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function p = wblcdf(x, scale, shape)
% Cumulative distribution function for the Weibull distribution.
%
% INPUTS
% - x [double] Positive real scalar or vector.
% - scale [double] Positive hyperparameter (scalar).
% - shape [double] Positive hyperparameter (scalar).
%
% OUTPUTS
% - p [double] Probability value(s) in [0,1], same size as x.
% Copyright © 2015-2026 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(x) || ~isreal(x)
error('First input argument must be a real scalar or vector!')
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
% Vectorized evaluation of the CDF.
p = zeros(size(x));
p(isinf(x) & x>0) = 1;
k = x > 0 & ~isinf(x);
if any(k(:))
p(k) = 1 - exp(-(x(k)./scale).^shape);
end
return;
%@test:1
try
p = wblcdf(-1, .5, .1);
t(1) = true;
catch
t(1) = false;
end
% Check the results
if t(1)
t(2) = isequal(p, 0);
end
T = all(t);
%@eof:1
%@test:2
try
p = wblcdf(Inf, .5, .1);
t(1) = true;
catch
t(1) = false;
end
% Check the results
if t(1)
t(2) = isequal(p, 1);
end
T = all(t);
%@eof:2
%@test:3
% Set the hyperparameters of a Weibull definition.
scale = .5;
shape = 1.5;
% Compute the median of the weibull distribution.
m = scale*log(2)^(1/shape);
try
p = wblcdf(m, scale, shape);
t(1) = true;
catch
t(1) = false;
end
% Check the results
if t(1)
t(2) = abs(p-.5)<1e-12;
end
T = all(t);
%@eof:3
%@test:4
% Consistency check between wblinv and wblcdf.
% Set the hyperparameters of a Weibull definition.
scale = .5;
shape = 1.5;
% Compute quatiles of the weibull distribution.
q = 0:.05:1;
m = zeros(size(q));
p = zeros(size(q));
for i=1:length(q)
m(i) = wblinv(q(i), scale, shape);
end
try
for i=1:length(q)
p(i) = wblcdf(m(i), scale, shape);
end
t(1) = true;
catch
t(1) = false;
end
% Check the results
if t(1)
for i=1:length(q)
t(i+1) = abs(p(i)-q(i))<1e-12;
end
end
T = all(t);
%@eof:4
%@test:5
% Test with vector-valued x input.
% Set the hyperparameters of a Weibull distribution.
scale = .5;
shape = 1.5;
% Build a vector of x values including boundary cases.
x = [-1, 0, scale*log(2)^(1/shape), 1, Inf];
try
p = wblcdf(x, scale, shape);
t(1) = true;
catch
t(1) = false;
end
% Check the results.
if t(1)
t(2) = isequal(size(p), size(x));
t(3) = isequal(p(1), 0); % x < 0 → p = 0
t(4) = isequal(p(2), 0); % x = 0 → p = 0
t(5) = abs(p(3) - 0.5) < 1e-12; % x = median → p = 0.5
t(6) = p(4) > 0 && p(4) < 1; % interior point
t(7) = isequal(p(5), 1); % x = Inf → p = 1
end
T = all(t);
%@eof:5
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