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Asymmetric Copulas and Their Application in Design of Experiments

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 336))

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Abstract

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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Acknowledgments

This article is devoted to Prof. Erich Peter Klement on the occasion of his retirement.

The first author has been supported by the Faculty of Economics and Management of Free University of Bozen-Bolzano, Italy, via the project “Model Uncertainty and Dependence”.

The second author would like to thank Prof. Werner Müller, for his support and useful suggestions. She was supported by the project ANR-2011-IS01-001-01 “DESIRE” and Austrian Science Fund (FWF) I 883-N18.

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Authors and Affiliations

  1. Faculty of Economics and Management, Free University of Bozen–Bolzano, Bolzano, Italy

    Fabrizio Durante

  2. Institute for Applied Statistics, Johannes Kepler University Linz, Linz, Austria

    Elisa Perrone

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  1. Fabrizio Durante
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Correspondence to Elisa Perrone .

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  1. Dept of Knowledge-Based Math. Systems, Johannes Kepler University Linz, Linz, Austria

    Susanne Saminger-Platz

  2. Dept. of Mathematics & Descriptive Geo., Slovak University of Technology, BRATISLAVA, Slovakia

    Radko Mesiar

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Durante, F., Perrone, E. (2016). Asymmetric Copulas and Their Application in Design of Experiments. In: Saminger-Platz, S., Mesiar, R. (eds) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-319-28808-6_9

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