149 lines
2.9 KiB
Matlab
149 lines
2.9 KiB
Matlab
function p = wblcdf(x, scale, shape)
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% Cumulative distribution function for the Weibull distribution.
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%
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% INPUTS
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% - x [double] Positive real scalar.
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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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% - p [double] Positive scalar between
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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(x) || ~isscalar(x) || ~isreal(x)
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error('First input argument must be a real scalar!')
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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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% Filter trivial polar cases.
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if x<=0
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p = 0;
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return
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end
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if isinf(x)
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p = 1;
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return
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end
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% Evaluate the CDF.
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p = 1-exp(-(x/scale)^shape);
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%@test:1
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try
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p = wblcdf(-1, .5, .1);
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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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% Check the results
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if t(1)
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t(2) = isequal(p, 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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p = wblcdf(Inf, .5, .1);
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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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% Check the results
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if t(1)
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t(2) = isequal(p, 1);
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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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% Set the hyperparameters of a Weibull definition.
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scale = .5;
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shape = 1.5;
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% Compute the median of the weibull distribution.
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m = scale*log(2)^(1/shape);
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try
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p = wblcdf(m, scale, shape);
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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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% Check the results
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if t(1)
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t(2) = abs(p-.5)<1e-12;
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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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% Consistency check between wblinv and wblcdf.
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% Set the hyperparameters of a Weibull definition.
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scale = .5;
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shape = 1.5;
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% Compute quatiles of the weibull distribution.
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q = 0:.05:1;
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m = zeros(size(q));
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p = zeros(size(q));
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for i=1:length(q)
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m(i) = wblinv(q(i), scale, shape);
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end
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try
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for i=1:length(q)
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p(i) = wblcdf(m(i), scale, shape);
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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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% Check the results
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if t(1)
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for i=1:length(q)
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t(i+1) = abs(p(i)-q(i))<1e-12;
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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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