Asymmetric Copulas and Their Application in Design of Experiments

We present an overview on definitions and properties of asymmetric copulas, i.e. copulas whose values are not invariant under any permutation of their arguments. In particular, we review an axiomatic approach in the definition of a measure of asymmetry (non–exchangeability) for copulas, starting with the seminal contributions by Klement and Mesiar [45] and Nelsen [56]. Then we discuss how asymmetric copulas may be useful also in the optimal design of experiments and how they may provide additional insights into these problems.

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