Mercurial > octave-nkf
view scripts/statistics/base/moment.m @ 20209:d9341b422488 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed statistics/ and @ftp/ in scripts directory.
* scripts/@ftp/ascii.m, scripts/@ftp/binary.m, scripts/@ftp/cd.m,
scripts/@ftp/dir.m, scripts/@ftp/ftp.m, scripts/@ftp/mget.m,
scripts/@ftp/mput.m, scripts/statistics/base/center.m,
scripts/statistics/base/cloglog.m, scripts/statistics/base/cov.m,
scripts/statistics/base/gls.m, scripts/statistics/base/histc.m,
scripts/statistics/base/iqr.m, scripts/statistics/base/kendall.m,
scripts/statistics/base/kurtosis.m, scripts/statistics/base/logit.m,
scripts/statistics/base/lscov.m, scripts/statistics/base/mahalanobis.m,
scripts/statistics/base/mean.m, scripts/statistics/base/meansq.m,
scripts/statistics/base/median.m, scripts/statistics/base/mode.m,
scripts/statistics/base/moment.m, scripts/statistics/base/ols.m,
scripts/statistics/base/ppplot.m, scripts/statistics/base/prctile.m,
scripts/statistics/base/probit.m, scripts/statistics/base/range.m,
scripts/statistics/base/ranks.m, scripts/statistics/base/run_count.m,
scripts/statistics/base/runlength.m, scripts/statistics/base/skewness.m,
scripts/statistics/base/spearman.m, scripts/statistics/base/statistics.m,
scripts/statistics/base/std.m, scripts/statistics/base/table.m,
scripts/statistics/base/var.m, scripts/statistics/base/zscore.m,
scripts/statistics/distributions/betainv.m,
scripts/statistics/distributions/binoinv.m,
scripts/statistics/distributions/binopdf.m,
scripts/statistics/distributions/cauchy_cdf.m,
scripts/statistics/distributions/cauchy_inv.m,
scripts/statistics/distributions/cauchy_pdf.m,
scripts/statistics/distributions/chi2cdf.m,
scripts/statistics/distributions/chi2inv.m,
scripts/statistics/distributions/chi2pdf.m,
scripts/statistics/distributions/discrete_cdf.m,
scripts/statistics/distributions/discrete_inv.m,
scripts/statistics/distributions/discrete_pdf.m,
scripts/statistics/distributions/empirical_cdf.m,
scripts/statistics/distributions/empirical_inv.m,
scripts/statistics/distributions/empirical_pdf.m,
scripts/statistics/distributions/expcdf.m,
scripts/statistics/distributions/expinv.m,
scripts/statistics/distributions/exppdf.m,
scripts/statistics/distributions/finv.m,
scripts/statistics/distributions/fpdf.m,
scripts/statistics/distributions/gamcdf.m,
scripts/statistics/distributions/gaminv.m,
scripts/statistics/distributions/gampdf.m,
scripts/statistics/distributions/geoinv.m,
scripts/statistics/distributions/geopdf.m,
scripts/statistics/distributions/hygecdf.m,
scripts/statistics/distributions/hygeinv.m,
scripts/statistics/distributions/hygepdf.m,
scripts/statistics/distributions/kolmogorov_smirnov_cdf.m,
scripts/statistics/distributions/laplace_cdf.m,
scripts/statistics/distributions/laplace_inv.m,
scripts/statistics/distributions/laplace_pdf.m,
scripts/statistics/distributions/logistic_inv.m,
scripts/statistics/distributions/logncdf.m,
scripts/statistics/distributions/logninv.m,
scripts/statistics/distributions/lognpdf.m,
scripts/statistics/distributions/nbincdf.m,
scripts/statistics/distributions/nbininv.m,
scripts/statistics/distributions/nbinpdf.m,
scripts/statistics/distributions/nbinrnd.m,
scripts/statistics/distributions/normcdf.m,
scripts/statistics/distributions/norminv.m,
scripts/statistics/distributions/normpdf.m,
scripts/statistics/distributions/poisscdf.m,
scripts/statistics/distributions/poissinv.m,
scripts/statistics/distributions/poisspdf.m,
scripts/statistics/distributions/stdnormal_cdf.m,
scripts/statistics/distributions/stdnormal_pdf.m,
scripts/statistics/distributions/tcdf.m,
scripts/statistics/distributions/tinv.m,
scripts/statistics/distributions/tpdf.m,
scripts/statistics/distributions/unidcdf.m,
scripts/statistics/distributions/unidinv.m,
scripts/statistics/distributions/unidpdf.m,
scripts/statistics/distributions/unidrnd.m,
scripts/statistics/distributions/unifcdf.m,
scripts/statistics/distributions/unifinv.m,
scripts/statistics/distributions/wblcdf.m,
scripts/statistics/distributions/wblinv.m,
scripts/statistics/distributions/wblpdf.m,
scripts/statistics/distributions/wienrnd.m,
scripts/statistics/models/private/logistic_regression_derivatives.m,
scripts/statistics/models/private/logistic_regression_likelihood.m,
scripts/statistics/tests/anova.m,
scripts/statistics/tests/chisquare_test_homogeneity.m,
scripts/statistics/tests/chisquare_test_independence.m,
scripts/statistics/tests/cor_test.m,
scripts/statistics/tests/f_test_regression.m,
scripts/statistics/tests/hotelling_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test.m,
scripts/statistics/tests/kolmogorov_smirnov_test_2.m,
scripts/statistics/tests/kruskal_wallis_test.m,
scripts/statistics/tests/manova.m, scripts/statistics/tests/mcnemar_test.m,
scripts/statistics/tests/prop_test_2.m, scripts/statistics/tests/run_test.m,
scripts/statistics/tests/sign_test.m, scripts/statistics/tests/t_test.m,
scripts/statistics/tests/t_test_2.m,
scripts/statistics/tests/t_test_regression.m,
scripts/statistics/tests/u_test.m, scripts/statistics/tests/var_test.m,
scripts/statistics/tests/welch_test.m,
scripts/statistics/tests/wilcoxon_test.m, scripts/statistics/tests/z_test.m,
scripts/statistics/tests/z_test_2.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 10 May 2015 16:07:41 -0700 |
parents | 9fc020886ae9 |
children |
line wrap: on
line source
## Copyright (C) 1995-2015 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 {Function File} {} moment (@var{x}, @var{p}) ## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{type}) ## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{dim}) ## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{type}, @var{dim}) ## @deftypefnx {Function File} {} moment (@var{x}, @var{p}, @var{dim}, @var{type}) ## Compute the @var{p}-th central moment of the vector @var{x}. ## ## @tex ## $$ ## {\sum_{i=1}^N (x_i - \bar{x})^p \over N} ## $$ ## @end tex ## @ifnottex ## ## @example ## @group ## 1/N SUM_i (x(i) - mean(x))^p ## @end group ## @end example ## ## @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 (x(i) - mean(x)))^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 (x) = 1/N SUM_i x(i)^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 (x(i)) )^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: expecting TYPE to 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)) || ! (1 <= dim && dim <= nd)) error ("moment: DIM must be an integer and a valid dimension"); endif endif n = sz(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)) ## 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 <expecting TYPE to 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) %!error <DIM must be an integer and a valid dimension> moment (1, 2, 4)