Probability Surveys

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

Alexander Gnedin, Ben Hansen, and Jim Pitman

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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.

Article information

Source
Probab. Surveys, Volume 4 (2007), 146-171.

Dates
First available in Project Euclid: 1 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.ps/1180728778

Digital Object Identifier
doi:10.1214/07-PS092

Mathematical Reviews number (MathSciNet)
MR2318403

Zentralblatt MATH identifier
1189.60050

Subjects
Primary: 60F05: Central limit and other weak theorems 60F15: Strong theorems
Secondary: 60C05: Combinatorial probability

Keywords
occupancy problem regular variation asymptotics poissonization species sampling

Citation

Gnedin, Alexander; Hansen, Ben; Pitman, Jim. Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws. Probab. Surveys 4 (2007), 146--171. doi:10.1214/07-PS092. https://projecteuclid.org/euclid.ps/1180728778


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