170 lines
3.3 KiB
Matlab
170 lines
3.3 KiB
Matlab
function t = wblinv(proba, scale, shape)
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% Inverse cumulative distribution function.
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%
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% INPUTS
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% - proba [double] Probability, scalar between 0 and 1.
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% - scale [double] Positive hyperparameter.
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% - shape [double] Positive hyperparameter.
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%
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% OUTPUTS
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% - t [double] scalar such that P(X<=t)=proba
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% Copyright © 2015-2023 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 <https://www.gnu.org/licenses/>.
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% Check input arguments.
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if nargin<3
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error('Three input arguments required!')
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end
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if ~isnumeric(proba) || ~isscalar(proba) || ~isreal(proba) || proba<0 || proba>1
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error('First input argument must be a real scalar between 0 and 1 (probability)!')
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end
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if ~isnumeric(scale) || ~isscalar(scale) || ~isreal(scale) || scale<=0
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error('Second input argument must be a real positive scalar (scale parameter of the Weibull distribution)!')
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end
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if ~isnumeric(shape) || ~isscalar(shape) || ~isreal(shape) || shape<=0
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error('Third input argument must be a real positive scalar (shape parameter of the Weibull distribution)!')
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end
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if proba<2*eps()
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t = 0;
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return
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end
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if proba>1-2*eps()
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t = Inf;
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return
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end
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t = exp(log(scale)+log(-log(1-proba))/shape);
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return % --*-- Unit tests --*--
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%@test:1
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try
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x = wblinv(0, 1, 2);
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = isequal(x, 0);
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end
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T = all(t);
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%@eof:1
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%@test:2
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try
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x = wblinv(1, 1, 2);
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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t(2) = isinf(x);
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end
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T = all(t);
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%@eof:2
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%@test:3
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scales = [.5, 1, 5];
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shapes = [.1, 1, 2];
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x = NaN(9,1);
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try
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k = 0;
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for i=1:3
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for j=1:3
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k = k+1;
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x(k) = wblinv(.5, scales(i), shapes(j));
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end
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end
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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k = 1;
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for i=1:3
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for j=1:3
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k = k+1;
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t(k) = abs(x(k-1)-scales(i)*log(2)^(1/shapes(j)))<1e-12;
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end
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end
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end
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T = all(t);
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%@eof:3
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%@test:4
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debug = false;
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scales = [ .5, 1, 5];
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shapes = [ 1, 2, 3];
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x = NaN(9,1);
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p = 1e-1;
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try
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k = 0;
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for i=1:3
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for j=1:3
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k = k+1;
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x(k) = wblinv(p, scales(i), shapes(j));
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end
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end
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t(1) = true;
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catch
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t(1) = false;
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end
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if t(1)
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k = 1;
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for i=1:3
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for j=1:3
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k = k+1;
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shape = shapes(j);
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scale = scales(i);
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density = @(z) exp(lpdfgweibull(z,shape,scale));
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if debug
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[shape, scale, x(k-1)]
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end
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if isoctave
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s = quadv(density, 0, x(k-1),1e-10);
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else
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s = integral(density, 0, x(k-1));
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end
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if debug
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[s, abs(p-s)]
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end
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if isoctave
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t(k) = abs(p-s)<1e-9;
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else
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t(k) = abs(p-s)<1e-12;
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end
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end
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end
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end
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T = all(t);
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%@eof:4
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