Mercurial > octave
view scripts/statistics/kurtosis.m @ 30920:47cbc69e66cd
eliminate direct access to call stack from evaluator
The call stack is an internal implementation detail of the evaluator.
Direct access to it outside of the evlauator should not be needed.
* pt-eval.h (tree_evaluator::get_call_stack): Delete.
author | John W. Eaton <jwe@octave.org> |
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date | Fri, 08 Apr 2022 15:19:22 -0400 |
parents | 5d3faba0342e |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 1996-2022 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 {} {@var{y} =} kurtosis (@var{x}) ## @deftypefnx {} {@var{y} =} kurtosis (@var{x}, @var{flag}) ## @deftypefnx {} {@var{y} =} 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 <Invalid call> kurtosis () %!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)