Soltani, A. R.; Roozegar, Rasool Averages for multivariate random vectors with random weights: distributional characterization and application. (English) Zbl 1455.62100 REVSTAT 18, No. 4, 453-460 (2020). 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. Cited in 3 Documents 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 Keywords:multivariate weighted average with random weights; multivariate Cauchy Stieltjes transform; Dirichlet distribution; multivariate stable distributions Citations:Zbl 0074.14203 PDFBibTeX XMLCite \textit{A. R. Soltani} and \textit{R. Roozegar}, REVSTAT 18, No. 4, 453--460 (2020; Zbl 1455.62100) Full Text: Link