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 dist...

Abstract For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number properties are already known, but many others not, even some basic ones. The present contribution aims at filling missing gaps. Specifically, moments up to fourth order obtained, from here expressions Mardia’s measures skewness kurtosis. Other ...

• Modeling real data sets, even when we have some potential (as)symmetric models for the underlying data distribution, is always a very difficult task due to some uncontrollable perturbation factors. The analysis of different data sets from diverse areas of application, and in particular from statistical process control (SPC), leads us to notice that they usually exhibit moderate to strong asym...

In this work we approach the problem of model comparison between skew families. For the univariate skew model, we measure the sensitivity of the skewness parameter using the L1-distance between symmetric and asymmetric models and we obtain explicit expressions for some of these models. The main result is that the L1-distance between a representable elliptical distribution and a representable sk...

Sums of lognormal random variables (RVs) occur in many important problems in wireless communications especially in interferences calculation. Several methods have been proposed to approximate the lognormal sum distribution. Most of them requires lengthy Monte Carlo simulations, or advanced slowly converging numerical integrations for curve fitting and parameters estimation. Recently, it has bee...

We discuss tail behaviors, subexponentiality and extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. It shows that the convergence rate of the distribution of the normalized maximum to the Gumbel extreme value distr...

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...