Averages for Multivariate Random Vectors with Random Weights

Distributional Characterization and Application

Abstract

We consider a random weights average of n independent continuous random vectors X1, ..., Xn, where random weights are cuts of [0, 1] by an increasing sequence of the order statistics of a random sample from a uniform [0, 1]. We employ the multivariate Stieltjes transform and Watson [15] celebrated formula involving the multivariate B-spline functions for distributional identification of multivariate random weights averages. We show that certain classes of Dirichlet and random scale stable random vectors are random weightes averages.