A coupon collector's problem with bonuses - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2006

A coupon collector's problem with bonuses


In this article, we study a variant of the coupon collector's problem introducing a notion of a \emphbonus. Suppose that there are c different types of coupons made up of bonus coupons and ordinary coupons, and that a collector gets every coupon with probability 1/c each day. Moreover suppose that every time he gets a bonus coupon he immediately obtains one more coupon. Under this setting, we consider the number of days he needs to collect in order to have at least one of each type. We then give not only the expectation but also the exact distribution represented by a gamma distribution. Moreover we investigate their limits as the Gumbel (double exponential) distribution and the Gauss (normal) distribution.
Fichier principal
Vignette du fichier
dmAG0114.pdf (215.12 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01184720 , version 1 (17-08-2015)



Toshio Nakata, Izumi Kubo. A coupon collector's problem with bonuses. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.215-224, ⟨10.46298/dmtcs.3515⟩. ⟨hal-01184720⟩


142 View
1014 Download



Gmail Facebook X LinkedIn More