## The t copula and related copulas (2005)

Venue: | INTERNATIONAL STATISTICAL REVIEW |

Citations: | 62 - 0 self |

### BibTeX

@ARTICLE{Demarta05thet,

author = {Stefano Demarta and Alexander J. McNeil},

title = {The t copula and related copulas},

journal = {INTERNATIONAL STATISTICAL REVIEW},

year = {2005},

volume = {73},

pages = {111--129}

}

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### OpenURL

### Abstract

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.