Ahad Jamalizadeh

Skew-elliptical distributions and their relationship with order statistics

In this talk, I will discuss some recent works of mine on skew- elliptical distributions and their relationship with order statis- tics from multivariate elliptical and multivariate unified skew- elliptical distributions. The first part of my talk will discuss dis- tributions 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 expressions 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 distri- butions and we look at the normal and t cases in details. The last part of my talk involves our most recent work where we show that the cumulative distribution functions (cdfs) of order statis- tics and linear combinations of order statistics from multivariate skew-elliptical distributions can be expressed as mixtures of cdfs of multivariate unified skew-elliptical distributions. These mix- ture representations can be used to obtain moment generating functions and moments of order statistics and linear combina- tions of order statistics, where they exist.