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Randomly weighted average with Dirichlet component proportions. (English) Zbl 1364.62033

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.

MSC:

62E10 Characterization and structure theory of statistical distributions
46F12 Integral transforms in distribution spaces
65R10 Numerical methods for integral transforms
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References:

[1] Debnath L., 2007
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