non_central_beta.hpp

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               Policy, 
               policies::promote_float<false>, 
               policies::promote_double<false>, 
               policies::discrete_quantile<>,
               policies::assert_undefined<> >::type forwarding_policy;

            value_type a = dist.alpha();
            value_type b = dist.beta();
            value_type l = dist.non_centrality();
            value_type r;
            if(!beta_detail::check_alpha(
               function,
               a, &r, Policy())
               ||
            !beta_detail::check_beta(
               function,
               b, &r, Policy())
               ||            
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy())
               ||
            !beta_detail::check_x(
               function,
               static_cast<value_type>(x),
               &r,
               Policy()))
                  return (RealType)r;

            BOOST_MATH_STD_USING
            if(l == 0)
               return pdf(boost::math::beta_distribution<RealType, Policy>(dist.alpha(), dist.beta()), x);
            return policies::checked_narrowing_cast<RealType, forwarding_policy>(
               non_central_beta_pdf(a, b, l, static_cast<value_type>(x), 1 - static_cast<value_type>(x), forwarding_policy()),
               "function");
         }

      } // namespace detail

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

         non_central_beta_distribution(RealType a_, RealType b_, RealType lambda) : a(a_), b(b_), ncp(lambda)
         { 
            const char* function = "boost::math::non_central_beta_distribution<%1%>::non_central_beta_distribution(%1%,%1%)";
            RealType r;
            beta_detail::check_alpha(
               function,
               a, &r, Policy());
            beta_detail::check_beta(
               function,
               b, &r, Policy());
            detail::check_non_centrality(
               function,
               lambda,
               &r,
               Policy());
         } // non_central_beta_distribution constructor.

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

      typedef non_central_beta_distribution<double> non_central_beta; // 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_beta_distribution<RealType, Policy>& /* dist */)
      { // Range of permissible values for random variable k.
         using boost::math::tools::max_value;
         return std::pair<RealType, RealType>(0, 1);
      }

      template <class RealType, class Policy>
      inline const std::pair<RealType, RealType> support(const non_central_beta_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, 1);
      }

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

         RealType a = dist.alpha();
         RealType b = dist.beta();
         RealType l = dist.non_centrality();
         RealType r;
         if(!beta_detail::check_alpha(
               function,
               a, &r, Policy())
               ||
            !beta_detail::check_beta(
               function,
               b, &r, Policy())
               ||            
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy()))
                  return (RealType)r;
         RealType c = a + b + l / 2;
         RealType mean = 1 - (b / c) * (1 + l / (2 * c * c));
         return detail::generic_find_mode_01(
            dist, 
            mean, 
            function);
      }

#if 0
      //
      // We don't have the necessary information to implement
      // these at present.  These are just disabled for now,
      // prototypes retained so we can fill in the blanks
      // later:
      //
      template <class RealType, class Policy>
      inline RealType mean(const non_central_beta_distribution<RealType, Policy>& dist)
      { 
         // TODO
         return 0;
      } // mean

      template <class RealType, class Policy>
      inline RealType variance(const non_central_beta_distribution<RealType, Policy>& dist)
      { // variance.
         const char* function = "boost::math::non_central_beta_distribution<%1%>::variance()";
         // TODO
         return 0;
      }

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

      template <class RealType, class Policy>
      inline RealType skewness(const non_central_beta_distribution<RealType, Policy>& dist)
      { // skewness = sqrt(l).
         const char* function = "boost::math::non_central_beta_distribution<%1%>::skewness()";
         // TODO
         return 0;
      }

      template <class RealType, class Policy>
      inline RealType kurtosis_excess(const non_central_beta_distribution<RealType, Policy>& dist)
      { 
         const char* function = "boost::math::non_central_beta_distribution<%1%>::kurtosis_excess()";
         // TODO
         return 0;
      } // kurtosis_excess

      template <class RealType, class Policy>
      inline RealType kurtosis(const non_central_beta_distribution<RealType, Policy>& dist)
      {
         return kurtosis_excess(dist) + 3;
      }
#endif
      template <class RealType, class Policy>
      inline RealType pdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
      { // Probability Density/Mass Function.
         return detail::nc_beta_pdf(dist, x);
      } // pdf

      template <class RealType, class Policy>
      RealType cdf(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& x)
      { 
         const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
            RealType a = dist.alpha();
            RealType b = dist.beta();
            RealType l = dist.non_centrality();
            RealType r;
            if(!beta_detail::check_alpha(
               function,
               a, &r, Policy())
               ||
            !beta_detail::check_beta(
               function,
               b, &r, Policy())
               ||            
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy())
               ||
            !beta_detail::check_x(
               function,
               x,
               &r,
               Policy()))
                  return (RealType)r;

         if(l == 0)
            return cdf(beta_distribution<RealType, Policy>(a, b), x);

         return detail::non_central_beta_cdf(x, 1 - x, a, b, l, false, Policy());
      } // cdf

      template <class RealType, class Policy>
      RealType cdf(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c)
      { // Complemented Cumulative Distribution Function
         const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
         non_central_beta_distribution<RealType, Policy> const& dist = c.dist;
            RealType a = dist.alpha();
            RealType b = dist.beta();
            RealType l = dist.non_centrality();
            RealType x = c.param;
            RealType r;
            if(!beta_detail::check_alpha(
               function,
               a, &r, Policy())
               ||
            !beta_detail::check_beta(
               function,
               b, &r, Policy())
               ||            
            !detail::check_non_centrality(
               function,
               l,
               &r,
               Policy())
               ||
            !beta_detail::check_x(
               function,
               x,
               &r,
               Policy()))
                  return (RealType)r;

         if(l == 0)
            return cdf(complement(beta_distribution<RealType, Policy>(a, b), x));

         return detail::non_central_beta_cdf(x, 1 - x, a, b, l, true, Policy());
      } // ccdf

      template <class RealType, class Policy>
      inline RealType quantile(const non_central_beta_distribution<RealType, Policy>& dist, const RealType& p)
      { // Quantile (or Percent Point) function.
         return detail::nc_beta_quantile(dist, p, false);
      } // quantile

      template <class RealType, class Policy>
      inline RealType quantile(const complemented2_type<non_central_beta_distribution<RealType, Policy>, RealType>& c)
      { // Quantile (or Percent Point) function.
         return detail::nc_beta_quantile(c.dist, c.param, true);
      } // 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_BETA_HPP