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The first divisible sum


Barbour, A D; Grübel, R (1995). The first divisible sum. Journal of Theoretical Probability, 8(1):39-47.

Abstract

We consider the distribution of the first sum of a sequence of positive integer valued iid random variables which is divisible byd. This is known to converge, when divided byd, to a geometric distribution asd. We obtain results on the rate of convergence using two contrasting approaches. In the first, Stein's method is adapted to geometric limit distributions. The second method is based on the theory of Banach algebras. Each method is shown to have its merits.

Abstract

We consider the distribution of the first sum of a sequence of positive integer valued iid random variables which is divisible byd. This is known to converge, when divided byd, to a geometric distribution asd. We obtain results on the rate of convergence using two contrasting approaches. In the first, Stein's method is adapted to geometric limit distributions. The second method is based on the theory of Banach algebras. Each method is shown to have its merits.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Discrete renewal theory - Stein's method - Banach algebras
Language:English
Date:1995
Deposited On:09 Apr 2010 08:45
Last Modified:05 Apr 2016 13:27
Publisher:Springer
ISSN:0894-9840
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/BF02213453

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