Let ϕ(u|θ) = (1 − u)θ, for some θ ≥ 1, and show that for the twodimensional case this generates the copula  C(u1, u2|θ) = max[0, 1 − {(1 − u1) θ + (1 − u2) θ}1/θ].  Further, show that as θ → ∞, C(u1,...


Let ϕ(u|θ) = (1 − u)θ, for some θ ≥ 1, and show that for the twodimensional case this generates the copula


 C(u1, u2|θ) = max[0, 1 − {(1 − u1) θ + (1 − u2) θ}1/θ].


 Further, show that as θ → ∞, C(u1, u2|θ) → min(u1, u2), the comonotonicity copula C+, and that as θ → 1, C(u1, u2|θ) → max(u1 + u2 − 1, 0), the counter-monotonicity copula C−.



May 26, 2022
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