Roozegar, Rasool Randomly weighted average with Dirichlet component proportions. (English) Zbl 1364.62033 Commun. Stat., Simulation Comput. 46, No. 3, 1808-1813 (2017). Summary: This article introduces a new average of \(n\) independent continuous random variables \(X_{1},\ldots,X_{n}\) weighted by Dirichlet random components. A relation between the Cauchy-Stieltjes transforms of the distribution functions of this weighted average and \(X_{1},\ldots,X_{n}\) is established. Several examples illustrate usefulness and applicability of the result. Cited in 2 Documents MSC: 62E10 Characterization and structure theory of statistical distributions 46F12 Integral transforms in distribution spaces 65R10 Numerical methods for integral transforms Keywords:Cauchy-Stieltjes transform; Dirichlet and beta distributions; multivariate B-spline; randomly weighted average PDFBibTeX XMLCite \textit{R. Roozegar}, Commun. Stat., Simulation Comput. 46, No. 3, 1808--1813 (2017; Zbl 1364.62033) Full Text: DOI References: [1] Debnath L., 2007 [2] Homei H., 2012 82 (8) pp 1515– [3] Johnson N. L., 1990 44 (3) pp 245– [4] Karlin S., 1986 20 (1) pp 69– [5] Nadaraya E. A., 1964 9 pp 141– [6] Soltani A. R., 2009 79 (9) pp 1215– [7] Van Assche W., 1987 49 pp 207– [8] Watson G. S., 1964 6 pp 359– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.