Copulas: Concepts and novel applications
A bivariate copula can be statistically interpreted as a bivariate distribution function with uniform marginals. Sklar (1959) argues that for any bivariate distribution function, say H with marginals F and G, there exists a copula functional, say C, such that H[x, y] = C[F[x], G[y]] , for (x, y) T in the support of H. What is to presented is self-contained review, mainly from a statistical point of view, of the concept of copulas vis-a-vis multivariate distributions and dependence and to motivate their utility via a number of applications to the design of clinical trials, microarray studies with survival endpoints and the analysis of dependent Receiver Operator Curves (ROC).
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