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Table 1 Examples of tail orders and dependence coefficients

From: New families of bivariate copulas via unit weibull distortion

Initial Copula

κLorλL

κUorλU

BB1

λL=2−1/θδ

λU=2−21/δ

Clayton

λL=2−1/θ

κU=2

Frank

κL=2

κU=2

Gaussian

κL=2/(1+ρ)

κU=2/(1+ρ)

UW-Copula

κT,Lor λT,L

κT,Uor λT,U

UW-BB1

λT,L=2b/θδ if a=1

λT,U=2−2a/δ

 

λT,L=1 if a<1

 

UW-Clayton

λT,L=2b/θ if a=1

λT,U=2−2a

 

λT,L=1 if a<1

 

UW-Frank

κT,L=2a

λT,U=2−2a

UW-Gaussian

κT,L=[2/(1+ρ)]a

λT,U=2−2a