关于无限多方框占用问题的注解:一般渐近性和幂律*

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2007-01-24 DOI:10.1214/07-PS092

A. Gnedin, Ben B. Hansen, J. Pitman

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引用次数: 165

摘要

本文收集了具有无穷多个正频率的经典箱中球占用方案中被占用的箱子的数目的事实，以及在具有无穷多个物种的种群的样本中所表示的物种数目的事实。我们给出了这个随机变量的矩，讨论了它们之间的渐近关系以及与相关随机变量的渐近关系，并画出了与各种表现形式的正则变分的联系。AMS 2000学科分类:初级60F05、60F15;二次

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

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 sam- ples from populations with infinitely many species. We present moments of this random variable, discuss asymptotic relations among them and with re- lated random variables, and draw connections with regular variation, which appears in various manifestations. AMS 2000 subject classifications: Primary 60F05, 60F15; secondary

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