/*************************************************************************
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 >>>
*************************************************************************/


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;
    }
  }
}