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kolmogorov_smirnov_test.m

## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
## 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; either version 2, 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. 
## 
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## usage:  
##   [pval, ks] = kolmogorov_smirnov_test (x, dist [, params] [, alt])
##
##
## Performs a Kolmogorov-Smirnov test of the null hypothesis that the
## sample x comes from the (continuous) distribution dist. I.e., if F
## and G are the CDFs corresponding to the sample and dist, respectively,
## then the null is that F == G.
##
## The optional argument params contains a list of parameters of dist.
## E.g., to test whether a sample x comes from a uniform distribution on
## [2,4], use `kolmogorov_smirnov_test(x, "uniform", 2, 4)'.
##
## With the optional argument string alt, the alternative of interest
## can be selected. If alt is "!=" or "<>", the null is tested against
## the two-sided alternative F != G.  In this case, the test statistic
## ks follows a two-sided Kolmogorov-Smirnov distribution.
## If alt is ">", the one-sided alternative F > G is considered,
## similarly for "<".  In this case, the test statistic ks has a
## one-sided Kolmogorov-Smirnov distribution.
## The default is the two-sided case.
##
## pval is the p-value of the test.
##
## If no output argument is given, the p-value is displayed.

## Author:  KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description:  One-sample Kolmogorov-Smirnov test

function [pval, ks] = kolmogorov_smirnov_test (x, dist, ...)
  
  if (nargin < 2)
    error (sprintf (["usage:\n\t", ...
      "[pval, ks] = ", ...
      "kolmogorov_smirnov_test (x, dist, [, params] [, alt])"]));
  endif

  if (! is_vector (x))
    error ("kolmogorov_smirnov_test:  x must be a vector.");
  endif

  n = length (x);
  s = sort (x);
  f = sprintf ("%s_cdf", dist);

  alt  = "!=";
  
  if (nargin == 2)
    z = reshape (feval (f, s), 1, n);
  else
    args = "";
    for k = 1 : (nargin-2);
      tmp  = va_arg ();
      if isstr (tmp)
      alt = tmp;
      else
      args = sprintf ("%s, %g", args, tmp);
      endif
    endfor
    z = reshape (eval (sprintf ("%s(s%s);", f, args)), 1, n);
  endif    

  if (strcmp (alt, "!=") || strcmp (alt, "<>"))
    ks   = sqrt(n) * max(max([abs(z - (0:(n-1))/n); abs(z - (1:n)/n)]));
    pval = 1 - kolmogorov_smirnov_cdf (ks);
  elseif (strcmp (alt, ">"))
    ks   = sqrt(n) * max (max ([z - (0:(n-1))/n; z - (1:n)/n]));
    pval = exp(- 2 * ks^2);
  elseif (strcmp (alt, "<"))
    ks   = - sqrt(n) * min (min ([z - (0:(n-1))/n; z - (1:n)/n]));
    pval = exp(- 2 * ks^2);
  else
    error (sprintf (["kolmogorov_smirnov_test:  ", ...
      "alternative %s not recognized"], alt));
  endif
    
  if (nargout == 0)
    printf ("pval:  %g\n", pval);
  endif
  
endfunction

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