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Notes on the occupancy problem with infinitely many boxes: general
asymptotics and power laws
release_dgfczt6zhve65ownuzabk5ixqy
by
Alexander Gnedin,
Ben Hansen,
Jim Pitman
Released
as a report
.
2007
Abstract
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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