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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: gamma_inv (x, a, b)
##
## For each component of x, compute the quantile (the inverse of the
## CDF) at x of the Gamma distribution with parameters a and b.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description: Quantile function of the Gamma distribution
function inv = gamma_inv (x, a, b)
if (nargin != 3)
usage ("gamma_inv (x, a, b)");
endif
[retval, x, a, b] = common_size (x, a, b);
if (retval > 0)
error ("gamma_inv: x, a and b must be of common size or scalars");
endif
[r, c] = size (x);
s = r * c;
x = reshape (x, s, 1);
a = reshape (a, s, 1);
b = reshape (b, s, 1);
inv = zeros (s, 1);
k = find ((x < 0) | (x > 1) | isnan (x) | !(a > 0) | !(b > 0));
if any (k)
inv (k) = NaN * ones (length (k), 1);
endif
k = find ((x == 1) & (a > 0) & (b > 0));
if any (k)
inv (k) = Inf * ones (length (k), 1);
endif
k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0));
if any (k)
a = a (k);
b = b (k);
x = x (k);
y = a ./ b;
l = find (x < eps);
if any (l)
y(l) = sqrt (eps) * ones (length (l), 1);
endif
y_old = y;
for i = 1 : 100
h = (gamma_cdf (y_old, a, b) - x) ./ gamma_pdf (y_old, a, b);
y_new = y_old - h;
ind = find (y_new <= eps);
if (any (ind))
y_new (ind) = y_old (ind) / 10;
h = y_old - y_new;
endif
if (max (abs (h)) < sqrt (eps))
break;
endif
y_old = y_new;
endfor
inv (k) = y_new;
endif
inv = reshape (inv, r, c);
endfunction
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