440 lines
8.2 KiB
Matlab
440 lines
8.2 KiB
Matlab
function [ldens,Dldens,D2ldens] = lpdfgweibull(x,a,b,c) % --*-- Unitary tests --*--
|
|
|
|
% Evaluates the logged Weibull PDF at x.
|
|
%
|
|
% INPUTS
|
|
% - x [double] m*n matrix of points where the (logged) density will be evaluated,
|
|
% - a [double] m*n matrix of First Weibull distribution parameters (shape parameter, k),
|
|
% - b [double] m*n matrix of Second Weibull distribution parameters (scale parameter, λ),
|
|
% - c [double] m*n matrix of Third Weibull distribution parameters (location parameter, default is 0).
|
|
%
|
|
% OUTPUTS
|
|
% - ldens [double] m*n matrix of logged (generalized) Weibull densities.
|
|
% - Dldens [double] m*n matrix (first order derivatives w.r.t. x)
|
|
% - D2ldens [double] m*n matrix (second order derivatives w.r.t. x)
|
|
%
|
|
% SPECIAL REQUIREMENTS
|
|
% none
|
|
|
|
% 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 <http://www.gnu.org/licenses/>.
|
|
|
|
% Initialize output arguments
|
|
ldens = -Inf(size(x));
|
|
if nargout>1
|
|
Dldens = NaN(size(x));
|
|
D2ldens = NaN(size(x));
|
|
end
|
|
|
|
% Check the number of input arguments
|
|
if nargin<3
|
|
error('CheckInputArgs','At least three input arguments required!')
|
|
end
|
|
|
|
% Set default value for location parameter(s).
|
|
if nargin<4
|
|
c = zeros(size(x));
|
|
end
|
|
|
|
% Reshape inputs if needed (and possible)
|
|
if ~isscalar(x)
|
|
if isscalar(a)
|
|
a = repmat(a, size(x));
|
|
end
|
|
if isscalar(b)
|
|
b = repmat(b, size(x));
|
|
end
|
|
if isscalar(c)
|
|
c = repmat(c, size(x));
|
|
end
|
|
end
|
|
|
|
% Get indices for which the densty is defined
|
|
idx = find((x-c)>=0);
|
|
|
|
% Check size of the inputs
|
|
if (~isequal(size(x), size(a)) || ~isequal(size(x), size(b)) || ~isequal(size(x), size(c)))
|
|
error('CheckInputArgs','All input arguments must have the same dimensions!')
|
|
end
|
|
|
|
if isempty(idx), return, end
|
|
|
|
% Compute the logged density
|
|
|
|
jdx = find( abs(a-1)<1e-12 & x>=c & (x-c)<1e-12) ;
|
|
ldens(jdx) = 1.0;
|
|
|
|
if ~isempty(idx)
|
|
x0 = x(idx)-c(idx);
|
|
x1 = x0./b(idx);
|
|
x2 = x1.^a(idx);
|
|
idx = setdiff(idx, jdx);
|
|
ldens(idx) = log(a(idx)) - a(idx).*log(b(idx)) + (a(idx)-1).*log(x0) - x2 ;
|
|
end
|
|
|
|
% Compute the first and second derivatives.
|
|
if nargout>1
|
|
x3 = (a(idx)-1)./x0;
|
|
x4 = a(idx).*x2./x1./b(idx);
|
|
Dldens(idx) = x3 - x4;
|
|
if nargout>2
|
|
D2ldens(idx) = -x3./x0 - (a(idx)-1).*x4./x1./b(idx);
|
|
end
|
|
end
|
|
|
|
%@test:1
|
|
%$ try
|
|
%$ lpdfgweibull(1.0);
|
|
%$ t(1) = false;
|
|
%$ catch
|
|
%$ t(1) = true;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:1
|
|
|
|
%@test:2
|
|
%$ try
|
|
%$ lpdfgweibull(1.0, .5);
|
|
%$ t(1) = false;
|
|
%$ catch
|
|
%$ t(1) = true;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:2
|
|
|
|
%@test:3
|
|
%$ try
|
|
%$ lpdfgweibull(ones(2,2), .5*ones(2,1), .1*ones(3,1));
|
|
%$ t(1) = false;
|
|
%$ catch
|
|
%$ t(1) = true;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:3
|
|
|
|
%@test:4
|
|
%$ try
|
|
%$ a = lpdfgweibull(-1, .5, .1);
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = isinf(a);
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:4
|
|
|
|
%@test:5
|
|
%$ try
|
|
%$ a = lpdfgweibull(0, 1, 1);
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = abs(a-1.0)<1e-10;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:5
|
|
|
|
%@test:6
|
|
%$ try
|
|
%$ a = lpdfgweibull([0, -1], [1 1], [1 1]);
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = abs(a(1)-1.0)<1e-10;
|
|
%$ t(3) = isinf(a(2));
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:6
|
|
|
|
%@test:7
|
|
%$ scale = 1;
|
|
%$ shape = 2;
|
|
%$ mode = scale*((shape-1)/shape)^(1/shape);
|
|
%$
|
|
%$ try
|
|
%$ [a, b, c] = lpdfgweibull(mode, shape, scale);
|
|
%$ p = rand(1000,1)*4;
|
|
%$ am = lpdfgweibull(p, shape*ones(size(p)), scale*ones(size(p)));
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$
|
|
%$ t(2) = abs(b)<1e-8;
|
|
%$ t(3) = c<0;
|
|
%$ t(4) = all(am<a);
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:7
|
|
|
|
%@test:8
|
|
%$ scale = 1;
|
|
%$ shape = 2;
|
|
%$ density = @(x) exp(lpdfgweibull(x,shape,scale));
|
|
%$
|
|
%$ try
|
|
%$ if isoctave
|
|
%$ s = quadl(density, .0000000001, 100000, 1e-10);
|
|
%$ else
|
|
%$ s = integral(density, 0, 100000);
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = abs(s-1)<1e-6;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:8
|
|
|
|
%@test:9
|
|
%$ scale = 1;
|
|
%$ shape = 1;
|
|
%$ density = @(x) exp(lpdfgweibull(x,shape,scale));
|
|
%$
|
|
%$ try
|
|
%$ if isoctave
|
|
%$ s = quadl(density, .0000000001, 100000, 1e-10);
|
|
%$ else
|
|
%$ s = integral(density, 0, 100000);
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = abs(s-1)<1e-6;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:9
|
|
|
|
%@test:10
|
|
%$ scale = 1;
|
|
%$ shape = .5;
|
|
%$ density = @(x) exp(lpdfgweibull(x,shape,scale));
|
|
%$
|
|
%$ try
|
|
%$ if isoctave
|
|
%$ s = quadl(density, .0000000001, 100000, 1e-10);
|
|
%$ else
|
|
%$ s = integral(density, 0, 100000);
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ if isoctave
|
|
%$ t(2) = abs(s-1)<5e-5;
|
|
%$ else
|
|
%$ t(2) = abs(s-1)<1e-6;
|
|
%$ end
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:10
|
|
|
|
%@test:11
|
|
%$ scale = 1;
|
|
%$ shape = 2;
|
|
%$ xdens = @(x) x.*exp(lpdfgweibull(x,shape,scale));
|
|
%$
|
|
%$ try
|
|
%$ if isoctave
|
|
%$ s = quadgk(xdens, .0000000001, 100000, 1e-10);
|
|
%$ else
|
|
%$ s = integral(xdens, 0, 100000);
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = abs(s-scale*gamma(1+1/shape))<1e-6;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:11
|
|
|
|
%@test:12
|
|
%$ scale = 1;
|
|
%$ shape = 1;
|
|
%$ xdens = @(x) x.*exp(lpdfgweibull(x,shape,scale));
|
|
%$
|
|
%$ try
|
|
%$ if isoctave
|
|
%$ s = quadl(xdens, .0000000001, 100000, 1e-10);
|
|
%$ else
|
|
%$ s = integral(xdens, 0, 100000);
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = abs(s-scale*gamma(1+1/shape))<1e-6;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:12
|
|
|
|
%@test:13
|
|
%$ scale = 1;
|
|
%$ shape = .5;
|
|
%$ xdens = @(x) x.*exp(lpdfgweibull(x,shape,scale));
|
|
%$
|
|
%$ try
|
|
%$ if isoctave
|
|
%$ s = quadl(xdens, .0000000001, 100000, 1e-10);
|
|
%$ else
|
|
%$ s = integral(xdens, 0, 100000);
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ t(2) = abs(s-scale*gamma(1+1/shape))<1e-6;
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:13
|
|
|
|
%@test:14
|
|
%$ scale = 1;
|
|
%$ shape = 2;
|
|
%$ density = @(x) exp(lpdfgweibull(x,shape,scale));
|
|
%$ n = 200;
|
|
%$
|
|
%$ try
|
|
%$ s = NaN(n, 1);
|
|
%$ for i=1:n
|
|
%$ if isoctave
|
|
%$ s(i) = quadl(density, .0000000001, .1*i, 1e-10);
|
|
%$ else
|
|
%$ s(i) = integral(density, 0, .1*i);
|
|
%$ end
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ for i=1:n
|
|
%$ x = .1*i;
|
|
%$ q = 1-exp(-(x/scale)^shape);
|
|
%$ t(i+1) = abs(s(i)-q)<1e-6;
|
|
%$ end
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:14
|
|
|
|
%@test:15
|
|
%$ scale = 1;
|
|
%$ shape = 1;
|
|
%$ density = @(x) exp(lpdfgweibull(x,shape,scale));
|
|
%$ n = 200;
|
|
%$
|
|
%$ try
|
|
%$ s = NaN(n, 1);
|
|
%$ for i=1:n
|
|
%$ if isoctave
|
|
%$ s(i) = quadl(density, .0000000001, .1*i, 1e-10);
|
|
%$ else
|
|
%$ s(i) = integral(density, 0, .1*i);
|
|
%$ end
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ for i=1:n
|
|
%$ x = .1*i;
|
|
%$ q = 1-exp(-(x/scale)^shape);
|
|
%$ t(i+1) = abs(s(i)-q)<1e-6;
|
|
%$ end
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:15
|
|
|
|
%@test:16
|
|
%$ scale = 1;
|
|
%$ shape = .5;
|
|
%$ density = @(x) exp(lpdfgweibull(x,shape,scale));
|
|
%$ n = 200;
|
|
%$
|
|
%$ try
|
|
%$ s = NaN(n, 1);
|
|
%$ for i=1:n
|
|
%$ if isoctave
|
|
%$ s(i) = quadl(density, .0000000001, .1*i, 1e-10);
|
|
%$ else
|
|
%$ s(i) = integral(density, 0, .1*i);
|
|
%$ end
|
|
%$ end
|
|
%$ t(1) = true;
|
|
%$ catch
|
|
%$ t(1) = false;
|
|
%$ end
|
|
%$
|
|
%$ if t(1)
|
|
%$ for i=1:n
|
|
%$ x = .1*i;
|
|
%$ q = 1-exp(-(x/scale)^shape);
|
|
%$ if isoctave
|
|
%$ t(i+1) = abs(s(i)-q)<5e-5;
|
|
%$ else
|
|
%$ t(i+1) = abs(s(i)-q)<1e-6;
|
|
%$ end
|
|
%$ end
|
|
%$ end
|
|
%$
|
|
%$ T = all(t);
|
|
%@eof:16
|