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Sklar's Theorem

Let $H$ be a 2-D distribution function with marginal distribution functions $F$ and $G$. Then there exists a Copula $C$ such that


Conversely, for any univariate distribution functions $F$ and $G$ and any Copula $C$, the function $H$ is a two-dimensional distribution function with marginals $F$ and $G$. Furthermore, if $F$ and $G$ are continuous, then $C$ is unique.

© 1996-9 Eric W. Weisstein