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Constructing and generalizing given multivariate copulas: a unifying approach. (English) Zbl 1314.62124

Summary: Recently, E. Liebscher [J. Multivariate Anal. 99, No. 10, 2234–2250 (2008; Zbl 1151.62043)] introduced a general construction scheme of \(d\)-variate copulas which generalizes the Archimedean family. Similarly, P. M. Morillas [Metrika 61, No. 2, 169–184 (2005; Zbl 1079.62056)] proposed a method to obtain a variety of new copulas from a given \(d\)-copula. Both approaches coincide only for the particular subclass of Archimedean copulas. Within this work, we present a unifying framework which includes both Liebscher and Morillas copulas as special cases. Above that, more general copulas may be constructed. First examples are given.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
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References:

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