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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: pascal_cdf (x, n, p)
##
## For each element of x, compute the CDF at x of the Pascal (negative
## binomial) distribution with parameters n and p.
##
## The number of failures in a Bernoulli experiment with success
## probability p before the n-th success follows this distribution.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: CDF of the Pascal (negative binomial) distribution
function cdf = pascal_cdf (x, n, p)
if (nargin != 3)
usage ("pascal_cdf (x, n, p)");
endif
[retval, x, n, p] = common_size (x, n, p);
if (retval > 0)
error (["pascal_cdf: ", ...
"x, n and p 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);
p = reshape (p, 1, s);
cdf = zeros (1, s);
k = find (isnan (x) | (n < 1) | (n == Inf) | (n != round (n)) ...
| (p < 0) | (p > 1));
if any (k)
cdf(k) = NaN * ones (1, length (k));
endif
k = find ((x == Inf) & (n > 0) & (n < Inf) & (n == round (n)) ...
& (p >= 0) & (p <= 1));
if any (k)
cdf(k) = ones (1, length (k));
endif
k = find ((x >= 0) & (x < Inf) & (x == round (x)) & (n > 0) ...
& (n < Inf) & (n == round (n)) & (p > 0) & (p <= 1));
if any (k)
## Does anyone know a better way to do the summation?
m = zeros (1, length (k));
x = floor (x(k));
n = n(k);
p = p(k);
y = cdf(k);
while (1)
l = find (m <= x);
if any (l)
y(l) = y(l) + pascal_pdf (m(l), n(l), p(l));
m(l) = m(l) + 1;
else
break;
endif
endwhile
cdf(k) = y;
endif
cdf = reshape (cdf, r, c);
endfunction
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