A new class of copula regression models for modelling multivariate heavy-tailed data
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A new class of copulas, termed the MGL copula class, is introduced. The new copula originates from extracting the dependence function of the multivariate generalized log-Moyal-gamma distribution whose marginals follow the univariate generalized log-Moyal-gamma (GLMGA) distribution as introduced in <cit.>. The MGL copula can capture nonelliptical, exchangeable, and asymmetric dependencies among marginal coordinates and provides a simple formulation for regression applications. We discuss the probabilistic characteristics of MGL copula and obtain the corresponding extreme-value copula, named the MGL-EV copula. While the survival MGL copula can be also regarded as a special case of the MGB2 copula from <cit.>, we show that the proposed model is effective in regression modelling of dependence structures. Next to a simulation study, we propose two applications illustrating the usefulness of the proposed model. This method is also implemented in a user-friendly R package: .
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