Table 3 IFML, AIC, \(\widehat {\tau }, \widehat {\lambda }_{L}, \widehat {\lambda }_{U}\), and parameter estimates with standard errors in parentheses for the base, UW and Beta distorted copula models
From: New families of bivariate copulas via unit weibull distortion
Family | IFML | AIC | \(\widehat {\tau }\) | \(\widehat {\lambda }_{L}\) | \(\widehat {\lambda }_{U}\) | \(\widehat {\theta }\) | \(\widehat {a}\) | \(\widehat {b}\) |
|---|---|---|---|---|---|---|---|---|
Frank | 172.6 | -343.1 | 0.316 | – | – | 3.11(0.17) | ||
Gaussian | 183.8 | -365.7 | 0.319 | – | – | 0.48(0.02) | ||
SClayton | 198.9 | -395.8 | 0.278 | – | 0.41 | 0.77(0.05) | ||
Gumbel | 204.9 | -407.8 | 0.306 | – | 0.38 | 1.44(0.03) | ||
SBB1 | 206.2 | -408.4 | 0.307 | 0.13 | 0.35 | 0.60(0.06) | ||
SBB1 | 1.11 (0.03) | |||||||
UW-SClayton | 204.2 | -402.5 | 0.269 | – | 0.36 | 0.53(0.10) | 0.90(0.03) | 0.98(0.06) |
UW-Frank | 205.5 | -405 | 0.311 | – | 0.35 | 0.38(0.36) | 0.72(0.03) | 0.63(0.46) |
UW-Gaussian | 205.1 | -404.2 | 0.319 | – | 0.36 | 0.02(0.04) | 0.71(0.03) | 0.14(0.36) |
UW-SBB1 | 207.8 | -407.6 | 0.317 | 1 | 0.32 | 0.24(0.15) | 0.78(0.07) | 0.97(0.30) |
UW-SBB1 | – | – | – | – | – | 1.01(0.02) | ||
B-SClayton | 204.7 | -403.3 | 0.287 | – | 0.53 | 0.89(0.72) | 1.24(0.74) | 0.89(0.33) |
B-Frank | 206.7 | -407.3 | 0.314 | – | 0.40 | 1.35(0.25) | 1.05(0.16) | 0.68(0.10) |
B-Gaussian | 204.3 | -402.6 | 0.216 | – | 0.15 | 0.26(0.05) | 1.10(0.67) | 0.89(0.13) |
B-SBB1 | 206.6 | -405.3 | 0.312 | 0.08 | 0.35 | 0.47(0.54) | 1.34(0.63) | 0.92(0.37) |
B-SBB1 | – | – | 1.13(0.05) |