An Examination of the Negative Occupancy Distribution and the Coupon-Collector Distribution

Ben O’Neill ()
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Ben O’Neill: Australian National University

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 4, 3229-3260

Abstract: Abstract We examine the negative occupancy distribution and the coupon-collector distribution, both of which arise as distributions relating to hitting times in the extended occupancy problem. These distributions constitute a full solution to a generalised version of the coupon collector problem, by describing the behaviour of the number of items we need to collect to obtain a full collection or a partial collection of any size. We examine the properties of these distributions and show how they can be computed and approximated. We give some practical guidance on the feasibility of computing large blocks of values from the distributions, and when approximation is required.

Keywords: Extended occupancy problem; Negative occupancy distribution; Coupon collector distribution; Coupon collector problem; 62E10; 62E17 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-022-09966-x

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