Mercurial > octave-nkf
view scripts/statistics/distributions/kolmogorov_smirnov_cdf.m @ 4030:22bd65326ec1
[project @ 2002-08-09 18:58:13 by jwe]
author | jwe |
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date | Fri, 09 Aug 2002 19:00:16 +0000 |
parents | 38c61cbf086c |
children | 265d566cc770 |
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## Copyright (C) 1995, 1996, 1997 Kurt Hornik ## ## This file is part of Octave. ## ## Octave 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. ## ## Octave 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 Octave; see the file COPYING. If not, write to the Free ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA ## 02111-1307, USA. ## -*- texinfo -*- ## @deftypefn {Function File} {} kolmogorov_smirnov_cdf (@var{x}, @var{tol}) ## Return the CDF at @var{x} of the Kolmogorov-Smirnov distribution, ## @iftex ## @tex ## $$ Q(x) = sum_{k=-\infty}^\infty (-1)^k exp(-2 k^2 x^2) $$ ## @end tex ## @end iftex ## @ifinfo ## @example ## Inf ## Q(x) = SUM (-1)^k exp(-2 k^2 x^2) ## k = -Inf ## @end example ## @end ifinfo ## ## @noindent ## for @var{x} > 0. ## ## The optional parameter @var{tol} specifies the precision up to which ## the series should be evaluated; the default is @var{tol} = @code{eps}. ## @end deftypefn ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: CDF of the Kolmogorov-Smirnov distribution function cdf = kolmogorov_smirnov_cdf (x, tol) if (nargin < 1 || nargin > 2) usage ("kolmogorov_smirnov_cdf (x, tol)"); endif if (nargin == 1) tol = eps; else if (! isscalar (tol) || ! (tol > 0)) error ("kolmogorov_smirnov_cdf: tol has to be a positive scalar"); endif endif [nr, nc] = size (x); if (min (nr, nc) == 0) error ("kolmogorov_smirnov_cdf: x must not be empty"); endif n = nr * nc; x = reshape (x, 1, n); cdf = zeros (1, n); ind = find (x > 0); if (length (ind) > 0) y = x(ind); K = ceil (sqrt (- log (tol) / 2) / min (y)); k = (1:K)'; A = exp (- 2 * k.^2 * y.^2); odd = find (rem (k, 2) == 1); A(odd,:) = -A(odd,:); cdf(ind) = 1 + 2 * sum (A); endif cdf = reshape (cdf, nr, nc); endfunction