Mercurial > hg > octave-lyh
annotate scripts/statistics/tests/kolmogorov_smirnov_test.m @ 14554:69eec23c8b3d
allow kron to work for two diag matrix arguments (bug #35647)
* kron.cc (dispatch_kron): Fix recursive call for case of two diagonal
matrix objects as arguments. New tests.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Thu, 12 Apr 2012 14:01:39 -0400 |
| parents | f3d52523cde1 |
| children | 5d3a684236b0 |
| rev | line source |
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1 ## Copyright (C) 1995-2012 Kurt Hornik |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 3200 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 3200 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 18 |
| 3454 | 19 ## -*- texinfo -*- |
| 20 ## @deftypefn {Function File} {[@var{pval}, @var{ks}] =} kolmogorov_smirnov_test (@var{x}, @var{dist}, @var{params}, @var{alt}) | |
| 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., |
| 3454 | 23 ## if F and G are the CDFs corresponding to the sample and dist, |
| 24 ## respectively, then the null is that F == G. | |
| 3200 | 25 ## |
| 3454 | 26 ## The optional argument @var{params} contains a list of parameters of |
| 27 ## @var{dist}. For example, to test whether a sample @var{x} comes from | |
| 28 ## a uniform distribution on [2,4], use | |
| 3200 | 29 ## |
| 3454 | 30 ## @example |
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31 ## kolmogorov_smirnov_test(x, "unif", 2, 4) |
| 3454 | 32 ## @end example |
| 3200 | 33 ## |
| 6754 | 34 ## @noindent |
| 35 ## @var{dist} can be any string for which a function @var{dist_cdf} | |
| 36 ## that calculates the CDF of distribution @var{dist} exists. | |
| 37 ## | |
| 3454 | 38 ## With the optional argument string @var{alt}, the alternative of |
| 39 ## interest can be selected. If @var{alt} is @code{"!="} or | |
| 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 |
| 3454 | 42 ## Kolmogorov-Smirnov distribution. If @var{alt} is @code{">"}, the |
| 3457 | 43 ## one-sided alternative F > G is considered. Similarly for @code{"<"}, |
| 44 ## the one-sided alternative F > G is considered. In this case, the | |
| 45 ## test statistic @var{ks} has a one-sided Kolmogorov-Smirnov | |
| 46 ## distribution. The default is the two-sided case. | |
| 3200 | 47 ## |
| 3454 | 48 ## The p-value of the test is returned in @var{pval}. |
| 3200 | 49 ## |
| 50 ## If no output argument is given, the p-value is displayed. | |
| 3454 | 51 ## @end deftypefn |
| 3200 | 52 |
| 5428 | 53 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 54 ## Description: One-sample Kolmogorov-Smirnov test |
| 3200 | 55 |
| 3979 | 56 function [pval, ks] = kolmogorov_smirnov_test (x, dist, varargin) |
| 3426 | 57 |
| 3200 | 58 if (nargin < 2) |
| 6046 | 59 print_usage (); |
| 3200 | 60 endif |
| 61 | |
| 4030 | 62 if (! isvector (x)) |
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63 error ("kolmogorov_smirnov_test: X must be a vector"); |
| 3200 | 64 endif |
| 65 | |
| 66 n = length (x); | |
| 67 s = sort (x); | |
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68 try |
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69 f = str2func (sprintf ("%scdf", dist)); |
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70 catch |
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71 try |
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72 f = str2func (sprintf ("%s_cdf", dist)); |
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73 catch |
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74 error ("kolmogorov_smirnov_test: no %scdf or %s_cdf function found", |
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75 dist, dist); |
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76 end_try_catch |
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77 end_try_catch |
| 3200 | 78 |
| 79 alt = "!="; | |
| 3426 | 80 |
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81 args{1} = s; |
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82 nvargs = numel (varargin); |
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83 if (nvargs > 0) |
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84 if (ischar (varargin{end})) |
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85 alt = varargin{end}; |
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86 args(2:nvargs) = varargin(1:end-1); |
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87 else |
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88 args(2:nvargs+1) = varargin; |
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89 endif |
| 3426 | 90 endif |
| 3200 | 91 |
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92 z = reshape (feval (f, args{:}), 1, n); |
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93 |
| 3200 | 94 if (strcmp (alt, "!=") || strcmp (alt, "<>")) |
| 3456 | 95 ks = sqrt (n) * max (max ([abs(z - (0:(n-1))/n); abs(z - (1:n)/n)])); |
| 3200 | 96 pval = 1 - kolmogorov_smirnov_cdf (ks); |
| 97 elseif (strcmp (alt, ">")) | |
| 3456 | 98 ks = sqrt (n) * max (max ([z - (0:(n-1))/n; z - (1:n)/n])); |
| 99 pval = exp (- 2 * ks^2); | |
| 3200 | 100 elseif (strcmp (alt, "<")) |
| 3456 | 101 ks = - sqrt (n) * min (min ([z - (0:(n-1))/n; z - (1:n)/n])); |
| 102 pval = exp (- 2 * ks^2); | |
| 3200 | 103 else |
| 3456 | 104 error ("kolmogorov_smirnov_test: alternative %s not recognized", alt); |
| 3200 | 105 endif |
| 3426 | 106 |
| 3200 | 107 if (nargout == 0) |
| 3456 | 108 printf ("pval: %g\n", pval); |
| 3200 | 109 endif |
| 3426 | 110 |
| 3200 | 111 endfunction |
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112 |
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113 |
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114 ## test for recognition of unifcdf function |
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115 %!assert (kolmogorov_smirnov_test (0:100, "unif", 0, 100), 1.0, eps) |
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116 ## test for recognition of logistic_cdf function |
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117 %!assert (kolmogorov_smirnov_test (0:100, "logistic"), 0) |
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118 ## test for F < G |
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119 %!assert (kolmogorov_smirnov_test (50:100, "unif", 0, 50, "<")) |
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120 |
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121 %!error kolmogorov_smirnov_test (1) |
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122 %!error <X must be a vector> kolmogorov_smirnov_test ({}, "unif", 2, 4) |
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123 %!error <no not_a_distcdf or not_a_dist_cdf function found> |
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124 %! kolmogorov_smirnov_test (1, "not_a_dist"); |
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125 %!error <alternative foo not recognized> |
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126 %! kolmogorov_smirnov_test (1, "unif", 2, 4, "foo"); |
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127 |