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// 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
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