Toshio Nakata ; Izumi Kubo

A coupon collector's problem with bonuses
dmtcs:3515 
Discrete Mathematics & Theoretical Computer Science,
January 1, 2006,
DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities

https://doi.org/10.46298/dmtcs.3515
A coupon collector's problem with bonusesArticle
Authors: Toshio Nakata ^{1}; Izumi Kubo ^{2}
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Toshio Nakata;Izumi Kubo
1 Department of Information Education
2 Department of Environmental Design
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.
Linda C. Meiser;Philipp L. Antkowiak;Julian Koch;Weida D. Chen;A. Xavier Kohll;et al., 2019, Reading and writing digital data in DNA, Nature Protocols, 15, 1, pp. 86101, 10.1038/s4159601902445.