Chris@16: //  Copyright Paul A. Bristow 2007.
Chris@16: //  Use, modification and distribution are subject to the
Chris@16: //  Boost Software License, Version 1.0. (See accompanying file
Chris@16: //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_STATS_rayleigh_HPP
Chris@16: #define BOOST_STATS_rayleigh_HPP
Chris@16: 
Chris@16: #include <boost/math/distributions/fwd.hpp>
Chris@16: #include <boost/math/constants/constants.hpp>
Chris@16: #include <boost/math/special_functions/log1p.hpp>
Chris@16: #include <boost/math/special_functions/expm1.hpp>
Chris@16: #include <boost/math/distributions/complement.hpp>
Chris@16: #include <boost/math/distributions/detail/common_error_handling.hpp>
Chris@16: #include <boost/config/no_tr1/cmath.hpp>
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: # pragma warning(push)
Chris@16: # pragma warning(disable: 4702) // unreachable code (return after domain_error throw).
Chris@16: #endif
Chris@16: 
Chris@16: #include <utility>
Chris@16: 
Chris@16: namespace boost{ namespace math{
Chris@16: 
Chris@16: namespace detail
Chris@16: { // Error checks:
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline bool verify_sigma(const char* function, RealType sigma, RealType* presult, const Policy& pol)
Chris@16:   {
Chris@16:      if((sigma <= 0) || (!(boost::math::isfinite)(sigma)))
Chris@16:      {
Chris@16:         *presult = policies::raise_domain_error<RealType>(
Chris@16:            function,
Chris@16:            "The scale parameter \"sigma\" must be > 0 and finite, but was: %1%.", sigma, pol);
Chris@16:         return false;
Chris@16:      }
Chris@16:      return true;
Chris@16:   } // bool verify_sigma
Chris@16: 
Chris@16:   template <class RealType, class Policy>
Chris@16:   inline bool verify_rayleigh_x(const char* function, RealType x, RealType* presult, const Policy& pol)
Chris@16:   {
Chris@16:      if((x < 0) || (boost::math::isnan)(x))
Chris@16:      {
Chris@16:         *presult = policies::raise_domain_error<RealType>(
Chris@16:            function,
Chris@16:            "The random variable must be >= 0, but was: %1%.", x, pol);
Chris@16:         return false;
Chris@16:      }
Chris@16:      return true;
Chris@16:   } // bool verify_rayleigh_x
Chris@16: } // namespace detail
Chris@16: 
Chris@16: template <class RealType = double, class Policy = policies::policy<> >
Chris@16: class rayleigh_distribution
Chris@16: {
Chris@16: public:
Chris@16:    typedef RealType value_type;
Chris@16:    typedef Policy policy_type;
Chris@16: 
Chris@16:    rayleigh_distribution(RealType l_sigma = 1)
Chris@16:       : m_sigma(l_sigma)
Chris@16:    {
Chris@16:       RealType err;
Chris@16:       detail::verify_sigma("boost::math::rayleigh_distribution<%1%>::rayleigh_distribution", l_sigma, &err, Policy());
Chris@16:    } // rayleigh_distribution
Chris@16: 
Chris@16:    RealType sigma()const
Chris@16:    { // Accessor.
Chris@16:      return m_sigma;
Chris@16:    }
Chris@16: 
Chris@16: private:
Chris@16:    RealType m_sigma;
Chris@16: }; // class rayleigh_distribution
Chris@16: 
Chris@16: typedef rayleigh_distribution<double> rayleigh;
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline const std::pair<RealType, RealType> range(const rayleigh_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>(static_cast<RealType>(0), 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 rayleigh_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>(static_cast<RealType>(0),  max_value<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType pdf(const rayleigh_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std function exp.
Chris@16: 
Chris@16:    RealType sigma = dist.sigma();
Chris@16:    RealType result = 0;
Chris@16:    static const char* function = "boost::math::pdf(const rayleigh_distribution<%1%>&, %1%)";
Chris@16:    if(false == detail::verify_sigma(function, sigma, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if(false == detail::verify_rayleigh_x(function, x, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if((boost::math::isinf)(x))
Chris@16:    {
Chris@16:       return 0;
Chris@16:    }
Chris@16:    RealType sigmasqr = sigma * sigma;
Chris@16:    result = x * (exp(-(x * x) / ( 2 * sigmasqr))) / sigmasqr;
Chris@16:    return result;
Chris@16: } // pdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const rayleigh_distribution<RealType, Policy>& dist, const RealType& x)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    RealType sigma = dist.sigma();
Chris@16:    static const char* function = "boost::math::cdf(const rayleigh_distribution<%1%>&, %1%)";
Chris@16:    if(false == detail::verify_sigma(function, sigma, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if(false == detail::verify_rayleigh_x(function, x, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    result = -boost::math::expm1(-x * x / ( 2 * sigma * sigma), Policy());
Chris@16:    return result;
Chris@16: } // cdf
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const rayleigh_distribution<RealType, Policy>& dist, const RealType& p)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    RealType sigma = dist.sigma();
Chris@16:    static const char* function = "boost::math::quantile(const rayleigh_distribution<%1%>&, %1%)";
Chris@16:    if(false == detail::verify_sigma(function, sigma, &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 0;
Chris@16:    }
Chris@16:    if(p == 1)
Chris@16:    {
Chris@16:      return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    }
Chris@16:    result = sqrt(-2 * sigma * sigma * boost::math::log1p(-p, Policy()));
Chris@16:    return result;
Chris@16: } // quantile
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType cdf(const complemented2_type<rayleigh_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    RealType sigma = c.dist.sigma();
Chris@16:    static const char* function = "boost::math::cdf(const rayleigh_distribution<%1%>&, %1%)";
Chris@16:    if(false == detail::verify_sigma(function, sigma, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    RealType x = c.param;
Chris@16:    if(false == detail::verify_rayleigh_x(function, x, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@101:    RealType ea = x * x / (2 * sigma * sigma);
Chris@101:    // Fix for VC11/12 x64 bug in exp(float):
Chris@101:    if (ea >= tools::max_value<RealType>())
Chris@101: 	   return 0;
Chris@101:    result =  exp(-ea);
Chris@16:    return result;
Chris@16: } // cdf complement
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType quantile(const complemented2_type<rayleigh_distribution<RealType, Policy>, RealType>& c)
Chris@16: {
Chris@16:    BOOST_MATH_STD_USING // for ADL of std functions, log & sqrt.
Chris@16: 
Chris@16:    RealType result = 0;
Chris@16:    RealType sigma = c.dist.sigma();
Chris@16:    static const char* function = "boost::math::quantile(const rayleigh_distribution<%1%>&, %1%)";
Chris@16:    if(false == detail::verify_sigma(function, sigma, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    RealType q = c.param;
Chris@16:    if(false == detail::check_probability(function, q, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    if(q == 1)
Chris@16:    {
Chris@16:       return 0;
Chris@16:    }
Chris@16:    if(q == 0)
Chris@16:    {
Chris@16:      return policies::raise_overflow_error<RealType>(function, 0, Policy());
Chris@16:    }
Chris@16:    result = sqrt(-2 * sigma * sigma * log(q));
Chris@16:    return result;
Chris@16: } // quantile complement
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mean(const rayleigh_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    RealType result = 0;
Chris@16:    RealType sigma = dist.sigma();
Chris@16:    static const char* function = "boost::math::mean(const rayleigh_distribution<%1%>&, %1%)";
Chris@16:    if(false == detail::verify_sigma(function, sigma, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    using boost::math::constants::root_half_pi;
Chris@16:    return sigma * root_half_pi<RealType>();
Chris@16: } // mean
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType variance(const rayleigh_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    RealType result = 0;
Chris@16:    RealType sigma = dist.sigma();
Chris@16:    static const char* function = "boost::math::variance(const rayleigh_distribution<%1%>&, %1%)";
Chris@16:    if(false == detail::verify_sigma(function, sigma, &result, Policy()))
Chris@16:    {
Chris@16:       return result;
Chris@16:    }
Chris@16:    using boost::math::constants::four_minus_pi;
Chris@16:    return four_minus_pi<RealType>() * sigma * sigma / 2;
Chris@16: } // variance
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType mode(const rayleigh_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    return dist.sigma();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType median(const rayleigh_distribution<RealType, Policy>& dist)
Chris@16: {
Chris@16:    using boost::math::constants::root_ln_four;
Chris@16:    return root_ln_four<RealType>() * dist.sigma();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType skewness(const rayleigh_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:   // using namespace boost::math::constants;
Chris@16:   return static_cast<RealType>(0.63111065781893713819189935154422777984404221106391L);
Chris@16:   // Computed using NTL at 150 bit, about 50 decimal digits.
Chris@16:   // return 2 * root_pi<RealType>() * pi_minus_three<RealType>() / pow23_four_minus_pi<RealType>();
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis(const rayleigh_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:   // using namespace boost::math::constants;
Chris@16:   return static_cast<RealType>(3.2450893006876380628486604106197544154170667057995L);
Chris@16:   // Computed using NTL at 150 bit, about 50 decimal digits.
Chris@16:   // return 3 - (6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
Chris@16:   // (four_minus_pi<RealType>() * four_minus_pi<RealType>());
Chris@16: }
Chris@16: 
Chris@16: template <class RealType, class Policy>
Chris@16: inline RealType kurtosis_excess(const rayleigh_distribution<RealType, Policy>& /*dist*/)
Chris@16: {
Chris@16:   //using namespace boost::math::constants;
Chris@16:   // Computed using NTL at 150 bit, about 50 decimal digits.
Chris@16:   return static_cast<RealType>(0.2450893006876380628486604106197544154170667057995L);
Chris@16:   // return -(6 * pi<RealType>() * pi<RealType>() - 24 * pi<RealType>() + 16) /
Chris@16:   //   (four_minus_pi<RealType>() * four_minus_pi<RealType>());
Chris@16: } // kurtosis
Chris@16: 
Chris@16: } // namespace math
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #ifdef BOOST_MSVC
Chris@16: # pragma warning(pop)
Chris@16: #endif
Chris@16: 
Chris@16: // This include must be at the end, *after* the accessors
Chris@16: // for this distribution have been defined, in order to
Chris@16: // keep compilers that support two-phase lookup happy.
Chris@16: #include <boost/math/distributions/detail/derived_accessors.hpp>
Chris@16: 
Chris@16: #endif // BOOST_STATS_rayleigh_HPP