- consider to add BB1 copula.
BB1 copula: two-parameter copula to model positive dependence
C(u,v,θ,δ)={1+[(u^(-θ)-1)^δ+(v^(-θ)-1)^δ ]^(1/δ) }^(-1/θ),δ≥1,θ>0
Limiting copulas:
δ=1: Clayton copula, θ→0: Gumbel-Houggard copula
Generating function: η(s)=η_(θ,δ) (s)=(1+s^(1/δ) )^(-1/θ).
This copula has both upper and lower tail dependence:
Upper: 2-2^(1/δ) which is the upper tail dependence of Gumbel-Houggard copula
Lower: 2^(-1/δθ).
Reference: Joe, H. (1997). Multivariate Models and Dependence Concepts
I personally found this copula is very useful.
BB1 copula: two-parameter copula to model positive dependence
C(u,v,θ,δ)={1+[(u^(-θ)-1)^δ+(v^(-θ)-1)^δ ]^(1/δ) }^(-1/θ),δ≥1,θ>0
Limiting copulas:
δ=1: Clayton copula, θ→0: Gumbel-Houggard copula
Generating function: η(s)=η_(θ,δ) (s)=(1+s^(1/δ) )^(-1/θ).
This copula has both upper and lower tail dependence:
Upper: 2-2^(1/δ) which is the upper tail dependence of Gumbel-Houggard copula
Lower: 2^(-1/δθ).
Reference: Joe, H. (1997). Multivariate Models and Dependence Concepts
I personally found this copula is very useful.