96 lines
2.6 KiB
Matlab
96 lines
2.6 KiB
Matlab
function inv = betainv (x, a, b)
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% BETAINV Quantile function of the Beta distribution
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% INV = betainv(X, A, B) computes, for each element of X, the
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% quantile (the inverse of the CDF) at X of the Beta distribution
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% with parameters A and B (i.e. mean of the distribution is
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% A/(A+B) and variance is A*B/(A+B)^2/(A+B+1) ).
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% Adapted for Matlab (R) from GNU Octave 3.0.1
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% Original file: statistics/distributions/betainv.m
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% Original author: KH <Kurt.Hornik@wu-wien.ac.at>
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% Copyright (C) 1995, 1996, 1997, 2005, 2006, 2007 Kurt Hornik
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% Copyright (C) 2008-2009 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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if (nargin ~= 3)
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error ('betainv: you must give three arguments');
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end
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if (~isscalar (a) || ~isscalar(b))
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[retval, x, a, b] = common_size (x, a, b);
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if (retval > 0)
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error ('betainv: x, a and b must be of common size or scalars');
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end
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end
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sz = size (x);
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inv = zeros (sz);
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k = find ((x < 0) | (x > 1) | ~(a > 0) | ~(b > 0) | isnan (x));
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if (any (k))
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inv (k) = NaN;
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end
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k = find ((x == 1) & (a > 0) & (b > 0));
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if (any (k))
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inv (k) = 1;
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end
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k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0));
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if (any (k))
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if (~isscalar(a) || ~isscalar(b))
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a = a (k);
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b = b (k);
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y = a ./ (a + b);
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else
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y = a / (a + b) * ones (size (k));
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end
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x = x (k);
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l = find (y < eps);
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if (any (l))
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y(l) = sqrt (eps) * ones (length (l), 1);
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end
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l = find (y > 1 - eps);
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if (any (l))
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y(l) = 1 - sqrt (eps) * ones (length (l), 1);
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end
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y_old = y;
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for i = 1 : 10000
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h = (betacdf (y_old, a, b) - x) ./ betapdf (y_old, a, b);
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y_new = y_old - h;
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ind = find (y_new <= eps);
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if (any (ind))
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y_new (ind) = y_old (ind) / 10;
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end
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ind = find (y_new >= 1 - eps);
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if (any (ind))
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y_new (ind) = 1 - (1 - y_old (ind)) / 10;
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end
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h = y_old - y_new;
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if (max (abs (h)) < sqrt (eps))
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break
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end
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y_old = y_new;
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end
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inv (k) = y_new;
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end
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end
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