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

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  • Li, Zhengxiao
  • Beirlant, Jan
  • Yang, Liang

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 Li et al. (2021). 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 Yang et al. (2011), 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: rMGLReg.

Suggested Citation

  • Li, Zhengxiao & Beirlant, Jan & Yang, Liang, 2022. "A new class of copula regression models for modelling multivariate heavy-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 243-261.
    • Handle: RePEc:eee:insuma:v:104:y:2022:i:c:p:243-261
    DOI: 10.1016/j.insmatheco.2022.02.002
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    More about this item

    Keywords

    MGL copula; MGB2 copula; Exchangeable and asymmetric dependency; Extreme-value copula; Copula regression;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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