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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)