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March 2012 The coupon collector's problem revisited: asymptotics of the variance
Aristides V. Doumas, Vassilis G. Papanicolaou
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Adv. in Appl. Probab. 44(1): 166-195 (March 2012). DOI: 10.1239/aap/1331216649

Abstract

We develop techniques for computing the asymptotics of the first and second moments of the number TN of coupons that a collector has to buy in order to find all N existing different coupons as N → ∞. The probabilities (occurring frequencies) of the coupons can be quite arbitrary. From these asymptotics we obtain the leading behavior of the variance V[TN] of TN (see Theorems 3.1 and 4.4). Then, we combine our results with the general limit theorems of Neal in order to derive the limit distribution of TN (appropriately normalized), which, for a large class of probabilities, turns out to be the standard Gumbel distribution. We also give various illustrative examples.

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Aristides V. Doumas. Vassilis G. Papanicolaou. "The coupon collector's problem revisited: asymptotics of the variance." Adv. in Appl. Probab. 44 (1) 166 - 195, March 2012. https://doi.org/10.1239/aap/1331216649

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1260.60035
MathSciNet: MR2951551
Digital Object Identifier: 10.1239/aap/1331216649

Subjects:
Primary: 60F05, 60F99

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 1 • March 2012
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