The t copula and related copulas

Stefano Demarta*, Alexander J. McNeil

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)111-129
Number of pages19
JournalInternational Statistical Review
Issue number1
Publication statusPublished - Apr 2005


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

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