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On non-central squared copulas. (English) Zbl 1440.62189

Summary: The goal of this paper is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. The R package NCSCopula [the author, “NCSCopula: non-central squared copula models estimation”, R package version 1.0.1 (2019)] can be used to estimate the parameters for several copula families.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H12 Estimation in multivariate analysis

Software:

R; CDVine; NCSCopula
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References:

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