Modeling and simulation of bivariate distribution of shear strength parameters using copulas - Risk and Reliability in Geotechnical Engineering - page 116

elseif Index_X1 = = 2
display('The best-fit margin for X1 using AIC is Lognormal
distribution');
elseif Index_X1 = = 3
display('The best-fit margin for X1 using AIC is TruncGumbel
distribution');
elseif Index_X1 = = 4
display('The best-fit margin for X1 using AIC is Weibull
distribution');
end
%
BIC_X1 = [BIC_TruncNormal_X1 BIC_Lognormal_X1 BIC_TruncGumbel_X1
BIC_Weibull_X1];
display(BIC_X1);
[BIC_min_X1 Index_X1] = min(BIC_X1,[],2);
if Index_X1 = = 1
display('The best-fit margin for X1 using BIC is TruncNormal
distribution');
elseif Index_X1 = = 2
display('The best-fit margin for X1 using BIC is Lognormal
distribution');
elseif Index_X1 = = 3
display('The best-fit margin for X1 using BIC is TruncGumbel
distribution');
elseif Index_X1 = = 4
display('The best-fit margin for X1 using BIC is Weibull
distribution');
end
%
% Calculate the AIC and BIC values for variable X2
PDF_TruncNormal_X2 = normpdf(data(:,2),mu(2),sigma(2))/(1-normcdf(-mu(2)/
sigma(2)));
AIC_TruncNormal_X2 = -2*sum(log(PDF_TruncNormal_X2)) + 2*Parameter_
Margin;
BIC_TruncNormal_X2 = -2*sum(log(PDF_TruncNormal_X2)) + log(rows)*Parameter_
Margin;
%
sLn = sqrt(log(1 + (sigma(2)/mu(2))^2)); mLn = log(mu(2))-sLn^2/2;
PDF_Lognormal_X2 = lognpdf(data(:,2),mLn,sLn);
AIC_Lognormal_X2 = -2*sum(log(PDF_Lognormal_X2)) + 2*Parameter_Margin;
BIC_Lognormal_X2 = -2*sum(log(PDF_Lognormal_X2)) + log(rows)*Parameter_
Margin;
%
a = 1.282549808/sigma(2); b = mu(2)-(0.5772156649/a);
PDF_TruncGumbel_X2 = a*exp(-a*(data(:,2)-b)-exp(-a*(data(:,2)-b)))/
(1-exp(-exp(a*b)));
AIC_TruncGumbel_X2 = -2*sum(log(PDF_TruncGumbel_X2)) + 2*Parameter_Margin;
BIC_TruncGumbel_X2 = -2*sum(log(PDF_TruncGumbel_X2)) + log(rows)*Parameter_
Margin;
%
k = k_solveWeibull(mu(2),sigma(2)); u = mu(2)/gamma(1 + 1/k);
PDF_Weibull_X2 = k/u*(data(:,2)/u).^(k-1).*exp(-(data(:,2)/u).^k);
AIC_Weibull_X2 = -2*sum(log(PDF_Weibull_X2)) + 2*Parameter_Margin;
BIC_Weibull_X2 = -2*sum(log(PDF_Weibull_X2)) + log(rows)*Parameter_Margin;
%