## 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: cauchy_inv (x [, lambda, sigma]) ## ## For each element of x, compute the quantile (the inverse of the CDF) ## at x of the Cauchy distribution with location parameter lambda and ## scale parameter sigma. Default values are lambda = 0, sigma = 1. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Quantile function of the Cauchy distribution function inv = cauchy_inv (x, location, scale) if !(nargin == 1 || nargin == 3) usage ("cauchy_inv (x [, lambda, sigma])"); endif if (nargin == 1) location = 0; scale = 1; endif [retval, x, location, scale] = common_size (x, location, scale); if (retval > 0) error (["cauchy_inv: ", ... "x, lambda and sigma must be of common size or scalar"]); endif [r, c] = size (x); s = r * c; x = reshape (x, 1, s); location = reshape (location, 1, s); scale = reshape (scale, 1, s); inv = NaN * ones (1, s); ok = ((location > -Inf) & (location < Inf) & (scale > 0) & (scale < Inf)); k = find ((x == 0) & ok); if any (k) inv(k) = -Inf * ones (1, length (k)); endif k = find ((x > 0) & (x < 1) & ok); if any (k) inv(k) = location(k) - scale(k) .* cot (pi * x(k)); endif k = find ((x == 1) & ok); if any (k) inv(k) = Inf * ones (1, length (k)); endif inv = reshape (inv, r, c); endfunction

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