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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}, @var{dim}) |
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22 ## If @var{x} is a vector of length @math{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 skewness along the |
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39 ## first non-singleton dimension of the matrix. If the optional |
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40 ## @var{dim} argument is given, operate along this dimension. |
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41 ## @end deftypefn |
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42 |
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43 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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44 ## Created: 29 July 1994 |
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45 ## Adapted-By: jwe |
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46 |
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47 function retval = skewness (x, dim) |
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48 |
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49 if (nargin != 1 && nargin != 2) |
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50 usage ("skewness (x, dim)"); |
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51 endif |
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52 |
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53 nd = ndims (x); |
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54 sz = size (x); |
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55 if (nargin != 2) |
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56 %% Find the first non-singleton dimension |
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57 dim = 1; |
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58 while (dim < nd + 1 && sz (dim) == 1) |
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59 dim = dim + 1; |
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60 endwhile |
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61 if (dim > nd) |
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62 dim = 1; |
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63 endif |
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64 else |
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65 if (! (isscalar (dim) && dim == round (dim)) && dim > 0 && |
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66 dim < (nd + 1)) |
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67 error ("skewness: dim must be an integer and valid dimension"); |
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68 endif |
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69 endif |
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70 |
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71 if (! ismatrix (x)) |
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72 error ("skewness: x has to be a matrix or a vector"); |
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73 endif |
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74 |
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75 c = sz (dim); |
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76 idx = ones (1, nd); |
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77 idx (dim) = c; |
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78 x = x - repmat (mean (x, dim), idx); |
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79 sz (dim) = 1; |
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80 retval = zeros (sz); |
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81 s = std (x, [], dim); |
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82 ind = find (s > 0); |
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83 x = sum (x .^ 3, dim); |
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84 retval (ind) = x (ind) ./ (c * s (ind) .^ 3); |
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85 |
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86 endfunction |
