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annotate scripts/statistics/distributions/kolmogorov_smirnov_cdf.m @ 11523:fd0a3ac60b0e
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 14 Jan 2011 05:47:45 -0500 |
| parents | 1740012184f9 |
| children | 19b9f17d22af |
| rev | line source |
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| 11523 | 1 ## Copyright (C) 1995-2011 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 |
| 3191 | 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 ## | |
| 3191 | 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/>. | |
| 3191 | 18 |
| 3456 | 19 ## -*- texinfo -*- |
| 20 ## @deftypefn {Function File} {} kolmogorov_smirnov_cdf (@var{x}, @var{tol}) | |
| 21 ## Return the CDF at @var{x} of the Kolmogorov-Smirnov distribution, | |
| 22 ## @tex | |
| 6754 | 23 ## $$ Q(x) = \sum_{k=-\infty}^\infty (-1)^k \exp(-2 k^2 x^2) $$ |
| 3456 | 24 ## @end tex |
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25 ## @ifnottex |
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26 ## |
| 3456 | 27 ## @example |
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28 ## @group |
| 3456 | 29 ## Inf |
| 30 ## Q(x) = SUM (-1)^k exp(-2 k^2 x^2) | |
| 31 ## k = -Inf | |
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32 ## @end group |
| 3456 | 33 ## @end example |
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34 ## |
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35 ## @end ifnottex |
| 3456 | 36 ## @noindent |
| 37 ## for @var{x} > 0. | |
| 38 ## | |
| 39 ## The optional parameter @var{tol} specifies the precision up to which | |
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40 ## the series should be evaluated; the default is @var{tol} = @code{eps}. |
| 3456 | 41 ## @end deftypefn |
| 3426 | 42 |
| 5428 | 43 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 44 ## Description: CDF of the Kolmogorov-Smirnov distribution |
| 3191 | 45 |
| 46 function cdf = kolmogorov_smirnov_cdf (x, tol) | |
| 3426 | 47 |
| 3191 | 48 if (nargin < 1 || nargin > 2) |
| 6046 | 49 print_usage (); |
| 3191 | 50 endif |
| 51 | |
| 52 if (nargin == 1) | |
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53 if (isa (x, "single")) |
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54 tol = eps ("single"); |
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55 else |
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56 tol = eps; |
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57 endif |
| 3426 | 58 else |
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59 if (! (isscalar (tol) && (tol > 0))) |
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60 error ("kolmogorov_smirnov_cdf: TOL must be a positive scalar"); |
| 3191 | 61 endif |
| 62 endif | |
| 63 | |
| 4859 | 64 n = numel (x); |
| 65 if (n == 0) | |
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66 error ("kolmogorov_smirnov_cdf: X must not be empty"); |
| 3191 | 67 endif |
| 68 | |
| 4859 | 69 cdf = zeros (size (x)); |
| 70 | |
| 3191 | 71 ind = find (x > 0); |
| 72 if (length (ind) > 0) | |
| 4859 | 73 if (size(ind,2) < size(ind,1)) |
| 74 y = x(ind.'); | |
| 75 else | |
| 76 y = x(ind); | |
| 77 endif | |
| 3457 | 78 K = ceil (sqrt (- log (tol) / 2) / min (y)); |
| 3191 | 79 k = (1:K)'; |
| 3457 | 80 A = exp (- 2 * k.^2 * y.^2); |
| 3191 | 81 odd = find (rem (k, 2) == 1); |
| 3457 | 82 A(odd,:) = -A(odd,:); |
| 3191 | 83 cdf(ind) = 1 + 2 * sum (A); |
| 84 endif | |
| 85 | |
| 86 endfunction |