From d676c67f033e307344b0ebf9f12ad999bffd2d5b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?St=C3=A9phane=20Adjemian=20=28Charybdis=29?=
 <stephane.adjemian@univ-lemans.fr>
Date: Fri, 11 Dec 2015 11:50:01 +0100
Subject: [PATCH] Added CDF for the Weibull distribution.

---
 matlab/missing/stats/wblcdf.m | 149 ++++++++++++++++++++++++++++++++++
 1 file changed, 149 insertions(+)
 create mode 100644 matlab/missing/stats/wblcdf.m

diff --git a/matlab/missing/stats/wblcdf.m b/matlab/missing/stats/wblcdf.m
new file mode 100644
index 000000000..14b0fc8e8
--- /dev/null
+++ b/matlab/missing/stats/wblcdf.m
@@ -0,0 +1,149 @@
+function p = wblcdf(x, scale, shape)   % --*-- Unitary tests --*--
+
+% Cumulative distribution function for the Weibull distribution.
+%
+% INPUTS 
+% - x     [double] Positive real scalar.
+% - scale [double] Positive hyperparameter.
+% - shape [double] Positive hyperparameter.
+%
+% OUTPUTS 
+% - p     [double] Positive scalar between 
+
+% Copyright (C) 2015 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/>.
+
+
+% Check input arguments.
+
+if nargin<3
+    error('Three input arguments required!')
+end
+
+if ~isnumeric(x) || ~isscalar(x) || ~isreal(x)
+    error('First input argument must be a real scalar!')
+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
+
+% Filter trivial polar cases.
+
+if x<=0
+    p = 0;
+    return
+end
+
+if isinf(x)
+    p = 1;
+    return
+end
+
+% Evaluate the CDF. 
+
+p = 1-exp(-(x/scale)^shape);
+
+%@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
+