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/usr/include/boost/math/distributions

Name	Size	Mode	Actions
detail/	-	0755	rm
arcsine.hpp	18797	0644	edit dl rm
bernoulli.hpp	12143	0644	edit dl rm
beta.hpp	18807	0644	edit dl rm
binomial.hpp	28654	0644	edit dl rm
cauchy.hpp	12310	0644	edit dl rm
chi_squared.hpp	12242	0644	edit dl rm
complement.hpp	5978	0644	edit dl rm
empirical_cumulative_distribution_function.hpp	1886	0644	edit dl rm
exponential.hpp	8944	0644	edit dl rm
extreme_value.hpp	10491	0644	edit dl rm
find_location.hpp	6713	0644	edit dl rm
find_scale.hpp	9674	0644	edit dl rm
fisher_f.hpp	14391	0644	edit dl rm
fwd.hpp	5461	0644	edit dl rm
gamma.hpp	10660	0644	edit dl rm
geometric.hpp	21156	0644	edit dl rm
hyperexponential.hpp	21887	0644	edit dl rm
hypergeometric.hpp	12220	0644	edit dl rm
inverse_chi_squared.hpp	15202	0644	edit dl rm
inverse_gamma.hpp	15389	0644	edit dl rm
inverse_gaussian.hpp	19760	0644	edit dl rm
laplace.hpp	10580	0644	edit dl rm
logistic.hpp	11273	0644	edit dl rm
lognormal.hpp	11714	0644	edit dl rm
negative_binomial.hpp	26139	0644	edit dl rm
non_central_beta.hpp	35837	0644	edit dl rm
non_central_chi_squared.hpp	40704	0644	edit dl rm
non_central_f.hpp	15848	0644	edit dl rm
non_central_t.hpp	47973	0644	edit dl rm
normal.hpp	10768	0644	edit dl rm
pareto.hpp	15516	0644	edit dl rm
poisson.hpp	20267	0644	edit dl rm
rayleigh.hpp	10344	0644	edit dl rm
skew_normal.hpp	25646	0644	edit dl rm
students_t.hpp	18476	0644	edit dl rm
triangular.hpp	18407	0644	edit dl rm
uniform.hpp	12963	0644	edit dl rm
weibull.hpp	12081	0644	edit dl rm

Edit: /usr/include/boost/math/distributions/rayleigh.hpp (10344B)

//  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

template <class RealType, class Policy>
inline RealType entropy(const rayleigh_distribution<RealType, Policy>& dist)
{
   using std::log;
   return 1 + log(dist.sigma()*constants::one_div_root_two<RealType>()) + constants::euler<RealType>()/2;
}

} // 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

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