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

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...

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Bibliographic Details
Published in:Journal of applied probability 2014-06, Vol.51 (2), p.483-491
Main Authors: Boutsikas, M. V., Antzoulakos, D. L., Rakitzis, A. C.
Format: Article
Language:English
Subjects:
60E05
60G09
60G50
62E15
Acceptance sampling
coupon collector's problem
Coupons
Cumulative distribution functions
Exchange
exchangeability
Mathematical analysis
Mathematical sequences
multistate trial
Probability distribution
Random sampling
Random variables
run and scan statistics
Statistics
stopped sum
Stopping distances
Stopping time
Studies
Sums
Symbols
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Summary: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.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1402578638