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arXiv · 2108.05511

A new class of copula regression models for modelling multivariate heavy-tailed data

Zhengxiao Li·Jan Beirlant·Liang Yang
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Abstract

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 \citet{li2019jan}. 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 \citet{yang2011generalized}, 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: \texttt{rMGLReg}.

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Zhengxiao Li, Jan Beirlant, Liang Yang. 2021-08-12. A new class of copula regression models for modelling multivariate heavy-tailed data. https://arxiv.org/abs/2108.05511

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