Some bounds on the coupon collector problem

Authors:
Servet Martinez
Affiliations:
DIM and CMM, UMR 2071 UCHILE-CNRS, Casilla 170-3 Correo 3, Santiago, Chile
Venue:
Random Structures & Algorithms
Year:
2004

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Abstract

This work addresses on the coupon collector problem and its generalization introduced by Flajolet, Gardy, and Thimonier. In our main results, we show a ratio limit theorem for the random time of the generalized coupon collector problem, and, further, we give the leading term and the geometric rate for the distribution of this random time, when the number of throws is large. For the classical coupon collector problem, we give a bound on the conditional second moment for the number of visits to the coupons, relying strongly on a result of Holst on extremal distributions.