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2007 Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws
Alexander Gnedin, Ben Hansen, Jim Pitman
Probab. Surveys 4: 146-171 (2007). DOI: 10.1214/07-PS092

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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Alexander Gnedin. Ben Hansen. Jim Pitman. "Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws." Probab. Surveys 4 146 - 171, 2007. https://doi.org/10.1214/07-PS092

Information

Published: 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1189.60050
MathSciNet: MR2318403
Digital Object Identifier: 10.1214/07-PS092

Subjects:
Primary: 60F05 , 60F15
Secondary: 60C05

Keywords: asymptotics , occupancy problem , poissonization , regular variation , Species sampling

Rights: Copyright © 2007 The Institute of Mathematical Statistics and the Bernoulli Society

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