Mercurial > octave-nkf
view scripts/statistics/base/kurtosis.m @ 5540:cda6a105ae9a before-ov-branch
[project @ 2005-11-17 05:47:13 by jwe]
author | jwe |
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date | Thu, 17 Nov 2005 05:47:13 +0000 |
parents | 2a16423e4aa0 |
children | 34f96dd5441b |
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## Copyright (C) 1996, 1997 John W. Eaton ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 2, or (at your option) ## any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, write to the Free ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA ## 02110-1301, USA. ## -*- texinfo -*- ## @deftypefn {Function File} {} kurtosis (@var{x}, @var{dim}) ## If @var{x} is a vector of length @math{N}, return the kurtosis ## @iftex ## @tex ## $$ ## {\rm kurtosis} (x) = {1\over N \sigma(x)^4} \sum_{i=1}^N (x_i-\bar{x})^4 - 3 ## $$ ## @end tex ## @end iftex ## @ifinfo ## ## @example ## kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3 ## @end example ## @end ifinfo ## ## @noindent ## of @var{x}. If @var{x} is a matrix, return the kurtosis over the ## first non-singleton dimension. The optional argument @var{dim} ## can be given to force the kurtosis to be given over that ## dimension. ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Created: 29 July 1994 ## Adapted-By: jwe function retval = kurtosis (x, dim) if (nargin != 1 && nargin != 2) usage ("kurtosis (x, dim)"); endif nd = ndims (x); sz = size (x); if (nargin != 2) ## Find the first non-singleton dimension. dim = 1; while (dim < nd + 1 && sz(dim) == 1) dim = dim + 1; endwhile if (dim > nd) dim = 1; endif else if (! (isscalar (dim) && dim == round (dim)) && dim > 0 && dim < (nd + 1)) error ("kurtosis: dim must be an integer and valid dimension"); endif endif if (! ismatrix (x)) error ("kurtosis: x has to be a matrix or a vector"); endif c = sz(dim); sz(dim) = 1; idx = ones (1, nd); idx(dim) = c; x = x - repmat (mean (x, dim), idx); retval = zeros (sz); s = std (x, [], dim); x = sum(x.^4, dim); ind = find (s > 0); retval(ind) = x(ind) ./ (c * s(ind) .^ 4) - 3; endfunction