Table 2 Widely used copula functions.
Name | Copula CDF | Parameter scale |
|---|---|---|
Gaussian | \(C(u,v)={{{\Phi }}}_{2}\left({{{\Phi }}}^{-1}(u),{{{\Phi }}}^{-1}(v);\rho \right)\) | ρ ∈ (−1, 1) |
t | \({C}_{\nu}(u,v)={T}_{\nu}\left({T}_{\nu }^{-1}(u),{T}_{\nu }^{-1}(v);\rho \right)\) | ρ ∈ (−1, 1) |
Clayton | \({C}_{Cl}(u,v;\theta )={\left({u}^{-\theta }+{v}^{-\theta }-1\right)}^{-\frac{1}{\theta }}\) | θ ∈ (0, + ∞) |
Gumbel | \({C}_{G}(u,v;\alpha )=\exp \left(-{\left[{\left(-\ln u\right)}^{\alpha }+{\left(-\ln v\right)}^{\alpha }\right]}^{\frac{1}{\alpha }}\right)\) | \(\alpha \in \left[1,+\infty \right)\) |
