## Copyright (C) 1995, 1996, 1997 Kurt Hornik ## ## This program 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 2, or (at your option) ## any later version. ## ## This program 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 this file. If not, write to the Free Software Foundation, ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ## usage: kendall (x [, y]) ## ## Computes Kendall's tau for each of the variables specified by the ## input arguments. ## ## For matrices, each row is an observation and each column a variable; ## vectors are always observations and may be row or column vectors. ## ## kendall (x) is equivalent to kendall (x, x). ## ## For two data vectors x, y of common length n, Kendall's tau is the ## correlation of the signs of all rank differences of x and y; i.e., ## if both x and y have distinct entries, then \tau = \frac{1}{n(n-1)} ## \sum_{i,j} SIGN(q_i-q_j) SIGN(r_i-r_j), where the q_i and r_i are the ## ranks of x and y, respectively. ## ## If x and y are drawn from independent distributions, Kendall's tau is ## asymptotically normal with mean 0 and variance (2 * (2n+5)) / (9 * n ## * (n-1)). ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Kendall's rank correlation tau function tau = kendall (x, y) if ((nargin < 1) || (nargin > 2)) usage ("kendall (x [, y])"); endif if (rows (x) == 1) x = x'; endif [n, c] = size (x); if (nargin == 2) if (rows (y) == 1) 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 r = ranks (x); m = sign (kron (r, ones (n, 1)) - kron (ones (n, 1), r)); tau = cor (m); if (nargin == 2) tau = tau (1 : c, (c + 1) : columns (x)); endif endfunction

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