The first divisible sum
type: Item
instance of: scholarly article
title: The first divisible sum
zbMATH Open document ID: 0814.60084
DOI: 10.1007/BF02213453
published in: Journal of Theoretical Probability
publication date: 1995-02-26T00:00:00Z
review text: The authors consider ``the distribution of the first sum of a sequence of positive integer valued i.i.d. random variables which is divisible by \(d\)''. It is known that this sum, divided by \(d\), converges to a geometric distribution as \(d \to \infty\). The rate of convergence is investigated by two methods. The first of them, Stein's method, is based on the coupling technique. The second one uses the theory of Banach algebras. An interesting comparison of the given approaches is presented.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 727274
zbMATH Keywords: renewal theory
zbMATH Keywords: coupling
zbMATH Keywords: geometric distribution
zbMATH Keywords: rate of convergence
zbMATH Keywords: Stein's method
zbMATH Keywords: Banach algebras
author: A. D. Barbour
author: Rudolf Grübel
reviewed by: Eugene Kozarovitsky
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 727274