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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} {[@var{pval}, @var{ks}] =} kolmogorov_smirnov_test (@var{x}, @var{dist}, @var{params}, @var{alt}) |
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21 ## Perform a Kolmogorov-Smirnov test of the null hypothesis that the |
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22 ## sample @var{x} comes from the (continuous) distribution dist. I.e., |
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23 ## if F and G are the CDFs corresponding to the sample and dist, |
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24 ## respectively, then the null is that F == G. |
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25 ## |
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26 ## The optional argument @var{params} contains a list of parameters of |
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27 ## @var{dist}. For example, to test whether a sample @var{x} comes from |
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28 ## a uniform distribution on [2,4], use |
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29 ## |
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30 ## @example |
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31 ## kolmogorov_smirnov_test(x, "uniform", 2, 4) |
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32 ## @end example |
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33 ## |
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34 ## @noindent |
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35 ## @var{dist} can be any string for which a function @var{dist_cdf} |
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36 ## that calculates the CDF of distribution @var{dist} exists. |
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37 ## |
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38 ## With the optional argument string @var{alt}, the alternative of |
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39 ## interest can be selected. If @var{alt} is @code{"!="} or |
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40 ## @code{"<>"}, the null is tested against the two-sided alternative F |
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41 ## != G. In this case, the test statistic @var{ks} follows a two-sided |
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42 ## Kolmogorov-Smirnov distribution. If @var{alt} is @code{">"}, the |
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43 ## one-sided alternative F > G is considered. Similarly for @code{"<"}, |
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44 ## the one-sided alternative F > G is considered. In this case, the |
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45 ## test statistic @var{ks} has a one-sided Kolmogorov-Smirnov |
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46 ## distribution. The default is the two-sided case. |
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47 ## |
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48 ## The p-value of the test is returned in @var{pval}. |
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49 ## |
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50 ## If no output argument is given, the p-value is displayed. |
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51 ## @end deftypefn |
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52 |
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53 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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54 ## Description: One-sample Kolmogorov-Smirnov test |
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55 |
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56 function [pval, ks] = kolmogorov_smirnov_test (x, dist, varargin) |
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57 |
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58 if (nargin < 2) |
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59 print_usage (); |
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60 endif |
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61 |
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62 if (! isvector (x)) |
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63 error ("kolmogorov_smirnov_test: x must be a vector"); |
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64 endif |
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65 |
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66 n = length (x); |
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67 s = sort (x); |
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68 f = str2func (sprintf ("%s_cdf", dist)); |
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69 |
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70 alt = "!="; |
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71 |
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72 if (nargin == 2) |
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73 z = reshape (feval (f, s), 1, n); |
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74 else |
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75 args = ""; |
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76 for k = 1 : (nargin-2); |
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77 tmp = varargin{k}; |
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78 if ischar (tmp) |
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79 alt = tmp; |
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80 else |
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81 args = sprintf ("%s, %g", args, tmp); |
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82 endif |
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83 endfor |
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84 z = reshape (eval (sprintf ("%s(s%s);", func2str (f), args)), 1, n); |
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85 endif |
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86 |
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87 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
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88 ks = sqrt (n) * max (max ([abs(z - (0:(n-1))/n); abs(z - (1:n)/n)])); |
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89 pval = 1 - kolmogorov_smirnov_cdf (ks); |
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90 elseif (strcmp (alt, ">")) |
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91 ks = sqrt (n) * max (max ([z - (0:(n-1))/n; z - (1:n)/n])); |
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92 pval = exp (- 2 * ks^2); |
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93 elseif (strcmp (alt, "<")) |
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94 ks = - sqrt (n) * min (min ([z - (0:(n-1))/n; z - (1:n)/n])); |
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95 pval = exp (- 2 * ks^2); |
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96 else |
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97 error ("kolmogorov_smirnov_test: alternative %s not recognized", alt); |
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98 endif |
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99 |
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100 if (nargout == 0) |
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101 printf ("pval: %g\n", pval); |
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102 endif |
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103 |
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104 endfunction |
