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1 ## Copyright (C) 1996, 1997 John W. Eaton |
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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 2, or (at your option) |
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8 ## 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, write to the Free |
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} skewness (@var{x}) |
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22 ## If @var{x} is a vector of length @var{N}, return the skewness |
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23 ## @iftex |
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24 ## @tex |
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25 ## $$ |
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26 ## {\rm skewness} (x) = {1\over N \sigma(x)^3} \sum_{i=1}^N (x_i-\bar{x})^3 |
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27 ## $$ |
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28 ## @end tex |
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29 ## @end iftex |
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30 ## @ifinfo |
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31 ## |
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32 ## @example |
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33 ## skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3) |
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34 ## @end example |
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35 ## @end ifinfo |
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36 ## |
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37 ## @noindent |
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38 ## of @var{x}. If @var{x} is a matrix, return the row vector containing |
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39 ## the skewness of each column. |
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40 ## @end deftypefn |
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41 |
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42 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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43 ## Created: 29 July 1994 |
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44 ## Adapted-By: jwe |
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45 |
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46 function retval = skewness (x) |
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47 |
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48 if (nargin != 1) |
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49 usage ("skewness (x)"); |
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50 endif |
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51 |
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52 if (is_vector (x)) |
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53 x = x - mean (x); |
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54 if (! any (x)) |
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55 retval = 0; |
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56 else |
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57 retval = sum (x .^ 3) / (length (x) * std (x) ^ 3); |
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58 endif |
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59 elseif (is_matrix (x)) |
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60 [nr, nc] = size (x); |
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61 x = x - ones (nr, 1) * mean (x); |
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62 retval = zeros (1, nc); |
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63 s = std (x); |
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64 ind = find (s > 0); |
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65 retval (ind) = sum (x (:, ind) .^ 3) ./ (nr * s (ind) .^ 3); |
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66 else |
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67 error ("skewness: x has to be a matrix or a vector."); |
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68 endif |
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69 |
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70 endfunction |
