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