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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/non_central_f.hpp (15848B)

// boost\math\distributions\non_central_f.hpp

// Copyright John Maddock 2008.

// 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_MATH_SPECIAL_NON_CENTRAL_F_HPP
#define BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP

#include <boost/math/distributions/non_central_beta.hpp>
#include <boost/math/distributions/detail/generic_mode.hpp>
#include <boost/math/special_functions/pow.hpp>

namespace boost
{
   namespace math
   {
      template <class RealType = double, class Policy = policies::policy<> >
      class non_central_f_distribution
      {
      public:
         typedef RealType value_type;
         typedef Policy policy_type;

non_central_f_distribution(RealType v1_, RealType v2_, RealType lambda) : v1(v1_), v2(v2_), ncp(lambda)
         {
            const char* function = "boost::math::non_central_f_distribution<%1%>::non_central_f_distribution(%1%,%1%)";
            RealType r;
            detail::check_df(
               function,
               v1, &r, Policy());
            detail::check_df(
               function,
               v2, &r, Policy());
            detail::check_non_centrality(
               function,
               lambda,
               &r,
               Policy());
         } // non_central_f_distribution constructor.

RealType degrees_of_freedom1()const
         {
            return v1;
         }
         RealType degrees_of_freedom2()const
         {
            return v2;
         }
         RealType non_centrality() const
         { // Private data getter function.
            return ncp;
         }
      private:
         // Data member, initialized by constructor.
         RealType v1;   // alpha.
         RealType v2;   // beta.
         RealType ncp; // non-centrality parameter
      }; // template <class RealType, class Policy> class non_central_f_distribution

typedef non_central_f_distribution<double> non_central_f; // Reserved name of type double.

// Non-member functions to give properties of the distribution.

template <class RealType, class Policy>
      inline const std::pair<RealType, RealType> range(const non_central_f_distribution<RealType, Policy>& /* dist */)
      { // Range of permissible values for random variable k.
         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 non_central_f_distribution<RealType, Policy>& /* dist */)
      { // Range of supported values for random variable k.
         // 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 mean(const non_central_f_distribution<RealType, Policy>& dist)
      {
         const char* function = "mean(non_central_f_distribution<%1%> const&)";
         RealType v1 = dist.degrees_of_freedom1();
         RealType v2 = dist.degrees_of_freedom2();
         RealType l = dist.non_centrality();
         RealType r;
         if(!detail::check_df(
            function,
            v1, &r, Policy())
               ||
            !detail::check_df(
               function,
               v2, &r, Policy())
               ||
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy()))
               return r;
         if(v2 <= 2)
            return policies::raise_domain_error(
               function,
               "Second degrees of freedom parameter was %1%, but must be > 2 !",
               v2, Policy());
         return v2 * (v1 + l) / (v1 * (v2 - 2));
      } // mean

template <class RealType, class Policy>
      inline RealType mode(const non_central_f_distribution<RealType, Policy>& dist)
      { // mode.
         static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)";

RealType n = dist.degrees_of_freedom1();
         RealType m = dist.degrees_of_freedom2();
         RealType l = dist.non_centrality();
         RealType r;
         if(!detail::check_df(
            function,
            n, &r, Policy())
               ||
            !detail::check_df(
               function,
               m, &r, Policy())
               ||
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy()))
               return r;
         RealType guess = m > 2 ? RealType(m * (n + l) / (n * (m - 2))) : RealType(1);
         return detail::generic_find_mode(
            dist,
            guess,
            function);
      }

template <class RealType, class Policy>
      inline RealType variance(const non_central_f_distribution<RealType, Policy>& dist)
      { // variance.
         const char* function = "variance(non_central_f_distribution<%1%> const&)";
         RealType n = dist.degrees_of_freedom1();
         RealType m = dist.degrees_of_freedom2();
         RealType l = dist.non_centrality();
         RealType r;
         if(!detail::check_df(
            function,
            n, &r, Policy())
               ||
            !detail::check_df(
               function,
               m, &r, Policy())
               ||
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy()))
               return r;
         if(m <= 4)
            return policies::raise_domain_error(
               function,
               "Second degrees of freedom parameter was %1%, but must be > 4 !",
               m, Policy());
         RealType result = 2 * m * m * ((n + l) * (n + l)
            + (m - 2) * (n + 2 * l));
         result /= (m - 4) * (m - 2) * (m - 2) * n * n;
         return result;
      }

// RealType standard_deviation(const non_central_f_distribution<RealType, Policy>& dist)
      // standard_deviation provided by derived accessors.

template <class RealType, class Policy>
      inline RealType skewness(const non_central_f_distribution<RealType, Policy>& dist)
      { // skewness = sqrt(l).
         const char* function = "skewness(non_central_f_distribution<%1%> const&)";
         BOOST_MATH_STD_USING
         RealType n = dist.degrees_of_freedom1();
         RealType m = dist.degrees_of_freedom2();
         RealType l = dist.non_centrality();
         RealType r;
         if(!detail::check_df(
            function,
            n, &r, Policy())
               ||
            !detail::check_df(
               function,
               m, &r, Policy())
               ||
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy()))
               return r;
         if(m <= 6)
            return policies::raise_domain_error(
               function,
               "Second degrees of freedom parameter was %1%, but must be > 6 !",
               m, Policy());
         RealType result = 2 * constants::root_two<RealType>();
         result *= sqrt(m - 4);
         result *= (n * (m + n - 2) *(m + 2 * n - 2)
            + 3 * (m + n - 2) * (m + 2 * n - 2) * l
            + 6 * (m + n - 2) * l * l + 2 * l * l * l);
         result /= (m - 6) * pow(n * (m + n - 2) + 2 * (m + n - 2) * l + l * l, RealType(1.5f));
         return result;
      }

template <class RealType, class Policy>
      inline RealType kurtosis_excess(const non_central_f_distribution<RealType, Policy>& dist)
      {
         const char* function = "kurtosis_excess(non_central_f_distribution<%1%> const&)";
         BOOST_MATH_STD_USING
         RealType n = dist.degrees_of_freedom1();
         RealType m = dist.degrees_of_freedom2();
         RealType l = dist.non_centrality();
         RealType r;
         if(!detail::check_df(
            function,
            n, &r, Policy())
               ||
            !detail::check_df(
               function,
               m, &r, Policy())
               ||
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy()))
               return r;
         if(m <= 8)
            return policies::raise_domain_error(
               function,
               "Second degrees of freedom parameter was %1%, but must be > 8 !",
               m, Policy());
         RealType l2 = l * l;
         RealType l3 = l2 * l;
         RealType l4 = l2 * l2;
         RealType result = (3 * (m - 4) * (n * (m + n - 2)
            * (4 * (m - 2) * (m - 2)
            + (m - 2) * (m + 10) * n
            + (10 + m) * n * n)
            + 4 * (m + n - 2) * (4 * (m - 2) * (m - 2)
            + (m - 2) * (10 + m) * n
            + (10 + m) * n * n) * l + 2 * (10 + m)
            * (m + n - 2) * (2 * m + 3 * n - 4) * l2
            + 4 * (10 + m) * (-2 + m + n) * l3
            + (10 + m) * l4))
            /
            ((-8 + m) * (-6 + m) * boost::math::pow<2>(n * (-2 + m + n)
            + 2 * (-2 + m + n) * l + l2));
            return result;
      } // kurtosis_excess

template <class RealType, class Policy>
      inline RealType kurtosis(const non_central_f_distribution<RealType, Policy>& dist)
      {
         return kurtosis_excess(dist) + 3;
      }

template <class RealType, class Policy>
      inline RealType pdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
      { // Probability Density/Mass Function.
         typedef typename policies::evaluation<RealType, Policy>::type value_type;
         typedef typename policies::normalise<
            Policy,
            policies::promote_float<false>,
            policies::promote_double<false>,
            policies::discrete_quantile<>,
            policies::assert_undefined<> >::type forwarding_policy;

value_type alpha = dist.degrees_of_freedom1() / 2;
         value_type beta = dist.degrees_of_freedom2() / 2;
         value_type y = x * alpha / beta;
         value_type r = pdf(boost::math::non_central_beta_distribution<value_type, forwarding_policy>(alpha, beta, dist.non_centrality()), y / (1 + y));
         return policies::checked_narrowing_cast<RealType, forwarding_policy>(
            r * (dist.degrees_of_freedom1() / dist.degrees_of_freedom2()) / ((1 + y) * (1 + y)),
            "pdf(non_central_f_distribution<%1%>, %1%)");
      } // pdf

template <class RealType, class Policy>
      RealType cdf(const non_central_f_distribution<RealType, Policy>& dist, const RealType& x)
      {
         const char* function = "cdf(const non_central_f_distribution<%1%>&, %1%)";
         RealType r;
         if(!detail::check_df(
            function,
            dist.degrees_of_freedom1(), &r, Policy())
               ||
            !detail::check_df(
               function,
               dist.degrees_of_freedom2(), &r, Policy())
               ||
            !detail::check_non_centrality(
               function,
               dist.non_centrality(),
               &r,
               Policy()))
               return r;

if((x < 0) || !(boost::math::isfinite)(x))
         {
            return policies::raise_domain_error<RealType>(
               function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
         }

RealType alpha = dist.degrees_of_freedom1() / 2;
         RealType beta = dist.degrees_of_freedom2() / 2;
         RealType y = x * alpha / beta;
         RealType c = y / (1 + y);
         RealType cp = 1 / (1 + y);
         //
         // To ensure accuracy, we pass both x and 1-x to the
         // non-central beta cdf routine, this ensures accuracy
         // even when we compute x to be ~ 1:
         //
         r = detail::non_central_beta_cdf(c, cp, alpha, beta,
            dist.non_centrality(), false, Policy());
         return r;
      } // cdf

template <class RealType, class Policy>
      RealType cdf(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
      { // Complemented Cumulative Distribution Function
         const char* function = "cdf(complement(const non_central_f_distribution<%1%>&, %1%))";
         RealType r;
         if(!detail::check_df(
            function,
            c.dist.degrees_of_freedom1(), &r, Policy())
               ||
            !detail::check_df(
               function,
               c.dist.degrees_of_freedom2(), &r, Policy())
               ||
            !detail::check_non_centrality(
               function,
               c.dist.non_centrality(),
               &r,
               Policy()))
               return r;

if((c.param < 0) || !(boost::math::isfinite)(c.param))
         {
            return policies::raise_domain_error<RealType>(
               function, "Random Variable parameter was %1%, but must be > 0 !", c.param, Policy());
         }

RealType alpha = c.dist.degrees_of_freedom1() / 2;
         RealType beta = c.dist.degrees_of_freedom2() / 2;
         RealType y = c.param * alpha / beta;
         RealType x = y / (1 + y);
         RealType cx = 1 / (1 + y);
         //
         // To ensure accuracy, we pass both x and 1-x to the
         // non-central beta cdf routine, this ensures accuracy
         // even when we compute x to be ~ 1:
         //
         r = detail::non_central_beta_cdf(x, cx, alpha, beta,
            c.dist.non_centrality(), true, Policy());
         return r;
      } // ccdf

template <class RealType, class Policy>
      inline RealType quantile(const non_central_f_distribution<RealType, Policy>& dist, const RealType& p)
      { // Quantile (or Percent Point) function.
         RealType alpha = dist.degrees_of_freedom1() / 2;
         RealType beta = dist.degrees_of_freedom2() / 2;
         RealType x = quantile(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, dist.non_centrality()), p);
         if(x == 1)
            return policies::raise_overflow_error<RealType>(
               "quantile(const non_central_f_distribution<%1%>&, %1%)",
               "Result of non central F quantile is too large to represent.",
               Policy());
         return (x / (1 - x)) * (dist.degrees_of_freedom2() / dist.degrees_of_freedom1());
      } // quantile

template <class RealType, class Policy>
      inline RealType quantile(const complemented2_type<non_central_f_distribution<RealType, Policy>, RealType>& c)
      { // Quantile (or Percent Point) function.
         RealType alpha = c.dist.degrees_of_freedom1() / 2;
         RealType beta = c.dist.degrees_of_freedom2() / 2;
         RealType x = quantile(complement(boost::math::non_central_beta_distribution<RealType, Policy>(alpha, beta, c.dist.non_centrality()), c.param));
         if(x == 1)
            return policies::raise_overflow_error<RealType>(
               "quantile(complement(const non_central_f_distribution<%1%>&, %1%))",
               "Result of non central F quantile is too large to represent.",
               Policy());
         return (x / (1 - x)) * (c.dist.degrees_of_freedom2() / c.dist.degrees_of_freedom1());
      } // quantile complement.

} // namespace math
} // namespace boost

// 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_MATH_SPECIAL_NON_CENTRAL_F_HPP

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