Table 2
The experimental study for the three copula functions. The 95% credible intervals for the copula and marginal distribution are estimated from the posterior distributions
| Copula | Parameter | True value | 2.50% | 50% | 97.50% |
|---|---|---|---|---|---|
| Clayton copula |  | 3.000 | 2.784 | 2.992 | 3.215 |
 | 1.000 | 0.912 | 0.984 | 1.061 | |
 | 1.000 | 0.970 | 1.003 | 1.039 | |
 | 0.500 | 0.516 | 0.497 | 0.479 | |
 | 4.066 | 3.474 | 3.910 | 4.394 | |
| Frank copula |  | 3.000 | 2.853 | 3.097 | 3.361 |
 | 1.000 | 0.941 | 1.030 | 1.125 | |
 | 1.000 | 0.975 | 1.006 | 1.041 | |
 | 0.500 | 0.517 | 0.496 | 0.476 | |
 | 9.563 | 8.443 | 9.371 | 10.290 | |
| Gumbel copula |  | 3.000 | 2.613 | 2.817 | 3.054 |
 | 1.000 | 0.867 | 0.940 | 1.020 | |
 | 1.000 | 0.977 | 1.013 | 1.046 | |
 | 0.500 | 0.532 | 0.512 | 0.492 | |
 | 3.015 | 2.777 | 3.020 | 3.273 |
| Copula | Parameter | True value | 2.50% | 50% | 97.50% |
|---|---|---|---|---|---|
| Clayton copula | | 3.000 | 2.784 | 2.992 | 3.215 |
| | 1.000 | 0.912 | 0.984 | 1.061 | |
| | 1.000 | 0.970 | 1.003 | 1.039 | |
| | 0.500 | 0.516 | 0.497 | 0.479 | |
| | 4.066 | 3.474 | 3.910 | 4.394 | |
| Frank copula | | 3.000 | 2.853 | 3.097 | 3.361 |
| | 1.000 | 0.941 | 1.030 | 1.125 | |
| | 1.000 | 0.975 | 1.006 | 1.041 | |
| | 0.500 | 0.517 | 0.496 | 0.476 | |
| | 9.563 | 8.443 | 9.371 | 10.290 | |
| Gumbel copula | | 3.000 | 2.613 | 2.817 | 3.054 |
| | 1.000 | 0.867 | 0.940 | 1.020 | |
| | 1.000 | 0.977 | 1.013 | 1.046 | |
| | 0.500 | 0.532 | 0.512 | 0.492 | |
| | 3.015 | 2.777 | 3.020 | 3.273 |