Index-mixed copulas

06/19/2023

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by   Klaus Herrmann, et al.

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Motivated by the construction of the often analytically tractable Farlie-Gumbel-Morgenstern (FGM) copula family, we introduce index-mixed copulas. In contrast to FGM copulas, index-mixed copulas allow one to model the full range of concordance as well as to model lower or upper tail dependence, while still retaining the analytical tractability of FGM copulas. Also, index-mixed copulas are straightforward to simulate from. The construction principle and its properties are easily comprehensible and allow for more flexibility in modeling realistic dependencies in applications than the limited FGM copula family can provide.