Mercurial > octave-nkf
view scripts/statistics/base/kurtosis.m @ 12575:d0b799dafede
Grammarcheck files for 3.4.1 release.
author | Rik <octave@nomad.inbox5.com> |
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date | Mon, 04 Apr 2011 15:33:46 -0700 |
parents | c792872f8942 |
children | 6b2f14af2360 |
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## Copyright (C) 1996-2011 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 3 of the License, 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, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} kurtosis (@var{x}) ## @deftypefnx {Function File} {} kurtosis (@var{x}, @var{dim}) ## Compute the kurtosis of the elements of the vector @var{x}. ## @tex ## $$ ## {\rm kurtosis} (x) = {1\over N \sigma^4} \sum_{i=1}^N (x_i-\bar{x})^4 - 3 ## $$ ## where $\bar{x}$ is the mean value of $x$. ## @end tex ## @ifnottex ## ## @example ## kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3 ## @end example ## ## @end ifnottex ## If @var{x} is a matrix, return the kurtosis over the ## first non-singleton dimension of the matrix. If the optional ## @var{dim} argument is given, operate along this dimension. ## ## Note: The definition of kurtosis above yields a kurtosis of zero for the ## stdnormal distribution and is sometimes referred to as "excess kurtosis". ## To calculate kurtosis without the normalization factor of @math{-3} use ## @code{moment (@var{x}, 4, 'c') / std (@var{x})^4}. ## @seealso{var, skewness, moment} ## @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) print_usage (); endif if (!isnumeric (x)) error ("kurtosis: X must be a numeric vector or matrix"); endif nd = ndims (x); sz = size (x); if (nargin != 2) ## Find the first non-singleton dimension. dim = find (sz > 1, 1); if (isempty (dim)) dim = 1; endif else if (!(isscalar (dim) && dim == fix (dim)) || !(1 <= dim && dim <= nd)) error ("kurtosis: DIM must be an integer and a valid dimension"); endif endif c = sz(dim); sz(dim) = 1; idx = ones (1, nd); idx(dim) = c; x = x - repmat (mean (x, dim), idx); retval = zeros (sz, class (x)); s = std (x, [], dim); x = sum (x.^4, dim); ind = find (s > 0); retval(ind) = x(ind) ./ (c * s(ind) .^ 4) - 3; endfunction %!test %! x = [-1; 0; 0; 0; 1]; %! y = [x, 2*x]; %! assert(all (abs (kurtosis (y) - [-1.4, -1.4]) < sqrt (eps))); %% Test input validation %!error kurtosis () %!error kurtosis (1, 2, 3) %!error kurtosis (true(1,2)) %!error kurtosis (1, ones(2,2)) %!error kurtosis (1, 1.5) %!error kurtosis (1, 0) %!error kurtosis (1, 3)