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

TL;DR

This paper introduces the MGL copula, a new class for modeling complex dependencies in multivariate heavy-tailed data, with applications demonstrated through simulations and real data, and implemented in an R package.

Contribution

The paper presents the novel MGL copula class derived from the multivariate generalized log-Moyal-gamma distribution, enabling flexible modeling of asymmetric and nonelliptical dependencies.

Findings

Effective in regression modeling of dependence structures

Captures nonelliptical, exchangeable, and asymmetric dependencies

Implemented in the R package rMGLReg

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}.