source: trunk/sources/ALGLIB/chisquaredistr.cs @ 2563

/*************************************************************************
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 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 chisquaredistr
    {
        /*************************************************************************
        Chi-square distribution

        Returns the area under the left hand tail (from 0 to x)
        of the Chi square probability density function with
        v degrees of freedom.


                                          x
                                           -
                               1          | |  v/2-1  -t/2
         P( x | v )   =   -----------     |   t      e     dt
                           v/2  -       | |
                          2    | (v/2)   -
                                          0

        where x is the Chi-square variable.

        The incomplete gamma integral is used, according to the
        formula

        y = chdtr( v, x ) = igam( v/2.0, x/2.0 ).

        The arguments must both be positive.

        ACCURACY:

        See incomplete gamma function


        Cephes Math Library Release 2.8:  June, 2000
        Copyright 1984, 1987, 2000 by Stephen L. Moshier
        *************************************************************************/
        public static double chisquaredistribution(double v,
            double x)
        {
            double result = 0;

            System.Diagnostics.Debug.Assert((double)(x)>=(double)(0) & (double)(v)>=(double)(1), "Domain error in ChiSquareDistribution");
            result = igammaf.incompletegamma(v/2.0, x/2.0);
            return result;
        }


        /*************************************************************************
        Complemented Chi-square distribution

        Returns the area under the right hand tail (from x to
        infinity) of the Chi square probability density function
        with v degrees of freedom:

                                         inf.
                                           -
                               1          | |  v/2-1  -t/2
         P( x | v )   =   -----------     |   t      e     dt
                           v/2  -       | |
                          2    | (v/2)   -
                                          x

        where x is the Chi-square variable.

        The incomplete gamma integral is used, according to the
        formula

        y = chdtr( v, x ) = igamc( v/2.0, x/2.0 ).

        The arguments must both be positive.

        ACCURACY:

        See incomplete gamma function

        Cephes Math Library Release 2.8:  June, 2000
        Copyright 1984, 1987, 2000 by Stephen L. Moshier
        *************************************************************************/
        public static double chisquarecdistribution(double v,
            double x)
        {
            double result = 0;

            System.Diagnostics.Debug.Assert((double)(x)>=(double)(0) & (double)(v)>=(double)(1), "Domain error in ChiSquareDistributionC");
            result = igammaf.incompletegammac(v/2.0, x/2.0);
            return result;
        }


        /*************************************************************************
        Inverse of complemented Chi-square distribution

        Finds the Chi-square argument x such that the integral
        from x to infinity of the Chi-square density is equal
        to the given cumulative probability y.

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

           x/2 = igami( df/2, y );

        ACCURACY:

        See inverse incomplete gamma function


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

            System.Diagnostics.Debug.Assert((double)(y)>=(double)(0) & (double)(y)<=(double)(1) & (double)(v)>=(double)(1), "Domain error in InvChiSquareDistribution");
            result = 2*igammaf.invincompletegammac(0.5*v, y);
            return result;
        }
    }
}