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function t = wblinv(proba, scale, shape) % --*-- Unitary tests --*--
% Inverse cumulative distribution function.
%
% INPUTS
% - proba [double] Probability, scalar between 0 and 1.
% - scale [double] Positive hyperparameter.
% - shape [double] Positive hyperparameter.
%
% OUTPUTS
% - t [double] scalar such that P(X<=t)=proba
% Copyright (C) 2015-2020 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 <https://www.gnu.org/licenses/>.
% Check input arguments.
if nargin<3
error('Three input arguments required!')
end
if ~isnumeric(proba) || ~isscalar(proba) || ~isreal(proba) || proba<0 || proba>1
error('First input argument must be a real scalar between 0 and 1 (probability)!')
end
if ~isnumeric(scale) || ~isscalar(scale) || ~isreal(scale) || scale<=0
error('Second input argument must be a real positive scalar (scale parameter of the Weibull distribution)!')
end
if ~isnumeric(shape) || ~isscalar(shape) || ~isreal(shape) || shape<=0
error('Third input argument must be a real positive scalar (shape parameter of the Weibull distribution)!')
end
if proba<2*eps()
t = 0;
return
end
if proba>1-2*eps()
t = Inf;
return
end
t = exp(log(scale)+log(-log(1-proba))/shape);
%@test:1
%$ try
%$ x = wblinv(0, 1, 2);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ t(2) = isequal(x, 0);
%$ end
%$ T = all(t);
%@eof:1
%@test:2
%$ try
%$ x = wblinv(1, 1, 2);
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ t(2) = isinf(x);
%$ end
%$ T = all(t);
%@eof:2
%@test:3
%$ scales = [.5, 1, 5];
%$ shapes = [.1, 1, 2];
%$ x = NaN(9,1);
%$
%$ try
%$ k = 0;
%$ for i=1:3
%$ for j=1:3
%$ k = k+1;
%$ x(k) = wblinv(.5, scales(i), shapes(j));
%$ end
%$ end
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ k = 1;
%$ for i=1:3
%$ for j=1:3
%$ k = k+1;
%$ t(k) = abs(x(k-1)-scales(i)*log(2)^(1/shapes(j)))<1e-12;
%$ end
%$ end
%$ end
%$ T = all(t);
%@eof:3
%@test:4
%$ debug = false;
%$ scales = [ .5, 1, 5];
%$ shapes = [ 1, 2, 3];
%$ x = NaN(9,1);
%$ p = 1e-1;
%$
%$ try
%$ k = 0;
%$ for i=1:3
%$ for j=1:3
%$ k = k+1;
%$ x(k) = wblinv(p, scales(i), shapes(j));
%$ end
%$ end
%$ t(1) = true;
%$ catch
%$ t(1) = false;
%$ end
%$
%$ if t(1)
%$ k = 1;
%$ for i=1:3
%$ for j=1:3
%$ k = k+1;
%$ shape = shapes(j);
%$ scale = scales(i);
%$ density = @(z) exp(lpdfgweibull(z,shape,scale));
%$ if debug
%$ [shape, scale, x(k-1)]
%$ end
%$ if isoctave
%$ s = quadv(density, 0, x(k-1),1e-10);
%$ else
%$ s = integral(density, 0, x(k-1));
%$ end
%$ if debug
%$ [s, abs(p-s)]
%$ end
%$ if isoctave
%$ t(k) = abs(p-s)<1e-9;
%$ else
%$ t(k) = abs(p-s)<1e-12;
%$ end
%$ end
%$ end
%$ end
%$ T = all(t);
%@eof:4
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