Mercurial > octave
view scripts/statistics/moment.m @ 33577:2506c2d30b32 bytecode-interpreter tip
maint: Merge default to bytecode-interpreter
author | Arun Giridhar <arungiridhar@gmail.com> |
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date | Sat, 11 May 2024 18:49:01 -0400 |
parents | 2e484f9f1f18 |
children |
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######################################################################## ## ## Copyright (C) 1995-2024 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{m} =} moment (@var{x}, @var{p}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{type}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{dim}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{type}, @var{dim}) ## @deftypefnx {} {@var{m} =} moment (@var{x}, @var{p}, @var{dim}, @var{type}) ## Compute the @var{p}-th central moment of the vector @var{x}. ## ## The @var{p}-th central moment of @var{x} is defined as: ## ## @tex ## $$ ## {\sum_{i=1}^N (x_i - \bar{x})^p \over N} ## $$ ## where $\bar{x}$ is the mean value of @var{x} and $N$ is the number of elements of @var{x}. ## ## ## @end tex ## @ifnottex ## ## @example ## @group ## 1/N SUM_i (@var{x}(i) - mean(@var{x}))^@var{p} ## @end group ## @end example ## ## @noindent ## where @math{N} is the length of the @var{x} vector. ## ## @end ifnottex ## ## If @var{x} is a matrix, return the row vector containing the @var{p}-th ## central moment of each column. ## ## If the optional argument @var{dim} is given, operate along this dimension. ## ## The optional string @var{type} specifies the type of moment to be computed. ## Valid options are: ## ## @table @asis ## @item @qcode{"c"} ## Central Moment (default). ## ## @item @qcode{"a"} ## @itemx @qcode{"ac"} ## Absolute Central Moment. The moment about the mean ignoring sign ## defined as ## @tex ## $$ ## {\sum_{i=1}^N {\left| x_i - \bar{x} \right|}^p \over N} ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## 1/N SUM_i (abs (@var{x}(i) - mean(@var{x})))^@var{p} ## @end group ## @end example ## ## @end ifnottex ## ## @item @qcode{"r"} ## Raw Moment. The moment about zero defined as ## ## @tex ## $$ ## {\rm moment} (x) = { \sum_{i=1}^N {x_i}^p \over N } ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## moment (@var{x}) = 1/N SUM_i @var{x}(i)^@var{p} ## @end group ## @end example ## ## @end ifnottex ## ## @item @nospell{@qcode{"ar"}} ## Absolute Raw Moment. The moment about zero ignoring sign defined as ## @tex ## $$ ## {\sum_{i=1}^N {\left| x_i \right|}^p \over N} ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## 1/N SUM_i ( abs (@var{x}(i)) )^@var{p} ## @end group ## @end example ## ## @end ifnottex ## @end table ## ## If both @var{type} and @var{dim} are given they may appear in any order. ## @seealso{var, skewness, kurtosis} ## @end deftypefn ## Can easily be made to work for continuous distributions (using quad) ## as well, but how does the general case work? function m = moment (x, p, opt1, opt2) if (nargin < 2) print_usage (); endif if (! (isnumeric (x) || islogical (x)) || isempty (x)) error ("moment: X must be a non-empty numeric matrix or vector"); endif if (! (isnumeric (p) && isscalar (p))) error ("moment: P must be a numeric scalar"); endif need_dim = false; if (nargin == 2) type = ""; need_dim = true; elseif (nargin == 3) if (ischar (opt1)) type = opt1; need_dim = true; else dim = opt1; type = ""; endif elseif (nargin == 4) if (ischar (opt1)) type = opt1; dim = opt2; elseif (ischar (opt2)) type = opt2; dim = opt1; else error ("moment: TYPE must be a string"); endif endif nd = ndims (x); sz = size (x); if (need_dim) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (! (isscalar (dim) && dim == fix (dim) && dim > 0)) error ("moment: DIM must be an integer and a valid dimension"); endif endif n = size (x, dim); if (! any (type == "r")) x = center (x, dim); endif if (any (type == "a")) x = abs (x); endif m = sum (x .^ p, dim) / n; endfunction %!shared x %! x = rand (10); %!assert (moment (x,1), mean (center (x)), eps) %!assert (moment (x,2), meansq (center (x)), eps) %!assert (moment (x,1,2), mean (center (x, 2), 2), eps) %!assert (moment (x,1,"a"), mean (abs (center (x))), eps) %!assert (moment (x,1,"r"), mean (x), eps) %!assert (moment (x,1,"ar"), mean (abs (x)), eps) %!assert (moment (single ([1 2 3]), 1, "r"), single (2)) %!assert (moment (1, 2, 4), 0) ## Test input validation %!error <Invalid call> moment () %!error <Invalid call> moment (1) %!error <X must be a non-empty numeric matrix> moment (['A'; 'B'], 2) %!error <X must be a non-empty numeric matrix> moment (ones (2,0,3), 2) %!error <P must be a numeric scalar> moment (1, true) %!error <P must be a numeric scalar> moment (1, ones (2,2)) %!error <TYPE must be a string> moment (1, 2, 3, 4) %!error <DIM must be an integer and a valid dimension> moment (1, 2, ones (2,2)) %!error <DIM must be an integer and a valid dimension> moment (1, 2, 1.5)