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Copulas and Their Applications

Copulas have recently been of great interest to statisticians as well as financial econometricians since they give a promising, flexible tool for understanding dependence among random variables, and for modeling and simulating nonnormal multivariate data. In its simplest form, a d-dimensional copula function (or simply d-copula) is a d-dimensional distribution function with all univariate marginals being U(0, 1) distribution. The usefulness of copulas comes from Sklar's theorem, which states that any d-dimensional distribution function F can be represented as