constructor. | |
: m_location(location), m_scale(scale) | |
{ | |
static const char* function = "boost::math::logistic_distribution<%1%>::logistic_distribution"; | |
RealType result; | |
detail::check_scale(function, scale, &result, Policy()); | |
detail::check_location(function, location, &result, Policy()); | |
} | |
// Accessor functions. | |
RealType scale()const | |
{ | |
return m_scale; | |
} | |
RealType location()const | |
{ | |
return m_location; | |
} | |
private: | |
// Data members: | |
RealType m_location; // distribution location aka mu. | |
RealType m_scale; // distribution scale aka s. | |
}; // class logistic_distribution | |
typedef logistic_distribution<double> logistic; | |
template <class RealType, class Policy> | |
inline const std::pair<RealType, RealType> range(const logistic_distribution<RealType, Policy>& /* dist */) | |
{ // Range of permissible values for random variable x. | |
using boost::math::tools::max_value; | |
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity | |
} | |
template <class RealType, class Policy> | |
inline const std::pair<RealType, RealType> support(const logistic_distribution<RealType, Policy>& /* dist */) | |
{ // Range of supported values for random variable x. | |
// This is range where cdf rises from 0 to 1, and outside it, the pdf is zero. | |
using boost::math::tools::max_value; | |
return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity | |
} | |
template <class RealType, class Policy> | |
inline RealType pdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x) | |
{ | |
RealType scale = dist.scale(); | |
RealType location = dist.location(); | |
static const char* function = "boost::math::pdf(const logistic_distribution<%1%>&, %1%)"; | |
if((boost::math::isinf)(x)) | |
{ | |
return 0; // pdf + and - infinity is zero. | |
} | |
RealType result; | |
if(false == detail::check_scale(function, scale , &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_location(function, location, &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_x(function, x, &result, Policy())) | |
{ | |
return result; | |
} | |
BOOST_MATH_STD_USING | |
RealType exp_term = (location - x) / scale; | |
if(fabs(exp_term) > tools::log_max_value<RealType>()) | |
return 0; | |
exp_term = exp(exp_term); | |
if((exp_term * scale > 1) && (exp_term > tools::max_value<RealType>() / (scale * exp_term))) | |
return 1 / (scale * exp_term); | |
return (exp_term) / (scale * (1 + exp_term) * (1 + exp_term)); | |
} | |
template <class RealType, class Policy> | |
inline RealType cdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x) | |
{ | |
RealType scale = dist.scale(); | |
RealType location = dist.location(); | |
RealType result; // of checks. | |
static const char* function = "boost::math::cdf(const logistic_distribution<%1%>&, %1%)"; | |
if(false == detail::check_scale(function, scale, &result, Policy())) | |
{ | |
return result; | |
} | |
if(false == detail::check_location(function, location, &result, Policy())) | |
{ | |
return result; | |
} | |
if((boost::math::isinf)(x)) | |
{ | |
if(x < 0) return 0; // -infinity | |
return 1; // + infinity | |
} | |
if(false == detail::check_x(function, x, &result, Policy())) | |
{ | |
return result; | |
} | |
BOOST_MATH_STD_USING | |
RealType power = (location - x) / scale; | |
if(power > tools::log_max_value<RealType>()) | |
return 0; | |
if(power < -tools::log_max_value<RealType>()) | |
return 1; | |
return 1 / (1 + exp(power)); | |
} | |
template <class RealType, class Policy> | |
inline RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p) | |
{ | |
BOOST_MATH_STD_USING | |
RealType location = dist.location(); | |
RealType scale = dist.scale(); | |
static const char* function = "boost::math::quantile(const logistic_distribution<%1%>&, %1%)"; | |
RealType result; | |
if(false == detail::check_scale(function, scale, &result, Policy())) | |
return result; | |
if(false == detail::check_location(function, location, &result, Policy())) | |
return result; | |
if(false == detail::check_probability(function, p, &result, Policy())) | |
return result; | |
if(p == 0) | |
{ | |
return -policies::raise_overflow_error<RealType>(function,"probability argument is 0, must be >0 and <1",Policy()); | |
} | |
if(p == 1) | |
{ | |
return policies::raise_overflow_error<RealType>(function,"probability argument is 1, must be >0 and <1",Policy()); | |
} | |
//Expressions to try | |
//return location+scale*log(p/(1-p)); | |
//return location+scale*log1p((2*p-1)/(1-p)); | |
//return location - scale*log( (1-p)/p); | |
//return location - scale*log1p((1-2*p)/p); | |
//return -scale*log(1/p-1) + location; | |
return location - scale * log((1 - p) / p); | |
} // RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p) | |
template <class RealType, class Policy> | |
inline RealType cdf(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c) | |
{ | |
BOOST_MATH_STD_USING | |
RealType location = c.dist.location(); | |
RealType scale = c.dist.scale(); | |
RealType x = c.param; | |
static const char* function = "boost::math::cdf(const complement(logistic_distribution<%1%>&), %1%)"; | |
if((boost::math::isinf)(x)) | |
{ | |
if(x < 0) return 1; // cdf complement -infinity is unity. | |
return 0; // cdf complement +infinity is zero | |
} | |
RealType result; | |
if(false == detail::check_scale(function, scale, &result, Policy())) | |
return result; | |
if(false == detail::check_location(function, location, &result, Policy())) | |
return result; | |
if(false == detail::check_x(function, x, &result, Policy())) | |
return result; | |
RealType power = (x - location) / scale; | |
if(power > tools::log_max_value<RealType>()) | |
return 0; | |
if(power < -tools::log_max_value<RealType>()) | |
return 1; | |
return 1 / (1 + exp(power)); | |
} | |
template <class RealType, class Policy> | |
inline RealType quantile(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c) | |
{ | |
BOOST_MATH_STD_USING | |
RealType scale = c.dist.scale(); | |
RealType location = c.dist.location(); | |
static const char* function = "boost::math::quantile(const complement(logistic_distribution<%1%>&), %1%)"; | |
RealType result; | |
if(false == detail::check_scale(function, scale, &result, Policy())) | |
return result; | |
if(false == detail::check_location(function, location, &result, Policy())) | |
return result; | |
RealType q = c.param; | |
if(false == detail::check_probability(function, q, &result, Policy())) | |
return result; | |
using boost::math::tools::max_value; | |
if(q == 1) | |
{ | |
return -policies::raise_overflow_error<RealType>(function,"probability argument is 1, but must be >0 and <1",Policy()); | |
} | |
if(q == 0) | |
{ | |
return policies::raise_overflow_error<RealType>(function,"probability argument is 0, but must be >0 and <1",Policy()); | |
} | |
//Expressions to try | |
//return location+scale*log((1-q)/q); | |
return location + scale * log((1 - q) / q); | |
//return location-scale*log(q/(1-q)); | |
//return location-scale*log1p((2*q-1)/(1-q)); | |
//return location+scale*log(1/q-1); | |
//return location+scale*log1p(1/q-2); | |
} | |
template <class RealType, class Policy> | |
inline RealType mean(const logistic_distribution<RealType, Policy>& dist) | |
{ | |
return dist.location(); | |
} // RealType mean(const logistic_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType variance(const logistic_distribution<RealType, Policy>& dist) | |
{ | |
BOOST_MATH_STD_USING | |
RealType scale = dist.scale(); | |
return boost::math::constants::pi<RealType>()*boost::math::constants::pi<RealType>()*scale*scale/3; | |
} // RealType variance(const logistic_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType mode(const logistic_distribution<RealType, Policy>& dist) | |
{ | |
return dist.location(); | |
} | |
template <class RealType, class Policy> | |
inline RealType median(const logistic_distribution<RealType, Policy>& dist) | |
{ | |
return dist.location(); | |
} | |
template <class RealType, class Policy> | |
inline RealType skewness(const logistic_distribution<RealType, Policy>& /*dist*/) | |
{ | |
return 0; | |
} // RealType skewness(const logistic_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& /*dist*/) | |
{ | |
return static_cast<RealType>(6)/5; | |
} // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist) | |
template <class RealType, class Policy> | |
inline RealType kurtosis(const logistic_distribution<RealType, Policy>& dist) | |
{ | |
return kurtosis_excess(dist) + 3; | |
} // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist) | |
}} | |
// Must come at the end: | |
#include <boost/math/distributions/detail/derived_accessors.hpp> | |