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v4 matlab: replaced CDF and quantile functions of the beta by GPL'd ones 

git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@1982 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
sebastien 2008-08-05 09:52:45 +00:00
parent 7c25303258
commit a5b3c829d8
8 changed files with 224 additions and 53 deletions
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16
matlab/dbeta.m
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@ -1,16 +0,0 @@
function d = dbeta(x,a,b)
%DBETA The beta density function
%
% f = dbeta(x,a,b)
% Anders Holtsberg, 18-11-93
% Copyright (c) Anders Holtsberg
if any(any((a<=0)|(b<=0)))
error('Parameter a or b is nonpositive')
end
I = find((x<0)|(x>1));
d = x.^(a-1) .* (1-x).^(b-1) ./ beta(a,b);
d(I) = 0*I;

64
matlab/distributions/betacdf.m Normal file
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@ -0,0 +1,64 @@
function cdf = betacdf (x, a, b)
% BETACDF CDF of the Beta distribution
% CDF = betacdf(X, A, B) computes, for each element of X, 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/betacdf.m
% Original author: KH <Kurt.Hornik@wu-wien.ac.at>
% Copyright (C) 1995, 1996, 1997, 2005, 2006, 2007 Kurt Hornik
% Copyright (C) 2008 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 ('betacdf: you should provide three arguments');
end
if (~isscalar (a) || ~isscalar(b))
[retval, x, a, b] = common_size (x, a, b);
if (retval > 0)
error ('betacdf: x, a and b must be of common size or scalar');
end
end
sz = size(x);
cdf = zeros (sz);
k = find (~(a > 0) | ~(b > 0) | isnan (x));
if (any (k))
cdf (k) = NaN;
end
k = find ((x >= 1) & (a > 0) & (b > 0));
if (any (k))
cdf (k) = 1;
end
k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0));
if (any (k))
if (isscalar (a) && isscalar(b))
cdf (k) = betainc (x(k), a, b);
else
cdf (k) = betainc (x(k), a(k), b(k));
end
end
end

95
matlab/distributions/betainv.m Normal file
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@ -0,0 +1,95 @@
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 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

60
matlab/distributions/betapdf.m Normal file
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@ -0,0 +1,60 @@
function pdf = betapdf (x, a, b)
% BETAPDF PDF of the Beta distribution
% PDF = betapdf(X, A, B) computes, for each element of X, the PDF
% 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/betapdf.m
% Original author: KH <Kurt.Hornik@wu-wien.ac.at>
% Copyright (C) 1995, 1996, 1997, 2005, 2006, 2007 Kurt Hornik
% Copyright (C) 2008 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 ('betapdf: you must give three arguments');
end
if (~isscalar (a) || ~isscalar(b))
[retval, x, a, b] = common_size (x, a, b);
if (retval > 0)
error ('betapdf: x, a and b must be of common size or scalar');
end
end
sz = size (x);
pdf = zeros (sz);
k = find (~(a > 0) | ~(b > 0) | isnan (x));
if (any (k))
pdf (k) = NaN;
end
k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0));
if (any (k))
if (isscalar(a) && isscalar(b))
pdf(k) = exp ((a - 1) .* log (x(k)) ...
+ (b - 1) .* log (1 - x(k))) ./ beta (a, b);
else
pdf(k) = exp ((a(k) - 1) .* log (x(k)) ...
+ (b(k) - 1) .* log (1 - x(k))) ./ beta (a(k), b(k));
end
end
end

2
matlab/distributions/betarnd.m
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@ -3,7 +3,7 @@ function rnd = betarnd(a, b)
% RND = betarnd(A,B) returns a random sample from 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).
% A*B/(A+B)^2/(A+B+1) ).
% Copyright (C) 2008 Dynare Team
%

4
matlab/draw_prior_density.m
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@ -52,8 +52,8 @@ if pshape(indx) == 1 %/* BETA Prior */
b = a*(1/mu-1);
aa = p3(indx);
bb = p4(indx);
infbound = qbeta(truncprior,a,b)*(bb-aa)+aa;
supbound = qbeta(1-truncprior,a,b)*(bb-aa)+aa;
infbound = betainv(truncprior,a,b)*(bb-aa)+aa;
supbound = betainv(1-truncprior,a,b)*(bb-aa)+aa;
stepsize = (supbound-infbound)/200;
abscissa = infbound:stepsize:supbound;
dens = density(abscissa,a,b,aa,bb);

4
matlab/prior_bounds.m
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@ -47,8 +47,8 @@ for i=1:n
stdd = p2(i)/(p4(i)-p3(i));
A = (1-mu)*mu^2/stdd^2 - mu;
B = A*(1/mu - 1);
bounds(i,1) = qbeta(options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i);
bounds(i,2) = qbeta(1-options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i);
bounds(i,1) = betainv(options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i);
bounds(i,2) = betainv(1-options_.prior_trunc,A,B)*(p4(i)-p3(i))+p3(i);
case 2
b = p2(i)^2/(pmean(i)-p3(i));
a = (pmean(i)-p3(i))/b;

32
matlab/qbeta.m
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@ -1,32 +0,0 @@
function x = qbeta(p,a,b)
%QBETA The beta inverse distribution function
%
% x = qbeta(p,a,b)
% Anders Holtsberg, 27-07-95
% Copyright (c) Anders Holtsberg
if any(any((a<=0)|(b<=0)))
error('Parameter a or b is nonpositive')
end
if any(any(abs(2*p-1)>1))
error('A probability should be 0<=p<=1, please!')
end
if exist('OCTAVE_VERSION')
x = betainv(p, a, b);
return
end
b = min(b,100000);
x = a ./ (a+b);
dx = 1;
while any(any(abs(dx)>256*eps*max(x,1)))
dx = (betainc(x,a,b) - p) ./ dbeta(x,a,b);
x = x - dx;
x = x + (dx - x) / 2 .* (x<0);
x = x + (1 + (dx - x)) / 2 .* (x>1);
end