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annotate scripts/statistics/base/kurtosis.m @ 9245:16f53d29049f
update copyright notices
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 22 May 2009 10:46:00 -0400 |
| parents | f0c3d3fc4903 |
| children | 95c3e38098bf |
| rev | line source |
|---|---|
| 7017 | 1 ## Copyright (C) 1996, 1997, 1998, 1999, 2000, 2002, 2004, 2005, 2006, |
| 8920 | 2 ## 2007, 2008, 2009 John W. Eaton |
| 3200 | 3 ## |
| 4 ## This file is part of Octave. | |
| 5 ## | |
| 6 ## Octave is free software; you can redistribute it and/or modify it | |
| 7 ## under the terms of the GNU General Public License as published by | |
| 7016 | 8 ## the Free Software Foundation; either version 3 of the License, or (at |
| 9 ## your option) any later version. | |
| 3200 | 10 ## |
| 11 ## Octave is distributed in the hope that it will be useful, but | |
| 12 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 14 ## General Public License for more details. | |
| 15 ## | |
| 16 ## You should have received a copy of the GNU General Public License | |
| 7016 | 17 ## along with Octave; see the file COPYING. If not, see |
| 18 ## <http://www.gnu.org/licenses/>. | |
| 3200 | 19 |
| 3367 | 20 ## -*- texinfo -*- |
| 4885 | 21 ## @deftypefn {Function File} {} kurtosis (@var{x}, @var{dim}) |
| 3499 | 22 ## If @var{x} is a vector of length @math{N}, return the kurtosis |
| 3367 | 23 ## @tex |
| 24 ## $$ | |
| 25 ## {\rm kurtosis} (x) = {1\over N \sigma(x)^4} \sum_{i=1}^N (x_i-\bar{x})^4 - 3 | |
| 26 ## $$ | |
| 6754 | 27 ## where $\bar{x}$ is the mean value of $x$. |
| 3367 | 28 ## @end tex |
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29 ## @ifnottex |
| 3426 | 30 ## |
| 3367 | 31 ## @example |
| 32 ## kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3 | |
| 33 ## @end example | |
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34 ## @end ifnottex |
| 3426 | 35 ## |
| 3367 | 36 ## @noindent |
| 4885 | 37 ## of @var{x}. If @var{x} is a matrix, return the kurtosis over the |
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38 ## first non-singleton dimension. The optional argument @var{dim} |
| 4885 | 39 ## can be given to force the kurtosis to be given over that |
| 40 ## dimension. | |
| 3367 | 41 ## @end deftypefn |
| 3200 | 42 |
| 5428 | 43 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3200 | 44 ## Created: 29 July 1994 |
| 45 ## Adapted-By: jwe | |
| 46 | |
| 4885 | 47 function retval = kurtosis (x, dim) |
| 3200 | 48 |
| 4885 | 49 if (nargin != 1 && nargin != 2) |
| 6046 | 50 print_usage (); |
| 3200 | 51 endif |
| 52 | |
| 4885 | 53 nd = ndims (x); |
| 54 sz = size (x); | |
| 55 if (nargin != 2) | |
| 4886 | 56 ## Find the first non-singleton dimension. |
| 4885 | 57 dim = 1; |
| 4886 | 58 while (dim < nd + 1 && sz(dim) == 1) |
| 4885 | 59 dim = dim + 1; |
| 60 endwhile | |
| 61 if (dim > nd) | |
| 62 dim = 1; | |
| 3200 | 63 endif |
| 64 else | |
| 4886 | 65 if (! (isscalar (dim) && dim == round (dim)) |
| 66 && dim > 0 | |
| 67 && dim < (nd + 1)) | |
| 4885 | 68 error ("kurtosis: dim must be an integer and valid dimension"); |
| 69 endif | |
| 70 endif | |
| 71 | |
| 72 if (! ismatrix (x)) | |
| 3458 | 73 error ("kurtosis: x has to be a matrix or a vector"); |
| 3200 | 74 endif |
| 75 | |
| 4886 | 76 c = sz(dim); |
| 77 sz(dim) = 1; | |
| 4885 | 78 idx = ones (1, nd); |
| 4886 | 79 idx(dim) = c; |
| 4885 | 80 x = x - repmat (mean (x, dim), idx); |
| 81 retval = zeros (sz); | |
| 82 s = std (x, [], dim); | |
| 83 x = sum(x.^4, dim); | |
| 84 ind = find (s > 0); | |
| 4886 | 85 retval(ind) = x(ind) ./ (c * s(ind) .^ 4) - 3; |
| 4885 | 86 |
| 3200 | 87 endfunction |
| 7411 | 88 |
| 89 %!test | |
| 90 %! x = [-1; 0; 0; 0; 1]; | |
| 91 %! y = [x, 2*x]; | |
| 92 %! assert(all (abs (kurtosis (y) - [-1.4, -1.4]) < sqrt (eps))); | |
| 93 | |
| 94 %!error kurtosis (); | |
| 95 | |
| 96 %!error kurtosis (1, 2, 3); | |
| 97 |