/*************************************************************************
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier

Contributors:
    * Sergey Bochkanov (ALGLIB project). Translation from C to
      pseudocode.

See subroutines comments for additional copyrights.

>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the 
License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses

>>> END OF LICENSE >>>
*************************************************************************/

using System;

namespace alglib
{
    public class poissondistr
    {
        /*************************************************************************
        Poisson distribution

        Returns the sum of the first k+1 terms of the Poisson
        distribution:

          k         j
          --   -m  m
          >   e    --
          --       j!
         j=0

        The terms are not summed directly; instead the incomplete
        gamma integral is employed, according to the relation

        y = pdtr( k, m ) = igamc( k+1, m ).

        The arguments must both be positive.
        ACCURACY:

        See incomplete gamma function

        Cephes Math Library Release 2.8:  June, 2000
        Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
        *************************************************************************/
        public static double poissondistribution(int k,
            double m)
        {
            double result = 0;

            System.Diagnostics.Debug.Assert(k>=0 & (double)(m)>(double)(0), "Domain error in PoissonDistribution");
            result = igammaf.incompletegammac(k+1, m);
            return result;
        }


        /*************************************************************************
        Complemented Poisson distribution

        Returns the sum of the terms k+1 to infinity of the Poisson
        distribution:

         inf.       j
          --   -m  m
          >   e    --
          --       j!
         j=k+1

        The terms are not summed directly; instead the incomplete
        gamma integral is employed, according to the formula

        y = pdtrc( k, m ) = igam( k+1, m ).

        The arguments must both be positive.

        ACCURACY:

        See incomplete gamma function

        Cephes Math Library Release 2.8:  June, 2000
        Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
        *************************************************************************/
        public static double poissoncdistribution(int k,
            double m)
        {
            double result = 0;

            System.Diagnostics.Debug.Assert(k>=0 & (double)(m)>(double)(0), "Domain error in PoissonDistributionC");
            result = igammaf.incompletegamma(k+1, m);
            return result;
        }


        /*************************************************************************
        Inverse Poisson distribution

        Finds the Poisson variable x such that the integral
        from 0 to x of the Poisson density is equal to the
        given probability y.

        This is accomplished using the inverse gamma integral
        function and the relation

           m = igami( k+1, y ).

        ACCURACY:

        See inverse incomplete gamma function

        Cephes Math Library Release 2.8:  June, 2000
        Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
        *************************************************************************/
        public static double invpoissondistribution(int k,
            double y)
        {
            double result = 0;

            System.Diagnostics.Debug.Assert(k>=0 & (double)(y)>=(double)(0) & (double)(y)<(double)(1), "Domain error in InvPoissonDistribution");
            result = igammaf.invincompletegammac(k+1, y);
            return result;
        }
    }
}