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A Collector's Problem with Renewal Arrival Processes

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella  and
Wolfgang Stadje
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Wolfgang Stadje*
Affiliation:
University of Osnabrück
*
∗Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, 91905, Israel. Email address: offer.kella@huji.ac.il
∗∗Postal address: Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany. Email address: wolfgang@mathematik.uni-osnabrueck.de
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Abstract

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We study a collector's problem with K renewal arrival processes for different type items, where the objective is to collect complete sets. In particular, we derive the asymptotic distribution of the sequence of interarrival times between set completions.

Keywords

Collector's problemcomplete setrenewal processessuperpositionasymptotic distributionmixture

MSC classification

Secondary: 60K05: Renewal theory 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 610 - 620
Copyright
Copyright © Applied Probability Trust 2008 

References

[1] Adler, I., Oren, S. and Ross, S. (2003). The coupon-collector's problem revisited. J. Appl. Prob. 40, 513–518.CrossRefGoogle Scholar
[2] Boneh, A. and Hofri, M. (1997). The coupon-collector problem revisited – a survey of engineering problems and computational methods. Stoch. Models 13, 39–66.CrossRefGoogle Scholar
[3] Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. 2, 2nd edn. John Wiley, New York.Google Scholar
[4] Flajolet, P., Gardy, D. and Thimonier, L. (1992). Birthday paradox, coupon collectors, catching algorithms and self-organizing search. Discrete Appl. Math. 39, 207–229.CrossRefGoogle Scholar
[5] Kobza, J. E., Jacobson, S. H. and Vaughan, D. E. (2007). A survey of the coupon collector's problem with random sample sizes. Methodol. Comput. Appl. Prob. 9, 573–584.CrossRefGoogle Scholar
[6] Myers, A. M. and Wilf, H. S. (2006). Some new aspects of the coupon collector's problem. SIAM Rev. 48, 549–565.CrossRefGoogle Scholar
[7] Stadje, W. (1990). The collector's problem with group drawings. Adv. Appl. Prob. 22, 866–882.CrossRefGoogle Scholar