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Sklar's Theorem


Let H be a two-dimensional distribution function with marginal distribution functions F and G. Then there exists a copula C such that

 H(x,y)=C(F(x),G(y)).

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.


See also

Copula

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Cite this as:

Weisstein, Eric W. "Sklar's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SklarsTheorem.html

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