You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
302 lines
9.9 KiB
302 lines
9.9 KiB
5 years ago
|
// 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) || (!(boost::math::isfinite)(sigma)))
|
||
|
{
|
||
|
*presult = policies::raise_domain_error<RealType>(
|
||
|
function,
|
||
|
"The scale parameter \"sigma\" must be > 0 and finite, 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) || (boost::math::isnan)(x))
|
||
|
{
|
||
|
*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 l_sigma = 1)
|
||
|
: m_sigma(l_sigma)
|
||
|
{
|
||
|
RealType err;
|
||
|
detail::verify_sigma("boost::math::rayleigh_distribution<%1%>::rayleigh_distribution", l_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), 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 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 = 0;
|
||
|
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;
|
||
|
}
|
||
|
if((boost::math::isinf)(x))
|
||
|
{
|
||
|
return 0;
|
||
|
}
|
||
|
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 = 0;
|
||
|
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 = 0;
|
||
|
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 = 0;
|
||
|
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;
|
||
|
}
|
||
|
RealType ea = x * x / (2 * sigma * sigma);
|
||
|
// Fix for VC11/12 x64 bug in exp(float):
|
||
|
if (ea >= tools::max_value<RealType>())
|
||
|
return 0;
|
||
|
result = exp(-ea);
|
||
|
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 = 0;
|
||
|
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 = 0;
|
||
|
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 = 0;
|
||
|
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
|