Journal of Applied Probability

On the joint distribution of stopping times and stopped sums in multistate exchangeable trials

M. V. Boutsikas, D. L. Antzoulakos, and A. C. Rakitzis

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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 ST,i be the stopped sum denoting the number of appearances of outcome 'i' in X1, . . . , XT, 0 ≤ im. 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.

Article information

Source
J. Appl. Probab., Volume 51, Number 2 (2014), 483-491.

Dates
First available in Project Euclid: 12 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1402578638

Digital Object Identifier
doi:10.1239/jap/1402578638

Mathematical Reviews number (MathSciNet)
MR3217780

Zentralblatt MATH identifier
1294.60013

Subjects
Primary: 60E05: Distributions: general theory 62E15: Exact distribution theory
Secondary: 60G09: Exchangeability 60G50: Sums of independent random variables; random walks

Keywords
Stopping time stopped sum exchangeability multistate trial run and scan statistics acceptance sampling coupon collector's problem

Citation

Boutsikas, M. V.; Antzoulakos, D. L.; Rakitzis, A. C. On the joint distribution of stopping times and stopped sums in multistate exchangeable trials. J. Appl. Probab. 51 (2014), no. 2, 483--491. doi:10.1239/jap/1402578638. https://projecteuclid.org/euclid.jap/1402578638


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