International Statistical Review

The $t$ Copula and Related Copulas

Stefano Demarta and Alexander J. Mcneil

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The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively.

Article information

Internat. Statist. Rev., Volume 73, Number 1 (2005), 111-129.

First available in Project Euclid: 31 March 2005

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Zentralblatt MATH identifier

Copula Multivariate t distribution Kendall's rank correlation Tail dependence Multivariate extreme value theory Gumbel copula Clayton copula


Demarta, Stefano; Mcneil, Alexander J. The $t$ Copula and Related Copulas. Internat. Statist. Rev. 73 (2005), no. 1, 111--129.

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