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view scripts/statistics/base/kurtosis.m @ 14327:4d917a6a858b stable
doc: Use Octave coding conventions in @example blocks of docstrings.
* accumarray.m, accumdim.m, bar.m, base2dec.m, bincoeff.m, bitcmp.m, bitset.m,
celldisp.m, chop.m, clabel.m, cloglog.m, colon.m, compass.m, computer.m,
contour3.m, contourc.m, corr.m, cstrcat.m, ctime.m, cylinder.m, date.m,
dec2base.m, demo.m, dir.m, dlmwrite.m, expm.m, ezcontourf.m, ezcontour.m,
ezmeshc.m, ezmesh.m, ezplot.m, ezsurfc.m, ezsurf.m, feather.m, findobj.m,
flipdim.m, fplot.m, genvarname.m, getfield.m, hankel.m, hilb.m, hist.m,
idivide.m, index.m, int2str.m, interp1.m, is_leap_year.m, ismember.m,
isocolors.m, isonormals.m, isosurface.m, kurtosis.m, legendre.m, linkprop.m,
logit.m, logm.m, __makeinfo__.m, __marching_cube__.m, median.m, mkoctfile.m,
moment.m, mpoles.m, orderfields.m, pcg.m, pcr.m, plot3.m, plotmatrix.m,
polyaffine.m, polygcd.m, poly.m, polyout.m, print.m, qp.m, quadgk.m, qzhess.m,
randi.m, rat.m, refreshdata.m, residue.m, rose.m, rot90.m, saveas.m, saveobj.m,
shiftdim.m, skewness.m, spaugment.m, spdiags.m, sqp.m, stem.m, str2num.m,
strcat.m, strjust.m, strread.m, strsplit.m, structfun.m, subplot.m,
subsindex.m, substruct.m, surfl.m, surfnorm.m, svds.m, uimenu.m, union.m,
voronoi.m, warning_ids.m, wblpdf.m: Use Octave coding conventions in
@example blocks of docstrings.
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Sat, 04 Feb 2012 22:12:50 -0800 |
parents | 72c96de7a403 |
children | f3d52523cde1 |
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## Copyright (C) 1996-2012 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) = 1/N 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) || islogical (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)) || (dim = 1); else if (!(isscalar (dim) && dim == fix (dim)) || !(1 <= dim && dim <= nd)) error ("kurtosis: DIM must be an integer and a valid dimension"); endif endif n = sz(dim); sz(dim) = 1; x = center (x, dim); # center also promotes integer to double for next line retval = zeros (sz, class (x)); s = std (x, [], dim); idx = find (s > 0); x = sum (x.^4, dim); retval(idx) = x(idx) ./ (n * s(idx) .^ 4) - 3; endfunction %!test %! x = [-1; 0; 0; 0; 1]; %! y = [x, 2*x]; %! assert (kurtosis (y), [-1.4, -1.4], sqrt (eps)); %!assert (kurtosis (single(1)), single(0)); %% Test input validation %!error kurtosis () %!error kurtosis (1, 2, 3) %!error kurtosis (['A'; 'B']) %!error kurtosis (1, ones(2,2)) %!error kurtosis (1, 1.5) %!error kurtosis (1, 0) %!error kurtosis (1, 3)