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Averages for multivariate random vectors with random weights: distributional characterization and application. (English) Zbl 1455.62100

Summary: We consider a random weights average of \(n\) independent continuous random vectors \(\mathbf{X}_1,\dots,\mathbf{X}_n\), 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 G. S. Watson [Biometrika 43, 161–168 (1956; Zbl 0074.14203)] 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.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H10 Multivariate distribution of statistics
46F12 Integral transforms in distribution spaces
65D07 Numerical computation using splines
65R10 Numerical methods for integral transforms

Citations:

Zbl 0074.14203
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