What is copula?

What is copula?

Approach: Define as function linking marginal distributions to joint distribution.

Function C: [0,1]^d → [0,1] such that for joint distribution F with marginals F_i, F(x) = C(F_1(x_1),...,F_d(x_d)). Captures dependence structure separately from marginals.

Follow-up: What is Gaussian copula?

Key concepts: Sklar's theorem, dependence structure, marginals.