In this talk, I will discuss some recent work of mine on skew-elliptical distributions and their relationship with order statistics from multivariate elliptical and multivariate unified skew-elliptical distributions. The first part of my talk will discuss distributions of order statistics from a bivariate normal distribution. We show that these distributions are mixtures of the univariate Azzalini skew-normal distributions (Azzalini, 1985). Followed by this, I will discuss our work on distributions of order statistics from a trivariate normal distribution and we will present explicit experssions for mean and variance of these order statistics. The next part of my talk will discuss an extension of this work where we will discuss order statistics from multivariate elliptical distributions and we look at the normal and t cases in details. The last part of my talk involves our recent submitted work where we show that the cumulative distribution functions (cdfs) of order statistics and linear combination of order statistics from multivariate skew-elliptical distributions can be expressed as mixtures of cdfs of multivariate unified skew-elliptical distributions. These mixture representations can be used to obtain moments of order statistics, where they exist.
Groupe d’études et de recherche en analyse des décisions