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Table 3

The experimental study for the selection of correct copula functions based on the DIC value. The presented values are median values estimated from the marginal posterior distributions of the parameters

Model	Lognormal		Gamma		Copula	Log-likelihood	DIC
Parameter	(3.0)	(1.0)	(1.0)	(0.5)	True/Sim.	Log-likelihood	DIC
Case A (Clayton copula)
Clayton	2.725	1.155	0.989	0.741	4.066/3.900	36.996	329.450
Frank	2.723	1.114	0.984	0.732	9.563/10.663	31.810	340.180
Gumbel	2.721	1.161	0.999	0.752	3.015/2.353	20.739	361.840
Case B (Frank copula)
Clayton	2.757	1.151	0.999	0.747	4.066/2.633	27.253	349.37
Frank	2.984	1.048	0.978	0.734	9.563/12.877	39.341	324.68
Gumbel	2.817	1.122	0.978	0.758	3.015/3.007	31.462	339.76
Case C (Gumbel copula)
Clayton	3.472	0.795	0.878	0.662	4.066/2.445	24.585	310.72
Frank	3.259	0.865	0.891	0.646	9.563/9.680	30.173	301.19
Gumbel	3.457	0.794	0.868	0.612	3.015/3,004	35.907	284.17

Model	Lognormal		Gamma		Copula	Log-likelihood	DIC
Parameter	(3.0)	(1.0)	(1.0)	(0.5)	True/Sim.	Log-likelihood	DIC
Case A (Clayton copula)
Clayton	2.725	1.155	0.989	0.741	4.066/3.900	36.996	329.450
Frank	2.723	1.114	0.984	0.732	9.563/10.663	31.810	340.180
Gumbel	2.721	1.161	0.999	0.752	3.015/2.353	20.739	361.840
Case B (Frank copula)
Clayton	2.757	1.151	0.999	0.747	4.066/2.633	27.253	349.37
Frank	2.984	1.048	0.978	0.734	9.563/12.877	39.341	324.68
Gumbel	2.817	1.122	0.978	0.758	3.015/3.007	31.462	339.76
Case C (Gumbel copula)
Clayton	3.472	0.795	0.878	0.662	4.066/2.445	24.585	310.72
Frank	3.259	0.865	0.891	0.646	9.563/9.680	30.173	301.19
Gumbel	3.457	0.794	0.868	0.612	3.015/3,004	35.907	284.17

The Log-likelihoods and DIC values in bold are the optimum copulas selected in the experimental study.

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