Tail dependence for multivariate t -copulas and its monotonicity

Chan, Yin; Li, Haijun

doi:10.1016/j.insmatheco.2007.08.008

Cited by 21 publications

(14 citation statements)

References 10 publications

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“…If the local dependence increase occurs within the subset of the components with indexes in J, then the dependence increase within J outweighs the dependence increase among all the components, and consequently, the orthant tail dependence is decreased. A similar phenomenon has been reported in [3] for multivariate tdistributions.…”

Section: Absolutely Continuous Min-stable Multivariate Exponential DIsupporting

confidence: 86%

“…Schmidt [27] showed that bivariate elliptical distributions possess the tail dependence property if the tail of their generating random variable is regularly varying. The explicit expressions of the orthant tail dependence for multivariate Marshall-Olkin distributions have been derived in [17], and the moment-based formulas for multivariate tail dependence of scale mixtures of multivariate distributions, such as multivariate t-distributions, have been established in [3,18]. The use of (1.5) to study the contagion risk among 25 European and US banks is reported in [6].…”

Section: Theorem 11 a Distribution G Is An Mev Distribution With Stmentioning

confidence: 99%

“…Such preservation properties, however, are no longer valid for the multivariate tail dependence parameters with J consisting of more than one index. In fact, increasing the dependence of a random vector might even decrease some of tail dependence parameters [17,3], as these parameters describe the relative strengths of extremal dependence of a random vector with respect to a subset of its components. This paper further illustrates this property in the context of MEV distributions.…”

Section: Theorem 11 a Distribution G Is An Mev Distribution With Stmentioning

confidence: 99%

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Orthant tail dependence of multivariate extreme value distributions

2009

Journal of Multivariate Analysis

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a b s t r a c tThe orthant tail dependence describes the relative deviation of upper-(or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its components, and can be used in the study of dependence among extreme values. Using the conditional approach, this paper examines the extremal dependence properties of multivariate extreme value distributions and their scale mixtures, and derives the explicit expressions of orthant tail dependence parameters for these distributions. Properties of the tail dependence parameters, including their relations with other extremal dependence measures used in the literature, are discussed. Various examples involving multivariate exponential, multivariate logistic distributions and copulas of Archimedean type are presented to illustrate the results.

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Section: Absolutely Continuous Min-stable Multivariate Exponential DIsupporting

confidence: 86%

Section: Theorem 11 a Distribution G Is An Mev Distribution With Stmentioning

confidence: 99%

Section: Theorem 11 a Distribution G Is An Mev Distribution With Stmentioning

confidence: 99%

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Orthant tail dependence of multivariate extreme value distributions

2009

Journal of Multivariate Analysis

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“…of the inverse-Gamma(ν/2, ν/2) distribution, which is not finite for every t > 0, since that the inverse Gamma distribution has heavy tail. The proof that the inverse Gamma distribution has heavy tail can be seen in Lemma 2.1. of Chan and Li (2008).…”

Section: Resultsmentioning

confidence: 95%

On the identifiability of finite mixture of Skew-Normal and Skew-t distributions

Otiniano

Rathie

Ozelim

2015

Statistics & Probability Letters

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“…An elaborate discussion on various t-distributions has been provided by Kotz and Nadarajah [30]. One may also refer to [1,8,35,3,9,28,6,[31][32][33]36] for related discussions.…”

Section: Introductionmentioning

confidence: 99%

On Pearson–Kotz Dirichlet distributions

Hashorva

2011

Journal of Multivariate Analysis

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a b s t r a c tIn this paper, we discuss some basic distributional and asymptotic properties of the Pearson-Kotz Dirichlet multivariate distributions. These distributions, which appear as the limit of conditional Dirichlet random vectors, possess many appealing properties and are interesting from theoretical as well as applied points of view. We illustrate an application concerning the approximation of the joint conditional excess distribution of elliptically symmetric random vectors.

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Tail dependence for multivariate t -copulas and its monotonicity

Cited by 21 publications

References 10 publications

Orthant tail dependence of multivariate extreme value distributions

Orthant tail dependence of multivariate extreme value distributions

On the identifiability of finite mixture of Skew-Normal and Skew-t distributions

On Pearson–Kotz Dirichlet distributions

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