385 lines
12 KiB
Matlab
385 lines
12 KiB
Matlab
function [lpd, dlpd, d2lpd, info] = density(o, x)
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% Evaluate the logged prior density at x.
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%
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% INPUTS
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% - o [dprior]
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% - x [double] m×1 vector, point where the prior density is evaluated.
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%
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% OUTPUTS
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% - lpd [double] scalar, value of the logged prior density at x.
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% - dlpd [double] m×1 vector, first order derivatives.
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% - d2lpd [double] m×1 vector, second order derivatives.
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%
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% REMARKS
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% Second order derivatives holder, d2lpd, has the same rank and shape than dlpd because the priors are
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% independent (we would have to use a matrix if non orthogonal priors were allowed in Dynare).
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%
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% EXAMPLE
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%
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% >> Prior = dprior(bayestopt_, options_.prior_trunc);
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% >> lpd = Prior.dsensity(x)
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% Copyright © 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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lpd = 0.0;
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if nargout>1
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dlpd = zeros(1, length(x));
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if nargout>2
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d2lpd = dlpd;
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if nargout>3
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info = [];
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end
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end
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end
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if o.isuniform
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if any(x(o.iduniform)-o.p3(o.iduniform)<0) || any(x(o.iduniform)-o.p4(o.iduniform)>0)
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lpd = -Inf ;
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if nargout==4
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info = o.iduniform((x(o.iduniform)-o.p3(o.iduniform)<0) || (x(o.iduniform)-o.p4(o.iduniform)>0));
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end
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return
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end
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lpd = lpd - sum(log(o.p4(o.iduniform)-o.p3(o.iduniform))) ;
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if nargout>1
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dlpd(o.iduniform) = zeros(length(o.iduniform), 1);
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if nargout>2
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d2lpd(o.iduniform) = zeros(length(o.iduniform), 1);
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end
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end
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end
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if o.isgaussian
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switch nargout
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case 1
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lpd = lpd + sum(lpdfnorm(x(o.idgaussian), o.p6(o.idgaussian), o.p7(o.idgaussian)));
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case 2
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[tmp, dlpd(o.idgaussian)] = lpdfnorm(x(o.idgaussian), o.p6(o.idgaussian), o.p7(o.idgaussian));
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lpd = lpd + sum(tmp);
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case {3,4}
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[tmp, dlpd(o.idgaussian), d2lpd(o.idgaussian)] = lpdfnorm(x(o.idgaussian), o.p6(o.idgaussian), o.p7(o.idgaussian));
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lpd = lpd + sum(tmp);
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end
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end
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if o.isgamma
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switch nargout
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case 1
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lpd = lpd + sum(lpdfgam(x(o.idgamma)-o.p3(o.idgamma), o.p6(o.idgamma), o.p7(o.idgamma)));
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if isinf(lpd), return, end
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case 2
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[tmp, dlpd(o.idgamma)] = lpdfgam(x(o.idgamma)-o.p3(o.idgamma), o.p6(o.idgamma), o.p7(o.idgamma));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 3
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[tmp, dlpd(o.idgamma), d2lpd(o.idgamma)] = lpdfgam(x(o.idgamma)-o.p3(o.idgamma), o.p6(o.idgamma), o.p7(o.idgamma));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 4
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[tmp, dlpd(o.idgamma), d2lpd(o.idgamma)] = lpdfgam(x(o.idgamma)-o.p3(o.idgamma), o.p6(o.idgamma), o.p7(o.idgamma));
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lpd = lpd + sum(tmp);
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if isinf(lpd)
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info = o.idgamma(isinf(tmp));
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return
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end
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end
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end
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if o.isbeta
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switch nargout
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case 1
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lpd = lpd + sum(lpdfgbeta(x(o.idbeta), o.p6(o.idbeta), o.p7(o.idbeta), o.p3(o.idbeta), o.p4(o.idbeta)));
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if isinf(lpd), return, end
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case 2
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[tmp, dlpd(o.idbeta)] = lpdfgbeta(x(o.idbeta), o.p6(o.idbeta), o.p7(o.idbeta), o.p3(o.idbeta), o.p4(o.idbeta));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 3
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[tmp, dlpd(o.idbeta), d2lpd(o.idbeta)] = lpdfgbeta(x(o.idbeta), o.p6(o.idbeta), o.p7(o.idbeta), o.p3(o.idbeta), o.p4(o.idbeta));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 4
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[tmp, dlpd(o.idbeta), d2lpd(o.idbeta)] = lpdfgbeta(x(o.idbeta), o.p6(o.idbeta), o.p7(o.idbeta), o.p3(o.idbeta), o.p4(o.idbeta));
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lpd = lpd + sum(tmp);
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if isinf(lpd)
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info = o.idbeta(isinf(tmp));
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return
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end
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end
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end
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if o.isinvgamma1
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switch nargout
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case 1
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lpd = lpd + sum(lpdfig1(x(o.idinvgamma1)-o.p3(o.idinvgamma1), o.p6(o.idinvgamma1), o.p7(o.idinvgamma1)));
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if isinf(lpd), return, end
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case 2
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[tmp, dlpd(o.idinvgamma1)] = lpdfig1(x(o.idinvgamma1)-o.p3(o.idinvgamma1), o.p6(o.idinvgamma1), o.p7(o.idinvgamma1));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 3
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[tmp, dlpd(o.idinvgamma1), d2lpd(o.idinvgamma1)] = lpdfig1(x(o.idinvgamma1)-o.p3(o.idinvgamma1), o.p6(o.idinvgamma1), o.p7(o.idinvgamma1));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 4
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[tmp, dlpd(o.idinvgamma1), d2lpd(o.idinvgamma1)] = lpdfig1(x(o.idinvgamma1)-o.p3(o.idinvgamma1), o.p6(o.idinvgamma1), o.p7(o.idinvgamma1));
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lpd = lpd + sum(tmp);
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if isinf(lpd)
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info = o.idinvgamma1(isinf(tmp));
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return
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end
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end
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end
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if o.isinvgamma2
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switch nargout
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case 1
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lpd = lpd + sum(lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2)));
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if isinf(lpd), return, end
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case 2
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[tmp, dlpd(o.idinvgamma2)] = lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 3
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[tmp, dlpd(o.idinvgamma2), d2lpd(o.idinvgamma2)] = lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 4
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[tmp, dlpd(o.idinvgamma2), d2lpd(o.idinvgamma2)] = lpdfig2(x(o.idinvgamma2)-o.p3(o.idinvgamma2), o.p6(o.idinvgamma2), o.p7(o.idinvgamma2));
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lpd = lpd + sum(tmp);
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if isinf(lpd)
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info = o.idinvgamma2(isinf(tmp));
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return
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end
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end
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end
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if o.isweibull
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switch nargout
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case 1
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lpd = lpd + sum(lpdfgweibull(x(o.idweibull), o.p6(o.idweibull), o.p7(o.idweibull)));
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if isinf(lpd), return, end
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case 2
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[tmp, dlpd(o.idweibull)] = lpdfgweibull(x(o.idweibull), o.p6(o.idweibull), o.p7(o.idweibull));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 3
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[tmp, dlpd(o.idweibull), d2lpd(o.idweibull)] = lpdfgweibull(x(o.idweibull), o.p6(o.idweibull), o.p7(o.idweibull));
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lpd = lpd + sum(tmp);
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if isinf(lpd), return, end
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case 4
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[tmp, dlpd(o.idweibull), d2lpd(o.idweibull)] = lpdfgweibull(x(o.idweibull), o.p6(o.idweibull), o.p7(o.idweibull));
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lpd = lpd + sum(tmp);
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if isinf(lpd)
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info = o.idweibull(isinf(tmp));
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return
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end
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end
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end
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return % --*-- Unit tests --*--
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%@test:1
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% Fill global structures with required fields...
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prior_trunc = 1e-10;
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p0 = repmat([1; 2; 3; 4; 5; 6; 8], 2, 1); % Prior shape
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p1 = .4*ones(14,1); % Prior mean
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p2 = .2*ones(14,1); % Prior std.
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p3 = NaN(14,1);
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p4 = NaN(14,1);
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p5 = NaN(14,1);
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p6 = NaN(14,1);
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p7 = NaN(14,1);
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for i=1:14
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switch p0(i)
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case 1
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% Beta distribution
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p3(i) = 0;
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p4(i) = 1;
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[p6(i), p7(i)] = beta_specification(p1(i), p2(i)^2, p3(i), p4(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 1);
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case 2
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% Gamma distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = gamma_specification(p1(i), p2(i)^2, p3(i), p4(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 2);
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case 3
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% Normal distribution
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p3(i) = -Inf;
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p4(i) = Inf;
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p6(i) = p1(i);
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p7(i) = p2(i);
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p5(i) = p1(i);
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case 4
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% Inverse Gamma (type I) distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 1, false);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 4);
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case 5
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% Uniform distribution
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[p1(i), p2(i), p6(i), p7(i)] = uniform_specification(p1(i), p2(i), p3(i), p4(i));
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p3(i) = p6(i);
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p4(i) = p7(i);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 5);
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case 6
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% Inverse Gamma (type II) distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 2, false);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 6);
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case 8
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% Weibull distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = weibull_specification(p1(i), p2(i)^2, p3(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 8);
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otherwise
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error('This density is not implemented!')
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end
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end
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BayesInfo.pshape = p0;
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BayesInfo.p1 = p1;
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BayesInfo.p2 = p2;
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BayesInfo.p3 = p3;
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BayesInfo.p4 = p4;
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BayesInfo.p5 = p5;
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BayesInfo.p6 = p6;
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BayesInfo.p7 = p7;
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% Call the tested routine
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try
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Prior = dprior(BayesInfo, prior_trunc, false);
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% Compute density at the prior mode
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lpdstar = Prior.density(p5);
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% Draw random deviates in a loop and evaluate the density.
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LPD = NaN(10000,1);
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parfor i = 1:10000
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x = Prior.draw();
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LPD(i) = Prior.density(x);
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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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if t(1)
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t(2) = all(LPD<=lpdstar);
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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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% Fill global structures with required fields...
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prior_trunc = 1e-10;
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p0 = repmat([1; 2; 3; 4; 5; 6; 8], 2, 1); % Prior shape
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p1 = .4*ones(14,1); % Prior mean
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p2 = .2*ones(14,1); % Prior std.
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p3 = NaN(14,1);
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p4 = NaN(14,1);
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p5 = NaN(14,1);
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p6 = NaN(14,1);
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p7 = NaN(14,1);
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for i=1:14
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switch p0(i)
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case 1
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% Beta distribution
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p3(i) = 0;
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p4(i) = 1;
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[p6(i), p7(i)] = beta_specification(p1(i), p2(i)^2, p3(i), p4(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 1);
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case 2
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% Gamma distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = gamma_specification(p1(i), p2(i)^2, p3(i), p4(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 2);
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case 3
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% Normal distribution
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p3(i) = -Inf;
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p4(i) = Inf;
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p6(i) = p1(i);
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p7(i) = p2(i);
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p5(i) = p1(i);
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case 4
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% Inverse Gamma (type I) distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 1, false);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 4);
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case 5
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% Uniform distribution
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[p1(i), p2(i), p6(i), p7(i)] = uniform_specification(p1(i), p2(i), p3(i), p4(i));
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p3(i) = p6(i);
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p4(i) = p7(i);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 5);
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case 6
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% Inverse Gamma (type II) distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = inverse_gamma_specification(p1(i), p2(i)^2, p3(i), 2, false);
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p5(i) = compute_prior_mode([p6(i) p7(i)], 6);
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case 8
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% Weibull distribution
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p3(i) = 0;
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p4(i) = Inf;
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[p6(i), p7(i)] = weibull_specification(p1(i), p2(i)^2, p3(i));
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p5(i) = compute_prior_mode([p6(i) p7(i)], 8);
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otherwise
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error('This density is not implemented!')
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end
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end
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BayesInfo.pshape = p0;
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BayesInfo.p1 = p1;
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BayesInfo.p2 = p2;
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BayesInfo.p3 = p3;
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BayesInfo.p4 = p4;
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BayesInfo.p5 = p5;
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BayesInfo.p6 = p6;
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BayesInfo.p7 = p7;
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% Call the tested routine
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try
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Prior = dprior(BayesInfo, prior_trunc, false);
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mu = NaN(14,1);
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std = NaN(14,1);
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for i=1:14
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% Define conditional density (it's also a marginal since priors are orthogonal)
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f = @(x) exp(Prior.densities(substitute(p5, i, x)));
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% TODO: Check the version of Octave we use (integral is available as a compatibility wrapper in latest Octave version)
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m = integral(f, p3(i), p4(i));
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density = @(x) f(x)/m; % rescaling is required since the probability mass depends on the conditioning.
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% Compute the conditional expectation
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mu(i) = integral(@(x) x.*density(x), p3(i), p4(i));
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std(i) = sqrt(integral(@(x) ((x-mu(i)).^2).*density(x), p3(i), p4(i)));
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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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if t(1)
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t(2) = all(abs(mu-.4)<1e-6);
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t(3) = all(abs(std-.2)<1e-6);
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end
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T = all(t);
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%@eof:2
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