Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws
概率论
2009-09-29 v2 统计理论
统计理论
摘要
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.
引用
@article{arxiv.math/0701718,
title = {Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws},
author = {Alexander Gnedin and Ben Hansen and Jim Pitman},
journal= {arXiv preprint arXiv:math/0701718},
year = {2009}
}
备注
Published at http://dx.doi.org/10.1214/07-PS092 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)