Mercurial > octave-nkf
annotate scripts/statistics/tests/kolmogorov_smirnov_test_2.m @ 10793:be55736a0783
Grammarcheck the documentation from m-files.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 18 Jul 2010 20:35:16 -0700 |
| parents | eb63fbe60fab |
| children | 1740012184f9 |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1995, 1996, 1997, 1998, 2000, 2002, 2004, 2005, 2006, |
| 8920 | 2 ## 2007, 2009 Kurt Hornik |
| 3426 | 3 ## |
| 3922 | 4 ## This file is part of Octave. |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3426 | 10 ## |
| 3922 | 11 ## Octave is distributed in the hope that it will be useful, but |
| 3200 | 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 14 ## General Public License for more details. |
| 15 ## | |
| 3200 | 16 ## You should have received a copy of the GNU General Public License |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 19 |
| 3454 | 20 ## -*- texinfo -*- |
| 3604 | 21 ## @deftypefn {Function File} {[@var{pval}, @var{ks}, @var{d}] =} kolmogorov_smirnov_test_2 (@var{x}, @var{y}, @var{alt}) |
| 3454 | 22 ## Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis |
| 23 ## that the samples @var{x} and @var{y} come from the same (continuous) | |
| 24 ## distribution. I.e., if F and G are the CDFs corresponding to the | |
| 25 ## @var{x} and @var{y} samples, respectively, then the null is that F == | |
| 26 ## G. | |
| 3200 | 27 ## |
| 3454 | 28 ## With the optional argument string @var{alt}, the alternative of |
| 29 ## interest can be selected. If @var{alt} is @code{"!="} or | |
| 30 ## @code{"<>"}, the null is tested against the two-sided alternative F | |
|
10793
be55736a0783
Grammarcheck the documentation from m-files.
Rik <octave@nomad.inbox5.com>
parents:
8920
diff
changeset
|
31 ## != G@. In this case, the test statistic @var{ks} follows a two-sided |
| 3454 | 32 ## Kolmogorov-Smirnov distribution. If @var{alt} is @code{">"}, the |
| 3457 | 33 ## one-sided alternative F > G is considered. Similarly for @code{"<"}, |
| 34 ## the one-sided alternative F < G is considered. In this case, the | |
| 35 ## test statistic @var{ks} has a one-sided Kolmogorov-Smirnov | |
| 36 ## distribution. The default is the two-sided case. | |
| 3200 | 37 ## |
| 3454 | 38 ## The p-value of the test is returned in @var{pval}. |
| 3200 | 39 ## |
| 3604 | 40 ## The third returned value, @var{d}, is the test statistic, the maximum |
| 41 ## vertical distance between the two cumulative distribution functions. | |
| 42 ## | |
| 3426 | 43 ## If no output argument is given, the p-value is displayed. |
| 3454 | 44 ## @end deftypefn |
| 3200 | 45 |
| 5428 | 46 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 47 ## Description: Two-sample Kolmogorov-Smirnov test |
| 3200 | 48 |
| 3604 | 49 function [pval, ks, d] = kolmogorov_smirnov_test_2 (x, y, alt) |
| 3426 | 50 |
| 3200 | 51 if (nargin < 2 || nargin > 3) |
| 6046 | 52 print_usage (); |
| 3200 | 53 endif |
| 54 | |
| 4030 | 55 if (! (isvector (x) && isvector (y))) |
| 3458 | 56 error ("kolmogorov_smirnov_test_2: both x and y must be vectors"); |
| 3200 | 57 endif |
| 58 | |
| 59 if (nargin == 2) | |
| 60 alt = "!="; | |
| 3426 | 61 else |
| 5443 | 62 if (! ischar (alt)) |
| 3458 | 63 error ("kolmogorov_smirnov_test_2: alt must be a string"); |
| 3200 | 64 endif |
| 65 endif | |
| 66 | |
| 67 n_x = length (x); | |
| 68 n_y = length (y); | |
| 69 n = n_x * n_y / (n_x + n_y); | |
| 70 x = reshape (x, n_x, 1); | |
| 71 y = reshape (y, n_y, 1); | |
| 72 [s, i] = sort ([x; y]); | |
| 73 count (find (i <= n_x)) = 1 / n_x; | |
| 74 count (find (i > n_x)) = - 1 / n_y; | |
| 3604 | 75 |
| 4689 | 76 z = cumsum (count); |
| 77 ds = diff (s); | |
| 78 if (any (ds == 0)) | |
| 3604 | 79 ## There are some ties, so keep only those changes. |
| 8664 | 80 warning ("cannot compute correct p-values with ties"); |
| 4689 | 81 elems = [find(ds); n_x+n_y]; |
| 3604 | 82 z = z(elems); |
| 83 endif | |
| 84 | |
| 3200 | 85 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
| 3604 | 86 d = max (abs (z)); |
| 87 ks = sqrt (n) * d; | |
| 3200 | 88 pval = 1 - kolmogorov_smirnov_cdf (ks); |
| 89 elseif (strcmp (alt, ">")) | |
| 3604 | 90 d = max (z); |
| 91 ks = sqrt (n) * d; | |
| 92 pval = exp (-2 * ks^2); | |
| 93 elseif (strcmp (alt, "<")) | |
| 94 d = min (z); | |
| 95 ks = -sqrt (n) * d; | |
| 96 pval = exp (-2 * ks^2); | |
| 3200 | 97 else |
| 3456 | 98 error ("kolmogorov_smirnov_test_2: option %s not recognized", alt); |
| 3200 | 99 endif |
| 3426 | 100 |
| 3200 | 101 if (nargout == 0) |
| 3456 | 102 printf (" pval: %g\n", pval); |
| 3200 | 103 endif |
| 104 | |
| 105 endfunction |