Generalized Logistic Models and its orthant tail dependence

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn (1990), Joe and Hu (1996) and Foug\`eres et al. (2009). The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li (2009)

Extremes of scale mixtures of multivariate time series

Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series \mb{Y}_n, n≥1, rescaled through random factors \mb{T}_n, n≥1, extending some scale mixture models in the literature. We analyze its extremal behavior by deriving the maximum domain of attraction and the multivariate extremal index, which leads to new ways to construct multivariate extreme value distributions. The computation of the multivariate extremal index and the characterization of the tail dependence show the interesting property of these models that however much it is the dependence within and between factors \mb{T}_n, n≥1, the extremal index of the model is unit whenever \mb{Y}_n, n≥1, presents cross-sectional and sequencial tail independence. We illustrate with examples of thinned multivariate time series and multivariate autoregressive processes with random coefficients. An application of these latter to financial data is presented at the end.Helena Ferreira was partially supported by the research unit ``Centro de Matemática" of the University of Beira Interior and the research project PEst-OE/MAT/UI0212/2014 through the Foundation for Science and Technology (FCT) co-financed by FEDER/COMPETE. Marta Ferreira was financed by FEDER Funds through "Programa Operacional Factores de Competitividade - COMPETE" and by Portuguese Funds through FCT - ``Fundação para a Ciência e a Tecnologia", within the project PEst-OE/MAT/UI0013/2014

On the variance of the trimmed mean

This note provides a new expression for the variance of the trimmed mean in terms of product moments of order statistics. An exact expression for the bias of the estimator of the variance of trimmed mean is also provided. As an illustration, exact calculations are carried out for small samples from various t-distributions using (Tiku and Kumra, 1985) product moment tables for the order statistics of the t-distribution.Order statistics t-distribution Winsorized mean

Bivariate Distributions with Given Extreme Value Attractor

A new class of bivariate distributions is introduced and studied, which encompasses Archimedean copulas and extreme value distributions as special cases. Its dependence structure is described, its maximum and minimum attractors are determined, and an algorithm is given for generating observations from any member of this class. It is also shown how it is possible to construct distributions in this family with a predetermined extreme value attractor. This construction is used to study via simulation the small-sample behavior of a bivariate threshold method suggested by H. Joe, R. L. Smith, and I. Weissman (1992, J. Roy. Statist. Soc. Ser. B54, 171-183) for estimating the joint distribution of extremes of two random variates.Archimedean copulas, bivariate threshold method, dependence functions, domains of attraction, extreme value distributions