International Statistical Review
- Internat. Statist. Rev.
- Volume 73, Number 1 (2005), 111-129.
The $t$ Copula and Related Copulas
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.
Internat. Statist. Rev., Volume 73, Number 1 (2005), 111-129.
First available in Project Euclid: 31 March 2005
Permanent link to this document
Zentralblatt MATH identifier
Demarta, Stefano; Mcneil, Alexander J. The $t$ Copula and Related Copulas. Internat. Statist. Rev. 73 (2005), no. 1, 111--129. https://projecteuclid.org/euclid.isr/1112304815