A generalization of Archimedean and Marshall-Olkin copulas family

In this paper, we consider a new family of multivariate copulas described by a sequence of functions, named as AMO copula. The set of AMO copulas corresponds to a class of multivariate shock models with the Archimedean type of dependence. Sufficient conditions on the involved sequence of functions t...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 428; pp. 1 - 33
Main Authors Xie, Jiehua, Yang, Jingping, Zhu, Wenhao, Zou, Wei
Format Journal Article
LanguageEnglish
Published Elsevier B.V 30.01.2022
Subjects
Archimedean copula
Marshall-Olkin copula
Multivariate shock model
n-Monotone decreasing function sequence
Singular component
Tail behavior
Singular component
Tail behavior
Multivariate shock model
Marshall-Olkin copula
Archimedean copula
n-Monotone decreasing function sequence
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Summary:In this paper, we consider a new family of multivariate copulas described by a sequence of functions, named as AMO copula. The set of AMO copulas corresponds to a class of multivariate shock models with the Archimedean type of dependence. Sufficient conditions on the involved sequence of functions to obtain a multivariate copula are given and the probabilistic structure of the AMO copula is provided. We show that the family of AMO copulas is a generalization of Archimedean and Marshall-Olkin copulas family, and it includes some well-known copulas as specific cases. An alternative method for generating random vectors from AMO copulas via distortion functions is provided. In addition, a singular component along the main diagonal of the AMO copula is also verified. Finally, the tail behaviors of AMO copulas are discussed and some numerical illustrations are provided.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2021.04.003