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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: poisson_inv (x, lambda)
##
## For each component of x, compute the quantile (the inverse of the
## CDF) at x of the Poisson distribution with parameter lambda.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Quantile function of the Poisson distribution
function inv = poisson_inv (x, l)
if (nargin != 2)
usage ("poisson_inv (x, lambda)");
endif
[retval, x, l] = common_size (x, l);
if (retval > 0)
error (["poisson_inv: ", ...
"x and lambda must be of common size or scalar"]);
endif
[r, c] = size (x);
s = r * c;
x = reshape (x, 1, s);
l = reshape (l, 1, s);
inv = zeros (1, s);
k = find ((x < 0) | (x > 1) | isnan (x) | !(l > 0));
if any (k)
inv(k) = NaN * ones (1, length (k));
endif
k = find ((x == 1) & (l > 0));
if any (k)
inv(k) = Inf * ones (1, length (k));
endif
k = find ((x > 0) & (x < 1) & (l > 0));
if any (k)
cdf = exp (-l(k));
while (1)
m = find (cdf < x(k));
if any (m)
inv(k(m)) = inv(k(m)) + 1;
cdf(m) = cdf(m) + poisson_pdf (inv(k(m)), l(k(m)));
else
break;
endif
endwhile
endif
inv = reshape (inv, r, c);
endfunction
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