Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws. (English) Zbl 1189.60050

Summary: This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in samples from populations with infinitely many species. We present moments of this random variable, discuss asymptotic relations among them and with related random variables, and draw connections with regular variation, which appears in various manifestations.


60F05 Central limit and other weak theorems
60F15 Strong limit theorems
60C05 Combinatorial probability
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
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