From octave-sources-request at bevo dot che dot wisc dot edu Tue Aug 28 17:04:12 2001
Subject: Kolmogorov-Smirnov CDF
From: "James R. Van Zandt" <jrv at vanzandt dot mv dot com>
To: "Octave contributions" at vanzandt dot mv dot com, octave-sources@bevo.che.wisc.edu
Cc: Kurt Hornik <Kurt dot Hornik at ci dot tuwien dot ac dot at>
Date: Mon, 27 Aug 2001 21:50:38 -0400 (EDT)


Kurt Hornik contributed kolmogorov_smirnov_cdf.m to Octave some time
ago.  It's described this way:

 - Function File:  kolmogorov_smirnov_cdf (X, TOL)
     Return the CDF at X of the Kolmogorov-Smirnov distribution,
                   Inf
          Q(x) =   SUM    (-1)^k exp(-2 k^2 x^2)
                 k = -Inf

     for X > 0.

However, the Kolmogorov-Smirnov tables I have found all have two
parameters, like the chi-square distribution.  One parameter is the
number of degrees of freedom.  The other is one of three values that
indicate the difference between the cumulative distribution of the
sample, S(x[j]), and the reference cumulative distribution, F(x):
  
     Dn+ = MAX( S(x[j]) - F(x[j]) )
     Dn- = MAX( F(x[j]) - S(x[j]) )
     Dn* = MAX( ABS( S(x[j]) - F(x[j]) ) )

(I think the third "two-sided" one is the most useful version, and
that is what I have found tabulated.  Apparently it is more difficult
to calculate its distribution than the "one-sided" versions.  The
latter are implemented here:
http://www.ciphersbyritter.com/JAVASCRP/NORMCHIK.HTM)

What is the relationship between the distribution calculated by
Octave's function and the tabulated distribution?  I'd like to add
that to the documentation.

		  - Jim Van Zandt