The Annals of Mathematical Statistics

Limit Theorems for Some Occupancy and Sequential Occupancy Problems

Lars Holst

Abstract

Consider a situation in which balls are falling into $N$ cells with arbitrary probabilities. A limiting distribution for the number of occupied cells after $n$ falls is obtained, when $n$ and $N \rightarrow \infty$, so that $n^2/N \rightarrow \infty$ and $n/N \rightarrow 0$. This result completes some theorems given by Chistyakov (1964), (1967). Limiting distributions of the number of falls to achieve $a_N + 1$ occupied cells are obtained when $\lim \sup a_N/N < 1$. These theorems generalize theorems given by Baum and Billingsley (1965), and David and Barton (1962), when the balls fall into cells with the same probability for every cell.

Article information

Source
Ann. Math. Statist., Volume 42, Number 5 (1971), 1671-1680.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177693165

Digital Object Identifier
doi:10.1214/aoms/1177693165

Mathematical Reviews number (MathSciNet)
MR343347

Zentralblatt MATH identifier
0231.60022

JSTOR

Citation

Holst, Lars. Limit Theorems for Some Occupancy and Sequential Occupancy Problems. Ann. Math. Statist. 42 (1971), no. 5, 1671--1680. doi:10.1214/aoms/1177693165. https://projecteuclid.org/euclid.aoms/1177693165