Waiting Time for a Small Subcollection in the Coupon Collector Problem with Universal Coupon

Jelena Jocković () and Bojana Todić ()
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Jelena Jocković: University of Belgrade
Bojana Todić: University of Belgrade

Journal of Theoretical Probability, 2024, vol. 37, issue 3, 1945-1957

Abstract: Abstract We consider a generalization of the classical coupon collector problem, where the set of available coupons consists of standard coupons (which can be part of the collection), and two coupons with special purposes: one that speeds up the collection process and one that slows it down. We obtain several asymptotic results related to the expectation and the variance of the waiting time until a portion of the collection is sampled, as the number of standard coupons tends to infinity.

Keywords: Coupon collector problem; Waiting time; Universal coupon; Asymptotic expansion; Recurrence relation; 60C05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01312-2

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