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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} kolmogorov_smirnov_cdf (@var{x}, @var{tol}) |
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21 ## Return the CDF at @var{x} of the Kolmogorov-Smirnov distribution, |
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22 ## @iftex |
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23 ## @tex |
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24 ## $$ Q(x) = \sum_{k=-\infty}^\infty (-1)^k \exp(-2 k^2 x^2) $$ |
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25 ## @end tex |
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26 ## @end iftex |
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27 ## @ifinfo |
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28 ## @example |
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29 ## Inf |
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30 ## Q(x) = SUM (-1)^k exp(-2 k^2 x^2) |
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31 ## k = -Inf |
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32 ## @end example |
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33 ## @end ifinfo |
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34 ## |
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35 ## @noindent |
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36 ## for @var{x} > 0. |
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37 ## |
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38 ## The optional parameter @var{tol} specifies the precision up to which |
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39 ## the series should be evaluated; the default is @var{tol} = @code{eps}. |
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40 ## @end deftypefn |
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41 |
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42 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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43 ## Description: CDF of the Kolmogorov-Smirnov distribution |
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44 |
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45 function cdf = kolmogorov_smirnov_cdf (x, tol) |
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46 |
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47 if (nargin < 1 || nargin > 2) |
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48 print_usage (); |
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49 endif |
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50 |
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51 if (nargin == 1) |
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52 tol = eps; |
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53 else |
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54 if (! isscalar (tol) || ! (tol > 0)) |
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55 error ("kolmogorov_smirnov_cdf: tol has to be a positive scalar"); |
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56 endif |
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57 endif |
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58 |
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59 n = numel (x); |
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60 if (n == 0) |
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61 error ("kolmogorov_smirnov_cdf: x must not be empty"); |
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62 endif |
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63 |
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64 cdf = zeros (size (x)); |
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65 |
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66 ind = find (x > 0); |
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67 if (length (ind) > 0) |
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68 if (size(ind,2) < size(ind,1)) |
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69 y = x(ind.'); |
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70 else |
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71 y = x(ind); |
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72 endif |
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73 K = ceil (sqrt (- log (tol) / 2) / min (y)); |
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74 k = (1:K)'; |
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75 A = exp (- 2 * k.^2 * y.^2); |
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76 odd = find (rem (k, 2) == 1); |
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77 A(odd,:) = -A(odd,:); |
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78 cdf(ind) = 1 + 2 * sum (A); |
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79 endif |
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80 |
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81 endfunction |
