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## 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_cdf (x, n)
##
## For each element of x, compute the CDF at x of the Student (t)
## distribution with n degrees of freedom, i.e., PROB( t(n) <= x ).
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: CDF of the t distribution
function cdf = t_cdf (x, n)
if (nargin != 2)
usage ("t_cdf (x, n)");
endif
[retval, x, n] = common_size (x, n);
if (retval > 0)
error ("t_cdf: 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);
cdf = zeros (1, s);
k = find (isnan (x) | !(n > 0));
if any (k)
cdf(k) = NaN * ones (1, length (k));
endif
k = find ((x == Inf) & (n > 0));
if any (k)
cdf(k) = ones (1, length (k));
endif
k = find ((x > -Inf) & (x < Inf) & (n > 0));
if any (k)
cdf(k) = betai (n(k) / 2, 1 / 2, 1 ./ (1 + x(k) .^ 2 ./ n(k))) / 2;
ind = find (x(k) > 0);
if any (ind)
cdf(k(ind)) = 1 - cdf(k(ind));
endif
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");
cdf(k) = NaN * ones (1, length (k));
endif
cdf = reshape (cdf, r, c);
endfunction
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