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view scripts/statistics/kurtosis.m @ 28789:28de41192f3c
Eliminate unneeded verification of nargin, nargout in m-files.
* FIRfilter.m, FIRfilter_aggregation.m, get.m, polynomial.m,
polynomial_superiorto.m, polynomial2.m, makeUniqueStrings.m, base64decode.m,
base64encode.m, cd.m, lin2mu.m, record.m, sound.m, soundsc.m, accumarray.m,
accumdim.m, bitcmp.m, bitset.m, cart2pol.m, celldisp.m, circshift.m,
cplxpair.m, cumtrapz.m, flip.m, idivide.m, interpft.m, logspace.m, pol2cart.m,
polyarea.m, postpad.m, prepad.m, rat.m, rot90.m, rotdim.m, shift.m, shiftdim.m,
sortrows.m, trapz.m, dsearch.m, dsearchn.m, getappdata.m, getpixelposition.m,
guidata.m, guihandles.m, isappdata.m, listfonts.m, uigetdir.m,
waitforbuttonpress.m, __makeinfo__.m, doc.m, get_first_help_sentence.m,
autumn.m, bone.m, brighten.m, cmpermute.m, cmunique.m, colorcube.m, contrast.m,
cool.m, copper.m, cubehelix.m, flag.m, gray.m, gray2ind.m, hot.m, hsv.m,
im2double.m, im2frame.m, imformats.m, jet.m, lines.m, ocean.m, pink.m, prism.m,
rainbow.m, rgbplot.m, spinmap.m, spring.m, summer.m, viridis.m, white.m,
winter.m, beep.m, importdata.m, is_valid_file_id.m, javachk.m, javaclasspath.m,
findstr.m, genvarname.m, strmatch.m, bandwidth.m, commutation_matrix.m, cond.m,
cross.m, isdefinite.m, ishermitian.m, issymmetric.m, krylov.m, linsolve.m,
logm.m, lscov.m, null.m, ordeig.m, orth.m, rank.m, rref.m, vecnorm.m,
bunzip2.m, citation.m, computer.m, copyfile.m, dir.m, dos.m, fileattrib.m,
gunzip.m, inputParser.m, inputname.m, ismac.m, ispc.m, isunix.m, license.m,
list_primes.m, methods.m, mkdir.m, movefile.m, nargchk.m, news.m,
orderfields.m, recycle.m, tar.m, unix.m, unpack.m, untar.m, unzip.m, ver.m,
version.m, what.m, zip.m, decic.m, fminbnd.m, fminunc.m, fsolve.m, fzero.m,
glpk.m, humps.m, lsqnonneg.m, optimget.m, pqpnonneg.m, sqp.m, pathdef.m,
camlookat.m, hidden.m, specular.m, plotmatrix.m, smooth3.m, sombrero.m,
stemleaf.m, __gnuplot_drawnow__.m, __opengl_info__.m, ancestor.m, cla.m,
close.m, closereq.m, copyobj.m, gca.m, gcf.m, ginput.m, graphics_toolkit.m,
groot.m, hgload.m, hgsave.m, isgraphics.m, ishold.m, linkaxes.m, meshgrid.m,
newplot.m, refresh.m, refreshdata.m, rotate.m, saveas.m, struct2hdl.m, conv.m,
mkpp.m, mpoles.m, padecoef.m, pchip.m, polyder.m, polyfit.m, polygcd.m,
polyint.m, polyout.m, polyval.m, ppder.m, ppint.m, getpref.m, ispref.m,
rmpref.m, profexport.m, profshow.m, powerset.m, arch_fit.m, arma_rnd.m,
blackman.m, detrend.m, diffpara.m, fftconv.m, fftfilt.m, filter2.m, freqz.m,
freqz_plot.m, hamming.m, hanning.m, sinetone.m, sinewave.m, spectral_adf.m,
spectral_xdf.m, stft.m, unwrap.m, gplot.m, ichol.m, ilu.m, spdiags.m, sprand.m,
sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, betainc.m,
betaincinv.m, ellipke.m, gammainc.m, gammaincinv.m, legendre.m, pow2.m,
hankel.m, pascal.m, rosser.m, toeplitz.m, bounds.m, corr.m, cov.m, histc.m,
kendall.m, kurtosis.m, mad.m, mode.m, moment.m, prctile.m, quantile.m, range.m,
ranks.m, run_count.m, skewness.m, spearman.m, std.m, var.m, zscore.m,
dec2base.m, dec2bin.m, dec2hex.m, index.m, mat2str.m, native2unicode.m,
ostrsplit.m, strjoin.m, strjust.m, strtok.m, substr.m, unicode2native.m,
untabify.m, __debug_octave__.m, demo.m, example.m, fail.m, oruntests.m,
dump_demos.m, speed.m, test.m, date.m, datenum.m, datestr.m, datevec.m,
is_leap_year.m, now.m, weekday.m:
Eliminate unneeded verification of nargin, nargout in m-files now that
the interpreter checks these values.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 24 Sep 2020 14:44:58 -0700 |
parents | 9f9ac219896d |
children | d8318c12d903 |
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######################################################################## ## ## Copyright (C) 1996-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {} kurtosis (@var{x}) ## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}) ## @deftypefnx {} {} kurtosis (@var{x}, @var{flag}, @var{dim}) ## Compute the sample kurtosis of the elements of @var{x}. ## ## The sample kurtosis is defined as ## @tex ## $$ ## \kappa_1 = {{{1\over N}\, ## \sum_{i=1}^N (x_i - \bar{x})^4} \over \sigma^4}, ## $$ ## where $N$ is the length of @var{x}, $\bar{x}$ its mean, and $\sigma$ ## its (uncorrected) standard deviation. ## @end tex ## @ifnottex ## ## @example ## @group ## mean ((@var{x} - mean (@var{x})).^4) ## k1 = ------------------------ ## std (@var{x}).^4 ## @end group ## @end example ## ## @end ifnottex ## ## @noindent ## The optional argument @var{flag} controls which normalization is used. ## If @var{flag} is equal to 1 (default value, used when @var{flag} is omitted ## or empty), return the sample kurtosis as defined above. If @var{flag} is ## equal to 0, return the @w{"bias-corrected"} kurtosis coefficient instead: ## @tex ## $$ ## \kappa_0 = 3 + {\scriptstyle N - 1 \over \scriptstyle (N - 2)(N - 3)} \, ## \left( (N + 1)\, \kappa_1 - 3 (N - 1) \right) ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## N - 1 ## k0 = 3 + -------------- * ((N + 1) * k1 - 3 * (N - 1)) ## (N - 2)(N - 3) ## @end group ## @end example ## ## @noindent ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## The bias-corrected kurtosis coefficient is obtained by replacing the sample ## second and fourth central moments by their unbiased versions. It is an ## unbiased estimate of the population kurtosis for normal populations. ## ## If @var{x} is a matrix, or more generally a multi-dimensional array, return ## the kurtosis along the first non-singleton dimension. If the optional ## @var{dim} argument is given, operate along this dimension. ## ## @seealso{var, skewness, moment} ## @end deftypefn function y = kurtosis (x, flag, dim) if (nargin < 1) print_usage (); endif if (! (isnumeric (x) || islogical (x))) error ("kurtosis: X must be a numeric vector or matrix"); endif if (nargin < 2 || isempty (flag)) flag = 1; # default: do not use the "bias corrected" version else if (! isscalar (flag) || (flag != 0 && flag != 1)) error ("kurtosis: FLAG must be 0 or 1"); endif endif nd = ndims (x); sz = size (x); if (nargin < 3) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("kurtosis: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); sz(dim) = 1; x = center (x, dim); # center also promotes integer, logical to double v = var (x, 1, dim); # normalize with 1/N y = sum (x .^ 4, dim); idx = (v != 0); y(idx) = y(idx) ./ (n * v(idx) .^ 2); y(! idx) = NaN; ## Apply bias correction to the second and fourth central sample moment if (flag == 0) if (n > 3) C = (n - 1) / ((n - 2) * (n - 3)); y = 3 + C * ((n + 1) * y - 3 * (n - 1)); else y(:) = NaN; endif endif endfunction %!test %! x = [-1; 0; 0; 0; 1]; %! y = [x, 2*x]; %! assert (kurtosis (y), [2.5, 2.5], sqrt (eps)); %!assert (kurtosis ([-3, 0, 1]) == kurtosis ([-1, 0, 3])) %!assert (kurtosis (ones (3, 5)), NaN (1, 5)) %!assert (kurtosis (1, [], 3), NaN) %!assert (kurtosis ([1:5 10; 1:5 10], 0, 2), 5.4377317925288901 * [1; 1], 8 * eps) %!assert (kurtosis ([1:5 10; 1:5 10], 1, 2), 2.9786509002956195 * [1; 1], 8 * eps) %!assert (kurtosis ([1:5 10; 1:5 10], [], 2), 2.9786509002956195 * [1; 1], 8 * eps) ## Test behavior on single input %!assert (kurtosis (single ([1:5 10])), single (2.9786513), eps ("single")) %!assert (kurtosis (single ([1 2]), 0), single (NaN)) ## Verify no warnings %!test %! lastwarn (""); # clear last warning %! kurtosis (1); %! assert (lastwarn (), ""); ## Test input validation %!error kurtosis () %!error kurtosis (1, 2, 3) %!error <X must be a numeric vector or matrix> kurtosis (['A'; 'B']) %!error <FLAG must be 0 or 1> kurtosis (1, 2) %!error <FLAG must be 0 or 1> kurtosis (1, [1 0]) %!error <DIM must be an integer> kurtosis (1, [], ones (2,2)) %!error <DIM must be an integer> kurtosis (1, [], 1.5) %!error <DIM must be .* a valid dimension> kurtosis (1, [], 0)