## 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: t_inv (x, n) ## ## For each component of x, compute the quantile (the inverse of the ## CDF) at x of the t (Student) distribution with parameter n. ## For very large n, the "correct" formula does not really work well, ## and the quantiles of the standard normal distribution are used ## directly. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Quantile function of the t distribution function inv = t_inv (x, n) if (nargin != 2) usage ("t_inv (x, n)"); endif [retval, x, n] = common_size (x, n); if (retval > 0) error ("t_inv: x and n must be of common size or scalar"); endif [r, c] = size (x); s = r * c; x = reshape (x, 1, s); n = reshape (n, 1, s); inv = zeros (1, s); k = find ((x < 0) | (x > 1) | isnan (x) | !(n > 0)); if any (k) inv(k) = NaN * ones (1, length (k)); endif k = find ((x == 0) & (n > 0)); if any (k) inv(k) = (-Inf) * ones (1, length (k)); endif k = find ((x == 1) & (n > 0)); if any (k) inv(k) = Inf * ones (1, length (k)); endif k = find ((x > 0) & (x < 1) & (n > 0) & (n < 10000)); if any (k) inv(k) = sign (x(k) - 1/2) .* sqrt (n(k) .* (1 ... ./ beta_inv (2 * min (x(k), 1 - x(k)), n(k) / 2, 1 / 2) - 1)); endif ## For large n, use the quantiles of the standard normal k = find ((x > 0) & (x < 1) & (n >= 10000)); if any (k) inv(k) = stdnormal_inv (x(k)); endif ## should we really only allow for positive integer n? k = find (n != round (n)); if any (k) fprintf (stderr, ... "WARNING: n should be positive integer\n"); inv(k) = NaN * ones (1, length (k)); endif inv = reshape (inv, r, c); endfunction

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