Mercurial > octave
view scripts/statistics/base/moment.m @ 24511:4f0e6ee6c9b8 stable
Make documentation Sec 26.1 more consistent and Sec 25.4 clearer (bug #52685)
* corr.m: Add space in LaTeX formula. For the example, place variables in a
@var qualifier.
* cov.m: Use @var in LaTeX for x and y when referring to function input vector.
Correct Octave-help formula by placing parentheses around N-1 so that -1 is
in the denominator. Define N after the formula in which it is used.
* gls.m: Define what GLS stands for. Use @var instead of @math for function
input and output variables. Move the description of matrix O and scalar s
to a third paragraph, ensuring s is lower case. Give a little more context
to the description of X and Y in the second paragraph. Add an expansive
paragraph three for details about the error variables E including the
description of O and s along with their dimensions. Add "matrix" before
B and "scalar" before s for clarity. Place @var around variables r, y, x
and beta to make those upper case in Octave-help.
* histc.m: Use LaTeX math rather than @code for the @tex scenario.
* kendall.m: Treat tau differently for LaTeX and Octave-help scenarios. Add
space in LaTeX formulas. Treat tau as @var in Octave-help case. Use lower
case 'i' for index variable and upper case 'N' for vector length.
* kurtosis.m: For mean value of x, use script rather than non-script. Define
N after the formula in which it is used for Octave-help case.
* mean.m: Indicate N is number of elements. Use @var on input vector x for
Octave-help case.
* meansq.m: Indicate N is number of elements, but drop the reference to mean
value because there is none. Use @var on input vector x for Octave-help
case. Use "If x is a matrix" consistent with all others.
* median.m: Indicate N is number of elements for LaTeX case. For Octave-help
place some vertical lines to represent case curly-bracket. Place @math
around N. Define an intermediate vector S representing sorted X and use
that in the math formula.
* moment.m: Define x-bar as mean and N as number of elements. Use @var on
x and p in the Octave-help formulas.
* ols.m: Define meaning of OLS. Add @var to LaTeX variables to make them
non-script vectors. Use @var instead of @math for function input and output
variables. Use hyphens for matrix dimensions in Octave-help formula. Move
the description of matrix S to a third paragraph. Give a little more context
to the description of X and Y in the second paragraph. Add an expansive
paragraph three for details about the error variables E including the
description of matrix S along with its dimensions, ensuring S is upper case.
Add "matrix" before B for clarity. Make the definition of SIGMA one line for
appearance in Octave-help.
* prctile.m: Change a mistaken 'y' to 'q' to work in LaTeX as well.
* quantile.m: Use @var{method} rather than METHOD. Break up all the method
formulas for p(k) into LaTeX and Octave-help versions for better control.
Use upper case N for the length of P.
* skewness.m: Remove @var from x when referring to vector elements in LaTeX.
Indicate N is number of elements.
* spearman.m: Break into separate LaTeX and Octave-help cases rather than
use @code for LaTeX. Use Greek symbol rho in LaTeX.
* std.m: Add @var to x variable to indicate LaTeX or Octave-help vector. Add
clarification about N being number elements of x to both LaTeX and
Octave-help formulas.
* var.m: Indicate N is number of elements. Apply @var to x to show it is a
vector. Change == to "is equal to" for normal text.
author | Daniel J Sebald <daniel.sebald@ieee.org> |
---|---|
date | Wed, 27 Dec 2017 23:38:25 -0600 |
parents | 3ac9f9ecfae5 |
children | 3fc1c8ebe5c3 |
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## Copyright (C) 1995-2017 Kurt Hornik ## ## 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 {} {} moment (@var{x}, @var{p}) ## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{type}) ## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{dim}) ## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{type}, @var{dim}) ## @deftypefnx {} {} moment (@var{x}, @var{p}, @var{dim}, @var{type}) ## Compute the @var{p}-th central moment of the vector @var{x}: ## ## @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 ## ## 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? ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Compute moments function m = moment (x, p, opt1, opt2) if (nargin < 2 || nargin > 4) 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 moment () %!error moment (1) %!error moment (1, 2, 3, 4, 5) %!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)