# Tail dependence in bivariate skew-Normal and skew-t distributions

@inproceedings{Bortot2008TailDI, title={Tail dependence in bivariate skew-Normal and skew-t distributions}, author={Paola Bortot}, year={2008} }

Quantifying dependence between extreme values is a central problem in many theoretical and applied studies. The main distinction is between asymptotically independent and asymptotically dependent extremes, with important theoretical examples of these general limiting classes being the extremal behaviour of a bivariate Normal distribution, for asymptotic independence, and of the bivariate t distribution, for asymptotic dependence. In this paper we study the tail dependence of skewed extensions…

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## References

SHOWING 1-10 OF 13 REFERENCES

Statistical applications of the multivariate skew normal distribution

- Mathematics
- 1999

Azzalini and Dalla Valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the…

The Skew‐normal Distribution and Related Multivariate Families *

- Mathematics
- 2005

Abstract. This paper provides an introductory overview of a portion of distribution theory which is currently under intense development. The starting point of this topic has been the so‐called…

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution

- Mathematics
- 2003

Summary. A fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non‐symmetric densities. The approach…

Statistics for near independence in multivariate extreme values

- Mathematics
- 1996

We propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence. We…

The t copula and related copulas

- Computer Science
- 2007

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 tCopula, which allow more heterogeneity in the modelling of dependent observations.

Modelling Dependence within Joint Tail Regions

- Mathematics
- 1997

Standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max‐stability, a particular form of joint tail dependence. We develop joint tail…

A conditional approach for multivariate extreme values (with discussion)

- Mathematics
- 2004

Summary. Multivariate extreme value theory and methods concern the characterization, estimation and extrapolation of the joint tail of the distribution of a d‐dimensional random variable. Existing…

Modelling heavy tails and skewness in film returns

- Business
- 2005

The average of box-office revenue is dominated by extreme outcomes, with most films earning little and most revenues flowing to a few blockbusters. In this paper the skewness and heavy tails of film…

The multivariate Gaussian tail model: an application to oceanographic data

- Environmental Science
- 2000

Optimal design of sea‐walls requires the extreme value analysis of a variety of oceanographic data. Asymptotic arguments suggest the use of multivariate extreme value models, but empirical studies…