non_central_f.hpp

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// 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>(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>(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;
         return detail::generic_find_mode(
            dist, 
            m * (n + l) / (n * (m - 2)), 
            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());