// 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