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function inv = betainv (x, a, b)
% BETAINV Quantile function of the Beta distribution
% INV = betainv(X, A, B) computes, for each element of X, the
% quantile (the inverse of the CDF) at X of the Beta distribution
% with parameters A and B (i.e. mean of the distribution is
% A/(A+B) and variance is A*B/(A+B)^2/(A+B+1) ).
% Adapted for Matlab (R) from GNU Octave 3.0.1
% Original file: statistics/distributions/betainv.m
% Original author: KH <Kurt.Hornik@wu-wien.ac.at>
% Copyright (C) 1995, 1996, 1997, 2005, 2006, 2007 Kurt Hornik
% Copyright (C) 2008-2009 Dynare Team
%
% This file is part of Dynare.
%
% Dynare 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 3 of the License, or
% (at your option) any later version.
%
% Dynare 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 Dynare. If not, see <http://www.gnu.org/licenses/>.
if (nargin ~= 3)
error ('betainv: you must give three arguments');
end
if (~isscalar (a) || ~isscalar(b))
[retval, x, a, b] = common_size (x, a, b);
if (retval > 0)
error ('betainv: x, a and b must be of common size or scalars');
end
end
sz = size (x);
inv = zeros (sz);
k = find ((x < 0) | (x > 1) | ~(a > 0) | ~(b > 0) | isnan (x));
if (any (k))
inv (k) = NaN;
end
k = find ((x == 1) & (a > 0) & (b > 0));
if (any (k))
inv (k) = 1;
end
k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0));
if (any (k))
if (~isscalar(a) || ~isscalar(b))
a = a (k);
b = b (k);
y = a ./ (a + b);
else
y = a / (a + b) * ones (size (k));
end
x = x (k);
l = find (y < eps);
if (any (l))
y(l) = sqrt (eps) * ones (length (l), 1);
end
l = find (y > 1 - eps);
if (any (l))
y(l) = 1 - sqrt (eps) * ones (length (l), 1);
end
y_old = y;
for i = 1 : 10000
h = (betacdf (y_old, a, b) - x) ./ betapdf (y_old, a, b);
y_new = y_old - h;
ind = find (y_new <= eps);
if (any (ind))
y_new (ind) = y_old (ind) / 10;
end
ind = find (y_new >= 1 - eps);
if (any (ind))
y_new (ind) = 1 - (1 - y_old (ind)) / 10;
end
h = y_old - y_new;
if (max (abs (h)) < sqrt (eps))
break
end
y_old = y_new;
end
inv (k) = y_new;
end
end
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