You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
299 lines
11 KiB
299 lines
11 KiB
// 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) |
|
|
|
#ifndef BOOST_MATH_DISTRIBUTIONS_LOGISTIC |
|
#define BOOST_MATH_DISTRIBUTIONS_LOGISTIC |
|
|
|
#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 l_location=0, RealType l_scale=1) // Constructor. |
|
: m_location(l_location), m_scale(l_scale) |
|
{ |
|
static const char* function = "boost::math::logistic_distribution<%1%>::logistic_distribution"; |
|
|
|
RealType result; |
|
detail::check_scale(function, l_scale, &result, Policy()); |
|
detail::check_location(function, l_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>( |
|
std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), |
|
std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>()); |
|
} |
|
|
|
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) |
|
{ |
|
static const char* function = "boost::math::pdf(const logistic_distribution<%1%>&, %1%)"; |
|
RealType scale = dist.scale(); |
|
RealType location = dist.location(); |
|
RealType result = 0; |
|
|
|
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)) |
|
{ |
|
return 0; // pdf + and - infinity is zero. |
|
} |
|
|
|
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 = 0; // 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 = 0; |
|
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%)"; |
|
|
|
RealType result = 0; |
|
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 1; // cdf complement -infinity is unity. |
|
return 0; // cdf complement +infinity is zero. |
|
} |
|
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 = 0; |
|
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> |
|
|
|
#endif // BOOST_MATH_DISTRIBUTIONS_LOGISTIC
|
|
|