Chris@16: // Copyright 2008 Gautam Sewani
Chris@16: //
Chris@16: // Use, modification and distribution are subject to the
Chris@16: // Boost Software License, Version 1.0.
Chris@16: // (See accompanying file LICENSE_1_0.txt
Chris@16: // or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_MATH_DISTRIBUTIONS_LOGISTIC
Chris@16: #define BOOST_MATH_DISTRIBUTIONS_LOGISTIC
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: #include <boost/math/distributions/complement.hpp>
Chris@16: #include <boost/math/special_functions/log1p.hpp>
Chris@16: #include <boost/math/constants/constants.hpp>
Chris@16: #include <utility>
Chris@16: 
Chris@16: namespace boost { namespace math { 
Chris@16: 
Chris@16:     template <class RealType = double, class Policy = policies::policy<> >
Chris@16:     class logistic_distribution
Chris@16:     {
Chris@16:     public:
Chris@16:       typedef RealType value_type;
Chris@16:       typedef Policy policy_type;
Chris@16:       
Chris@16:       logistic_distribution(RealType l_location=0, RealType l_scale=1) // Constructor.
Chris@16:         : m_location(l_location), m_scale(l_scale) 
Chris@16:       {
Chris@16:         static const char* function = "boost::math::logistic_distribution<%1%>::logistic_distribution";
Chris@16:         
Chris@16:         RealType result;
Chris@16:         detail::check_scale(function, l_scale, &result, Policy());
Chris@16:         detail::check_location(function, l_location, &result, Policy());
Chris@16:       }
Chris@16:       // Accessor functions.
Chris@16:       RealType scale()const
Chris@16:       {
Chris@16:         return m_scale;
Chris@16:       }
Chris@16:       
Chris@16:       RealType location()const
Chris@16:       {
Chris@16:         return m_location;
Chris@16:       }
Chris@16:     private:
Chris@16:       // Data members:
Chris@16:       RealType m_location;  // distribution location aka mu.
Chris@16:       RealType m_scale;  // distribution scale aka s.
Chris@16:     }; // class logistic_distribution
Chris@16:     
Chris@16:     
Chris@16:     typedef logistic_distribution<double> logistic;
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline const std::pair<RealType, RealType> range(const logistic_distribution<RealType, Policy>& /* dist */)
Chris@16:     { // Range of permissible values for random variable x.
Chris@16:       using boost::math::tools::max_value;
Chris@16:       return std::pair<RealType, RealType>(
Chris@16:          std::numeric_limits<RealType>::has_infinity ? -std::numeric_limits<RealType>::infinity() : -max_value<RealType>(), 
Chris@16:          std::numeric_limits<RealType>::has_infinity ? std::numeric_limits<RealType>::infinity() : max_value<RealType>());
Chris@16:     }
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline const std::pair<RealType, RealType> support(const logistic_distribution<RealType, Policy>& /* dist */)
Chris@16:     { // Range of supported values for random variable x.
Chris@16:       // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
Chris@16:       using boost::math::tools::max_value;
Chris@16:       return std::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + infinity
Chris@16:     }
Chris@16:      
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType pdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16:     {
Chris@16:        static const char* function = "boost::math::pdf(const logistic_distribution<%1%>&, %1%)";
Chris@16:        RealType scale = dist.scale();
Chris@16:        RealType location = dist.location();
Chris@16:        RealType result = 0;
Chris@16: 
Chris@16:        if(false == detail::check_scale(function, scale , &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16:        if(false == detail::check_location(function, location, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16: 
Chris@16:        if((boost::math::isinf)(x))
Chris@16:        {
Chris@16:           return 0; // pdf + and - infinity is zero.
Chris@16:        }
Chris@16: 
Chris@16:        if(false == detail::check_x(function, x, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16: 
Chris@16:        BOOST_MATH_STD_USING
Chris@16:        RealType exp_term = (location - x) / scale;
Chris@16:        if(fabs(exp_term) > tools::log_max_value<RealType>())
Chris@16:           return 0;
Chris@16:        exp_term = exp(exp_term);
Chris@16:        if((exp_term * scale > 1) && (exp_term > tools::max_value<RealType>() / (scale * exp_term)))
Chris@16:           return 1 / (scale * exp_term);
Chris@16:        return (exp_term) / (scale * (1 + exp_term) * (1 + exp_term));
Chris@16:     } 
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType cdf(const logistic_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16:     {
Chris@16:        RealType scale = dist.scale();
Chris@16:        RealType location = dist.location();
Chris@16:        RealType result = 0; // of checks.
Chris@16:        static const char* function = "boost::math::cdf(const logistic_distribution<%1%>&, %1%)";
Chris@16:        if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16:        if(false == detail::check_location(function, location, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16: 
Chris@16:        if((boost::math::isinf)(x))
Chris@16:        {
Chris@16:           if(x < 0) return 0; // -infinity
Chris@16:           return 1; // + infinity
Chris@16:        }
Chris@16: 
Chris@16:        if(false == detail::check_x(function, x, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16:        BOOST_MATH_STD_USING
Chris@16:        RealType power = (location - x) / scale;
Chris@16:        if(power > tools::log_max_value<RealType>())
Chris@16:           return 0;
Chris@16:        if(power < -tools::log_max_value<RealType>())
Chris@16:           return 1;
Chris@16:        return 1 / (1 + exp(power)); 
Chris@16:     } 
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16:     {
Chris@16:        BOOST_MATH_STD_USING
Chris@16:        RealType location = dist.location();
Chris@16:        RealType scale = dist.scale();
Chris@16: 
Chris@16:        static const char* function = "boost::math::quantile(const logistic_distribution<%1%>&, %1%)";
Chris@16: 
Chris@16:        RealType result = 0;
Chris@16:        if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:           return result;
Chris@16:        if(false == detail::check_location(function, location, &result, Policy()))
Chris@16:           return result;
Chris@16:        if(false == detail::check_probability(function, p, &result, Policy()))
Chris@16:           return result;
Chris@16: 
Chris@16:        if(p == 0)
Chris@16:        {
Chris@16:           return -policies::raise_overflow_error<RealType>(function,"probability argument is 0, must be >0 and <1",Policy());
Chris@16:        }
Chris@16:        if(p == 1)
Chris@16:        {
Chris@16:           return policies::raise_overflow_error<RealType>(function,"probability argument is 1, must be >0 and <1",Policy());
Chris@16:        }
Chris@16:        //Expressions to try
Chris@16:        //return location+scale*log(p/(1-p));
Chris@16:        //return location+scale*log1p((2*p-1)/(1-p));
Chris@16: 
Chris@16:        //return location - scale*log( (1-p)/p);
Chris@16:        //return location - scale*log1p((1-2*p)/p);
Chris@16: 
Chris@16:        //return -scale*log(1/p-1) + location;
Chris@16:        return location - scale * log((1 - p) / p);
Chris@16:      } // RealType quantile(const logistic_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType cdf(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c)
Chris@16:     {
Chris@16:        BOOST_MATH_STD_USING
Chris@16:        RealType location = c.dist.location();
Chris@16:        RealType scale = c.dist.scale();
Chris@16:        RealType x = c.param;
Chris@16:        static const char* function = "boost::math::cdf(const complement(logistic_distribution<%1%>&), %1%)";
Chris@16: 
Chris@16:        RealType result = 0;
Chris@16:        if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16:        if(false == detail::check_location(function, location, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16:        if((boost::math::isinf)(x))
Chris@16:        {
Chris@16:           if(x < 0) return 1; // cdf complement -infinity is unity.
Chris@16:           return 0; // cdf complement +infinity is zero.
Chris@16:        }
Chris@16:        if(false == detail::check_x(function, x, &result, Policy()))
Chris@16:        {
Chris@16:           return result;
Chris@16:        }
Chris@16:        RealType power = (x - location) / scale;
Chris@16:        if(power > tools::log_max_value<RealType>())
Chris@16:           return 0;
Chris@16:        if(power < -tools::log_max_value<RealType>())
Chris@16:           return 1;
Chris@16:        return 1 / (1 + exp(power)); 
Chris@16:     } 
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType quantile(const complemented2_type<logistic_distribution<RealType, Policy>, RealType>& c)
Chris@16:     {
Chris@16:        BOOST_MATH_STD_USING
Chris@16:        RealType scale = c.dist.scale();
Chris@16:        RealType location = c.dist.location();
Chris@16:        static const char* function = "boost::math::quantile(const complement(logistic_distribution<%1%>&), %1%)";
Chris@16:        RealType result = 0;
Chris@16:        if(false == detail::check_scale(function, scale, &result, Policy()))
Chris@16:           return result;
Chris@16:        if(false == detail::check_location(function, location, &result, Policy()))
Chris@16:           return result;
Chris@16:        RealType q = c.param;
Chris@16:        if(false == detail::check_probability(function, q, &result, Policy()))
Chris@16:           return result;
Chris@16:        using boost::math::tools::max_value;
Chris@16: 
Chris@16:        if(q == 1)
Chris@16:        {
Chris@16:           return -policies::raise_overflow_error<RealType>(function,"probability argument is 1, but must be >0 and <1",Policy());
Chris@16:        }
Chris@16:        if(q == 0)
Chris@16:        {
Chris@16:           return policies::raise_overflow_error<RealType>(function,"probability argument is 0, but must be >0 and <1",Policy());
Chris@16:        }
Chris@16:        //Expressions to try 
Chris@16:        //return location+scale*log((1-q)/q);
Chris@16:        return location + scale * log((1 - q) / q);
Chris@16: 
Chris@16:        //return location-scale*log(q/(1-q));
Chris@16:        //return location-scale*log1p((2*q-1)/(1-q));
Chris@16: 
Chris@16:        //return location+scale*log(1/q-1);
Chris@16:        //return location+scale*log1p(1/q-2);
Chris@16:     } 
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType mean(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     {
Chris@16:       return dist.location();
Chris@16:     } // RealType mean(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType variance(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     {
Chris@16:       BOOST_MATH_STD_USING
Chris@16:       RealType scale = dist.scale();
Chris@16:       return boost::math::constants::pi<RealType>()*boost::math::constants::pi<RealType>()*scale*scale/3;
Chris@16:     } // RealType variance(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType mode(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     {
Chris@16:       return dist.location();
Chris@16:     }
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType median(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     {
Chris@16:       return dist.location();
Chris@16:     }
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType skewness(const logistic_distribution<RealType, Policy>& /*dist*/)
Chris@16:     {
Chris@16:       return 0;
Chris@16:     } // RealType skewness(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& /*dist*/)
Chris@16:     {
Chris@16:       return static_cast<RealType>(6)/5; 
Chris@16:     } // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist)
Chris@16: 
Chris@16:     template <class RealType, class Policy>
Chris@16:     inline RealType kurtosis(const logistic_distribution<RealType, Policy>& dist)
Chris@16:     {
Chris@16:       return kurtosis_excess(dist) + 3;
Chris@16:     } // RealType kurtosis_excess(const logistic_distribution<RealType, Policy>& dist)
Chris@16:   }}
Chris@16: 
Chris@16: 
Chris@16: // Must come at the end:
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #endif // BOOST_MATH_DISTRIBUTIONS_LOGISTIC