Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws

Details Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws

2007-01-24

arxiv.org/abs/math/0701718v2

Probability Surveys 2007, Vol. 4, 146-171

Mathematics

Probability

Published at http://dx.doi.org/10.1214/07-PS092 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of

Scientific paper

10.1214/07-PS092

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.

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