FM / distributions

/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/fisher_f.hpp (14391B)

// Copyright John Maddock 2006.

// 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_DISTRIBUTIONS_FISHER_F_HPP
#define BOOST_MATH_DISTRIBUTIONS_FISHER_F_HPP

#include <boost/math/distributions/fwd.hpp>
#include <boost/math/special_functions/beta.hpp> // for incomplete beta.
#include <boost/math/distributions/complement.hpp> // complements
#include <boost/math/distributions/detail/common_error_handling.hpp> // error checks
#include <boost/math/special_functions/fpclassify.hpp>

#include <utility>

namespace boost{ namespace math{

template <class RealType = double, class Policy = policies::policy<> >
class fisher_f_distribution
{
public:
   typedef RealType value_type;
   typedef Policy policy_type;

fisher_f_distribution(const RealType& i, const RealType& j) : m_df1(i), m_df2(j)
   {
      static const char* function = "fisher_f_distribution<%1%>::fisher_f_distribution";
      RealType result;
      detail::check_df(
         function, m_df1, &result, Policy());
      detail::check_df(
         function, m_df2, &result, Policy());
   } // fisher_f_distribution

RealType degrees_of_freedom1()const
   {
      return m_df1;
   }
   RealType degrees_of_freedom2()const
   {
      return m_df2;
   }

private:
   //
   // Data members:
   //
   RealType m_df1;  // degrees of freedom are a real number.
   RealType m_df2;  // degrees of freedom are a real number.
};

typedef fisher_f_distribution<double> fisher_f;

template <class RealType, class Policy>
inline const std::pair<RealType, RealType> range(const fisher_f_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 fisher_f_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>
RealType pdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
{
   BOOST_MATH_STD_USING  // for ADL of std functions
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   static const char* function = "boost::math::pdf(fisher_f_distribution<%1%> const&, %1%)";
   if(false == (detail::check_df(
         function, df1, &error_result, Policy())
         && detail::check_df(
         function, df2, &error_result, Policy())))
      return error_result;

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());
   }

if(x == 0)
   {
      // special cases:
      if(df1 < 2)
         return policies::raise_overflow_error<RealType>(
            function, 0, Policy());
      else if(df1 == 2)
         return 1;
      else
         return 0;
   }

//
   // You reach this formula by direct differentiation of the
   // cdf expressed in terms of the incomplete beta.
   //
   // There are two versions so we don't pass a value of z
   // that is very close to 1 to ibeta_derivative: for some values
   // of df1 and df2, all the change takes place in this area.
   //
   RealType v1x = df1 * x;
   RealType result;
   if(v1x > df2)
   {
      result = (df2 * df1) / ((df2 + v1x) * (df2 + v1x));
      result *= ibeta_derivative(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy());
   }
   else
   {
      result = df2 + df1 * x;
      result = (result * df1 - x * df1 * df1) / (result * result);
      result *= ibeta_derivative(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
   }
   return result;
} // pdf

template <class RealType, class Policy>
inline RealType cdf(const fisher_f_distribution<RealType, Policy>& dist, const RealType& x)
{
   static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   if(false == detail::check_df(
         function, df1, &error_result, Policy())
         && detail::check_df(
         function, df2, &error_result, Policy()))
      return error_result;

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 v1x = df1 * x;
   //
   // There are two equivalent formulas used here, the aim is
   // to prevent the final argument to the incomplete beta
   // from being too close to 1: for some values of df1 and df2
   // the rate of change can be arbitrarily large in this area,
   // whilst the value we're passing will have lost information
   // content as a result of being 0.999999something.  Better
   // to switch things around so we're passing 1-z instead.
   //
   return v1x > df2
      ? boost::math::ibetac(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
      : boost::math::ibeta(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
} // cdf

template <class RealType, class Policy>
inline RealType quantile(const fisher_f_distribution<RealType, Policy>& dist, const RealType& p)
{
   static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   if(false == (detail::check_df(
            function, df1, &error_result, Policy())
         && detail::check_df(
            function, df2, &error_result, Policy())
         && detail::check_probability(
            function, p, &error_result, Policy())))
      return error_result;

// With optimizations turned on, gcc wrongly warns about y being used
   // uninitialized unless we initialize it to something:
   RealType x, y(0);

x = boost::math::ibeta_inv(df1 / 2, df2 / 2, p, &y, Policy());

return df2 * x / (df1 * y);
} // quantile

template <class RealType, class Policy>
inline RealType cdf(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
{
   static const char* function = "boost::math::cdf(fisher_f_distribution<%1%> const&, %1%)";
   RealType df1 = c.dist.degrees_of_freedom1();
   RealType df2 = c.dist.degrees_of_freedom2();
   RealType x = c.param;
   // Error check:
   RealType error_result = 0;
   if(false == detail::check_df(
         function, df1, &error_result, Policy())
         && detail::check_df(
         function, df2, &error_result, Policy()))
      return error_result;

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 v1x = df1 * x;
   //
   // There are two equivalent formulas used here, the aim is
   // to prevent the final argument to the incomplete beta
   // from being too close to 1: for some values of df1 and df2
   // the rate of change can be arbitrarily large in this area,
   // whilst the value we're passing will have lost information
   // content as a result of being 0.999999something.  Better
   // to switch things around so we're passing 1-z instead.
   //
   return v1x > df2
      ? boost::math::ibeta(df2 / 2, df1 / 2, df2 / (df2 + v1x), Policy())
      : boost::math::ibetac(df1 / 2, df2 / 2, v1x / (df2 + v1x), Policy());
}

template <class RealType, class Policy>
inline RealType quantile(const complemented2_type<fisher_f_distribution<RealType, Policy>, RealType>& c)
{
   static const char* function = "boost::math::quantile(fisher_f_distribution<%1%> const&, %1%)";
   RealType df1 = c.dist.degrees_of_freedom1();
   RealType df2 = c.dist.degrees_of_freedom2();
   RealType p = c.param;
   // Error check:
   RealType error_result = 0;
   if(false == (detail::check_df(
            function, df1, &error_result, Policy())
         && detail::check_df(
            function, df2, &error_result, Policy())
         && detail::check_probability(
            function, p, &error_result, Policy())))
      return error_result;

RealType x, y;

x = boost::math::ibetac_inv(df1 / 2, df2 / 2, p, &y, Policy());

return df2 * x / (df1 * y);
}

template <class RealType, class Policy>
inline RealType mean(const fisher_f_distribution<RealType, Policy>& dist)
{ // Mean of F distribution = v.
   static const char* function = "boost::math::mean(fisher_f_distribution<%1%> const&)";
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   if(false == detail::check_df(
            function, df1, &error_result, Policy())
         && detail::check_df(
            function, df2, &error_result, Policy()))
      return error_result;
   if(df2 <= 2)
   {
      return policies::raise_domain_error<RealType>(
         function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mean.", df2, Policy());
   }
   return df2 / (df2 - 2);
} // mean

template <class RealType, class Policy>
inline RealType variance(const fisher_f_distribution<RealType, Policy>& dist)
{ // Variance of F distribution.
   static const char* function = "boost::math::variance(fisher_f_distribution<%1%> const&)";
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   if(false == detail::check_df(
            function, df1, &error_result, Policy())
         && detail::check_df(
            function, df2, &error_result, Policy()))
      return error_result;
   if(df2 <= 4)
   {
      return policies::raise_domain_error<RealType>(
         function, "Second degree of freedom was %1% but must be > 4 in order for the distribution to have a valid variance.", df2, Policy());
   }
   return 2 * df2 * df2 * (df1 + df2 - 2) / (df1 * (df2 - 2) * (df2 - 2) * (df2 - 4));
} // variance

template <class RealType, class Policy>
inline RealType mode(const fisher_f_distribution<RealType, Policy>& dist)
{
   static const char* function = "boost::math::mode(fisher_f_distribution<%1%> const&)";
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   if(false == detail::check_df(
            function, df1, &error_result, Policy())
         && detail::check_df(
            function, df2, &error_result, Policy()))
      return error_result;
   if(df2 <= 2)
   {
      return policies::raise_domain_error<RealType>(
         function, "Second degree of freedom was %1% but must be > 2 in order for the distribution to have a mode.", df2, Policy());
   }
   return df2 * (df1 - 2) / (df1 * (df2 + 2));
}

//template <class RealType, class Policy>
//inline RealType median(const fisher_f_distribution<RealType, Policy>& dist)
//{ // Median of Fisher F distribution is not defined.
//  return tools::domain_error<RealType>(BOOST_CURRENT_FUNCTION, "Median is not implemented, result is %1%!", std::numeric_limits<RealType>::quiet_NaN());
//  } // median

// Now implemented via quantile(half) in derived accessors.

template <class RealType, class Policy>
inline RealType skewness(const fisher_f_distribution<RealType, Policy>& dist)
{
   static const char* function = "boost::math::skewness(fisher_f_distribution<%1%> const&)";
   BOOST_MATH_STD_USING // ADL of std names
   // See http://mathworld.wolfram.com/F-Distribution.html
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   if(false == detail::check_df(
            function, df1, &error_result, Policy())
         && detail::check_df(
            function, df2, &error_result, Policy()))
      return error_result;
   if(df2 <= 6)
   {
      return policies::raise_domain_error<RealType>(
         function, "Second degree of freedom was %1% but must be > 6 in order for the distribution to have a skewness.", df2, Policy());
   }
   return 2 * (df2 + 2 * df1 - 2) * sqrt((2 * df2 - 8) / (df1 * (df2 + df1 - 2))) / (df2 - 6);
}

template <class RealType, class Policy>
RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist);

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

template <class RealType, class Policy>
inline RealType kurtosis_excess(const fisher_f_distribution<RealType, Policy>& dist)
{
   static const char* function = "boost::math::kurtosis_excess(fisher_f_distribution<%1%> const&)";
   // See http://mathworld.wolfram.com/F-Distribution.html
   RealType df1 = dist.degrees_of_freedom1();
   RealType df2 = dist.degrees_of_freedom2();
   // Error check:
   RealType error_result = 0;
   if(false == detail::check_df(
            function, df1, &error_result, Policy())
         && detail::check_df(
            function, df2, &error_result, Policy()))
      return error_result;
   if(df2 <= 8)
   {
      return policies::raise_domain_error<RealType>(
         function, "Second degree of freedom was %1% but must be > 8 in order for the distribution to have a kurtosis.", df2, Policy());
   }
   RealType df2_2 = df2 * df2;
   RealType df1_2 = df1 * df1;
   RealType n = -16 + 20 * df2 - 8 * df2_2 + df2_2 * df2 + 44 * df1 - 32 * df2 * df1 + 5 * df2_2 * df1 - 22 * df1_2 + 5 * df2 * df1_2;
   n *= 12;
   RealType d = df1 * (df2 - 6) * (df2 - 8) * (df1 + df2 - 2);
   return n / d;
}

} // 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_DISTRIBUTIONS_FISHER_F_HPP

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