On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials. (June 2014)

• Record Type: Journal Article
• Authors: Boutsikas, M. V.; Antzoulakos, D. L.; Rakitzis, A. C.
• Is Part Of: Journal of applied probability. Volume 51:Number 2(2014)
• Page Start: 483
• Page End: 491
• Publication Date: 2014-06
• Subjects: Stopping time, -- stopped sum, -- exchangeability, -- multistate trial, -- run and scan statistics, -- acceptance sampling, -- coupon collector's problem; 60E05, -- 62E15, -- 60G09, -- 60G50; 519.2
• DOI: 10.1017/S0021900200011372
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : 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 S T, i be the stopped sum denoting the number of appearances of outcome ' i ' in X 1, …, X T, 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, S T, 0, S T, 1, …, S T, m ). Two applications, which have independent interest, are offered to illustrate the applicability and the usefulness of the main results.