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