Publication

Multivariate extreme models based on underlying skew-t and skew-normal distributions

Simone Padoan
2011
Journal Articles

Abstract

We derive for the first time the limiting distribution of maxima of skew-t random vectors and we show that its limiting case, as the degree of freedom goes to infinity, is the skewed version of the well-known FlOsler-Reiss model. The advantage of the new families of models is that they are particularly flexible, allowing for both symmetric and asymmetric dependence structures and permitting the modelling of multivariate extremes with dimensions greater than two. (C) 2011 Elsevier Inc. All rights reserved.

Official source

https://infoscience.epfl.ch/entities/publication/98f5608c-d738-4109-89ce-9b34c033e8fc

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Simone Padoan
2011
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/98f5608c-d738-4109-89ce-9b34c033e8fc

About this result

Related concepts (14)

Skewness

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution, negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule.

Generalized normal distribution

The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric" and "asymmetric"; however, this is not a standard nomenclature. The symmetric generalized normal distribution, also known as the exponential power distribution or the generalized error distribution, is a parametric family of symmetric distributions.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

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