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1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, 2006, |
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2 ## 2007 John W. Eaton |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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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 ## where $\bar{x}$ is the mean value of $x$. |
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29 ## @end tex |
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30 ## @end iftex |
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31 ## @ifinfo |
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32 ## |
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33 ## @example |
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34 ## skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3) |
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35 ## @end example |
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36 ## @end ifinfo |
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37 ## |
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38 ## @noindent |
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39 ## of @var{x}. If @var{x} is a matrix, return the skewness along the |
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40 ## first non-singleton dimension of the matrix. If the optional |
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41 ## @var{dim} argument is given, operate along this dimension. |
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42 ## @end deftypefn |
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43 |
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44 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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45 ## Created: 29 July 1994 |
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46 ## Adapted-By: jwe |
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47 |
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48 function retval = skewness (x, dim) |
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49 |
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50 if (nargin != 1 && nargin != 2) |
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51 print_usage (); |
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52 endif |
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53 |
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54 nd = ndims (x); |
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55 sz = size (x); |
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56 if (nargin != 2) |
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57 ## Find the first non-singleton dimension. |
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58 dim = 1; |
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59 while (dim < nd + 1 && sz(dim) == 1) |
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60 dim = dim + 1; |
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61 endwhile |
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62 if (dim > nd) |
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63 dim = 1; |
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64 endif |
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65 else |
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66 if (! (isscalar (dim) && dim == round (dim)) |
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67 && dim > 0 |
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68 && dim < (nd + 1)) |
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69 error ("skewness: dim must be an integer and valid dimension"); |
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70 endif |
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71 endif |
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72 |
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73 if (! ismatrix (x)) |
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74 error ("skewness: x has to be a matrix or a vector"); |
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75 endif |
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76 |
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77 c = sz(dim); |
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78 idx = ones (1, nd); |
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79 idx (dim) = c; |
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80 x = x - repmat (mean (x, dim), idx); |
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81 sz(dim) = 1; |
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82 retval = zeros (sz); |
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83 s = std (x, [], dim); |
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84 ind = find (s > 0); |
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85 x = sum (x .^ 3, dim); |
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86 retval(ind) = x(ind) ./ (c * s(ind) .^ 3); |
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87 |
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88 endfunction |
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89 |
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90 %!error skewness (); |
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91 |
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92 %!error skewness (1, 2, 3); |
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93 |
