Mercurial > octave-nkf
view scripts/statistics/base/kendall.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
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## 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} {} kendall (@var{x}) ## @deftypefnx {Function File} {} kendall (@var{x}, @var{y}) ## @cindex Kendall's Tau ## Compute Kendall's @var{tau}. ## ## For two data vectors @var{x}, @var{y} of common length @var{n}, Kendall's ## @var{tau} is the correlation of the signs of all rank differences of ## @var{x} and @var{y}; i.e., if both @var{x} and @var{y} have distinct ## entries, then ## ## @tex ## $$ \tau = {1 \over n(n-1)} \sum_{i,j} {\rm sign}(q_i-q_j) {\rm sign}(r_i-r_j) $$ ## @end tex ## @ifnottex ## ## @example ## @group ## 1 ## tau = ------- SUM sign (q(i) - q(j)) * sign (r(i) - r(j)) ## n (n-1) i,j ## @end group ## @end example ## ## @end ifnottex ## @noindent ## in which the ## @tex ## $q_i$ and $r_i$ ## @end tex ## @ifnottex ## @var{q}(@var{i}) and @var{r}(@var{i}) ## @end ifnottex ## are the ranks of @var{x} and @var{y}, respectively. ## ## If @var{x} and @var{y} are drawn from independent distributions, ## Kendall's @var{tau} is asymptotically normal with mean 0 and variance ## @tex ## ${2 (2n+5) \over 9n(n-1)}$. ## @end tex ## @ifnottex ## @code{(2 * (2@var{n}+5)) / (9 * @var{n} * (@var{n}-1))}. ## @end ifnottex ## ## @code{kendall (@var{x})} is equivalent to @code{kendall (@var{x}, ## @var{x})}. ## @seealso{ranks, spearman} ## @end deftypefn ## Author: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Kendall's rank correlation tau function tau = kendall (x, y = []) if (nargin < 1 || nargin > 2) print_usage (); endif if ( ! (isnumeric (x) || islogical (x)) || ! (isnumeric (y) || islogical (y))) error ("kendall: X and Y must be numeric matrices or vectors"); endif if (ndims (x) != 2 || ndims (y) != 2) error ("kendall: X and Y must be 2-D matrices or vectors"); endif if (isrow (x)) x = x.'; endif [n, c] = size (x); if (nargin == 2) if (isrow (y)) y = y.'; endif if (rows (y) != n) error ("kendall: X and Y must have the same number of observations"); else x = [x, y]; endif endif if (isa (x, "single") || isa (y, "single")) cls = "single"; else cls = "double"; endif r = ranks (x); m = sign (kron (r, ones (n, 1, cls)) - kron (ones (n, 1, cls), r)); tau = corr (m); if (nargin == 2) tau = tau(1 : c, (c + 1) : columns (x)); endif endfunction %!test %! x = [1:2:10]; %! y = [100:10:149]; %! assert (kendall (x,y), 1, 5*eps); %! assert (kendall (x,fliplr (y)), -1, 5*eps); %!assert (kendall (logical (1)), 1) %!assert (kendall (single (1)), single (1)) ## Test input validation %!error kendall () %!error kendall (1, 2, 3) %!error kendall (['A'; 'B']) %!error kendall (ones (2,1), ['A'; 'B']) %!error kendall (ones (2,2,2)) %!error kendall (ones (2,2), ones (2,2,2)) %!error kendall (ones (2,2), ones (3,2))