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On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials

Part of: Distribution theory Stochastic processes Distribution theory - Probability

Published online by Cambridge University Press:  19 February 2016

M. V. Boutsikas ,
D. L. Antzoulakos  and
A. C. Rakitzis
M. V. Boutsikas*
Affiliation:
University of Piraeus
D. L. Antzoulakos*
Affiliation:
University of Piraeus
A. C. Rakitzis*
Affiliation:
University of Cyprus
*
∗ Postal address: Department of Statistics and Insurance Science, University of Piraeus, Piraeus 18534, Greece.
∗ Postal address: Department of Statistics and Insurance Science, University of Piraeus, Piraeus 18534, Greece.
∗∗∗∗ Current address: LUNAM Université, Université de Nantes, IRCCyN UMR CNRS 6597, France. Email address: athanasios.rakitzis@univ-nantes.fr.
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Abstract

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Let T be a stopping time associated with a sequence of independent and identically distributed or exchangeable random variables taking values in {0, 1, 2, …, m}, and let ST,i be the stopped sum denoting the number of appearances of outcome 'i' in X1, …, XT, 0 ≤ i ≤ m. In this paper we present results revealing that, if the distribution of T is known, then we can also derive the joint distribution of (T, ST,0, ST,1, …, ST,m). Two applications, which have independent interest, are offered to illustrate the applicability and the usefulness of the main results.

Keywords

Stopping timestopped sumexchangeabilitymultistate trialrun and scan statisticsacceptance samplingcoupon collector's problem

MSC classification

Primary: 60E05: Distributions 62E15: Exact distribution theory
Secondary: 60G09: Exchangeability 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 2 , June 2014 , pp. 483 - 491
Copyright
© Applied Probability Trust 

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