A decomposition of the beta distribution, related order and asymptotic behavior
type: Item
instance of: scholarly article
title: A decomposition of the beta distribution, related order and asymptotic behavior
zbMATH Open document ID: 0531.60017
author: Julian Keilson
author: Ushio Sumita
published in: Annals of the Institute of Statistical Mathematics
publication date: 1983-01-01T00:00:00Z
review text: Let \(\beta_{v,w}\) be a random variable distributed according to the beta distribution with parameters v and w. The authors prove that \(U_{v,w}=^{def}-\log \beta_{v,w}=U^{CM}+U^{PF}\), where \(U^{CM}\) and \(U^{PF}\) are independent with completely monotone and \(PF_{\infty}\) densities, respectively. It is shown that \(U_{v,w}\) is infinitely divisible and \(\beta_{v,w}\) correspondingly infinitely factorizable. The asymptotic behavior of \(U_{v,w}\) and \(\beta_{v,w}\) for different modes of increase of v and w is studied. The decomposition is employed to provide an algorithm for generating random beta distributed numbers.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 3842865
zbMATH Keywords: beta distribution
zbMATH Keywords: infinite divisibility
reviewed by: Jarosław Bartoszewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3842865