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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 ## usage: kolmogorov_smirnov_cdf (x [, tol]) |
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18 ## |
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19 ## Returns the CDF at x of the Kolmogorov-Smirnov distribution, |
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20 ## i.e. Q(x) = sum_{k=-\infty}^\infty (-1)^k exp(-2 k^2 x^2), x > 0. |
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21 ## |
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22 ## The optional tol specifies the precision up to which the series |
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23 ## should be evaluated; the default is tol = eps. |
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24 |
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25 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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26 ## Description: CDF of the Kolmogorov-Smirnov distribution |
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27 |
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28 function cdf = kolmogorov_smirnov_cdf (x, tol) |
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29 |
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30 if (nargin < 1 || nargin > 2) |
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31 usage ("kolmogorov_smirnov_cdf (x [, tol])"); |
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32 endif |
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33 |
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34 if (nargin == 1) |
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35 tol = eps; |
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36 else |
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37 if (!is_scalar (tol) || !(tol > 0)) |
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38 error (["kolmogorov_smirnov_cdf: ", ... |
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39 "tol has to be a positive scalar."]); |
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40 endif |
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41 endif |
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42 |
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43 [nr, nc] = size(x); |
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44 if (min (nr, nc) == 0) |
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45 error ("kolmogorov_smirnov_cdf: x must not be empty."); |
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46 endif |
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47 |
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48 n = nr * nc; |
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49 x = reshape (x, 1, n); |
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50 cdf = zeros (1, n); |
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51 ind = find (x > 0); |
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52 if (length (ind) > 0) |
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53 y = x(ind); |
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54 K = ceil( sqrt( - log (tol) / 2 ) / min (y) ); |
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55 k = (1:K)'; |
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56 A = exp( - 2 * k.^2 * y.^2 ); |
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57 odd = find (rem (k, 2) == 1); |
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58 A(odd, :) = -A(odd, :); |
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59 cdf(ind) = 1 + 2 * sum (A); |
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60 endif |
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61 |
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62 cdf = reshape (cdf, nr, nc); |
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63 |
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64 endfunction |
