Gnedin, Alexander; Hansen, Ben; Pitman, Jim Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws. (English) Zbl 1189.60050 Probab. Surv. 4, 146-171 (2007). Summary: 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. Cited in 62 Documents MSC: 60F05 Central limit and other weak theorems 60F15 Strong limit theorems 60C05 Combinatorial probability 60-02 Research exposition (monographs, survey articles) pertaining to probability theory Keywords:occupancy problem; regular variation; asymptotics; Poissonization; species sampling PDFBibTeX XMLCite \textit{A. Gnedin} et al., Probab. Surv. 4, 146--171 (2007; Zbl 1189.60050) Full Text: DOI arXiv EuDML