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Comparing sums of exchangeable Bernoulli random variables

Part of: Markov processes Combinatorial probability Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Claude Lefèvre  and
Sergey Utev
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
Sergey Utev*
Affiliation:
Novosibirsk University
*
∗Postal address: Institut de Statistique, CP 210, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgique.
∗∗Postal address: Institute of Mathematics, Universitetsky pr. 4, Novosibirsk 630090, Russia.
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Abstract

The paper is first concerned with a comparison of the partial sums associated with two sequences of n exchangeable Bernoulli random variables. It then considers a situation where such partial sums are obtained through an iterative procedure of branching type stopped at the first-passage time in a linearly decreasing upper barrier. These comparison results are illustrated with applications to certain urn models, sampling schemes and epidemic processes. A key tool is a non-standard hierarchical class of stochastic orderings between discrete random variables valued in {0, 1,· ··, n}.

Keywords

STOCHASTIC ORDERINGSTAIL DISTRIBUTIONSURN MODELBRANCHING PROCESSCATCH–RECAPTURE SAMPLINGEPIDEMIC PROCESS

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60C05: Combinatorial probability 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 285 - 310
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Research partially supported by the Fonds National de la Recherche Scientifique Belge.

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