We study point processes associated with coupon collector’s problem, that are defined as follows. We draw with replacement from the set of the first n positive integers until all elements are sampled, assuming that all elements have equal probability of being drawn. The point process we are interested in is determined by ordinal numbers of drawing elements that didn’t appear before. The set of real numbers is considered as the state space. We prove that the point process obtained after a suitable linear transformation of the state space converges weakly to the limiting Poisson random measure whose mean measure is determined.
We also consider rates of convergence in certain limit theorems for the problem of collecting pairs.
Abraham, S., Brockman, G., Sapp, S. and Godbole, A. P., Omnibus sequences, coupon collection and missing word counts, Methodol. Comput. Appl. Probab., 15 (2013), 363–378.
Abraham, S., Brockman, G., Sapp, S. and Godbole, A. P., Omnibus sequences, coupon collection and missing word counts, Methodol. Comput. Appl. Probab., 15 (2013), 363–378.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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