source: branches/HeuristicLab.ALGLIB-2.5.0/ALGLIB-2.5.0/chisquaredistr.cs @ 5192

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


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;
    }
  }
}