Averages for Multivariate Random Vectors with Random Weights
Distributional Characterization and Application
Keywords:multivariate weighted average with random weights, multivariate Cauchy Stieltjes transform, Dirichlet distribution, multivariate stable distributions
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  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.
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