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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## -*- texinfo -*- |
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18 ## @deftypefn {Function File} {[@var{pval}, @var{ks}] =} kolmogorov_smirnov_test_2 (@var{x}, @var{y}, @var{alt}) |
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19 ## Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis |
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20 ## that the samples @var{x} and @var{y} come from the same (continuous) |
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21 ## distribution. I.e., if F and G are the CDFs corresponding to the |
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22 ## @var{x} and @var{y} samples, respectively, then the null is that F == |
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23 ## G. |
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24 ## |
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25 ## With the optional argument string @var{alt}, the alternative of |
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26 ## interest can be selected. If @var{alt} is @code{"!="} or |
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27 ## @code{"<>"}, the null is tested against the two-sided alternative F |
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28 ## != G. In this case, the test statistic @var{ks} follows a two-sided |
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29 ## Kolmogorov-Smirnov distribution. If @var{alt} is @code{">"}, the |
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30 ## one-sided alternative F > G is considered, similarly for @code{"<"}. |
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31 ## In this case, the test statistic @var{ks} has a one-sided |
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32 ## Kolmogorov-Smirnov distribution. The default is the two-sided case. |
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33 ## |
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34 ## The p-value of the test is returned in @var{pval}. |
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35 ## |
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36 ## If no output argument is given, the p-value is displayed. |
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37 ## @end deftypefn |
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38 |
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39 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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40 ## Description: Two-sample Kolmogorov-Smirnov test |
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41 |
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42 function [pval, ks] = kolmogorov_smirnov_test_2 (x, y, alt) |
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43 |
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44 if (nargin < 2 || nargin > 3) |
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45 usage ("[pval, ks] = kolmogorov_smirnov_test_2 (x, y, tol)"); |
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46 endif |
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47 |
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48 if !( is_vector (x) && is_vector (y)) |
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49 error ("kolmogorov_smirnov_test_2: both x and y must be vectors."); |
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50 endif |
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51 |
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52 if (nargin == 2) |
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53 alt = "!="; |
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54 else |
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55 if (! isstr (alt)) |
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56 error ("kolmogorov_smirnov_test_2: alt must be a string."); |
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57 endif |
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58 endif |
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59 |
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60 n_x = length (x); |
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61 n_y = length (y); |
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62 n = n_x * n_y / (n_x + n_y); |
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63 x = reshape (x, n_x, 1); |
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64 y = reshape (y, n_y, 1); |
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65 [s, i] = sort ([x; y]); |
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66 count (find (i <= n_x)) = 1 / n_x; |
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67 count (find (i > n_x)) = - 1 / n_y; |
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68 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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69 ks = sqrt (n) * max (abs (cumsum (count))); |
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70 pval = 1 - kolmogorov_smirnov_cdf (ks); |
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71 elseif (strcmp (alt, ">")) |
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72 ks = sqrt (n) * max (cumsum (count)); |
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73 pval = exp(- 2 * ks^2); |
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74 elseif (strcmp(alt, "<")) |
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75 ks = - sqrt (n) * min (cumsum (count)); |
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76 pval = exp(- 2 * ks^2); |
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77 else |
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78 error ("kolmogorov_smirnov_test_2: option %s not recognized", alt); |
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79 endif |
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80 |
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81 if (nargout == 0) |
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82 printf (" pval: %g\n", pval); |
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83 endif |
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84 |
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85 endfunction |
