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June, 1974 Asymptotic Distributions for Occupancy and Waiting Time Problems with Positive Probability of Falling Through the Cells
Ester Samuel-Cahn
Ann. Probab. 2(3): 515-521 (June, 1974). DOI: 10.1214/aop/1176996669

Abstract

Consider $N$ cells into which balls are being dropped independently, in such a way that the cells are equiprobable, and each ball has probability $p_N > 0$ of staying in the cell. Let $W_N(pN, k_N)$ denote the waiting time until $k_N + 1$ cells are occupied, and let $S_N(pN, jN)$ denote the number of distinct cells occupied after $j_N$ balls have been dropped. The full characterization of the limiting distributions of these two random variables is obtained, depending upon the joint behaviour of $p_N, k_N$ and $p_N, j_N$ respectively, as $N \rightarrow \infty$. The limit distributions obtained are the negative binomial, binomial, Poisson, chi-square and normal distributions.

Citation

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Ester Samuel-Cahn. "Asymptotic Distributions for Occupancy and Waiting Time Problems with Positive Probability of Falling Through the Cells." Ann. Probab. 2 (3) 515 - 521, June, 1974. https://doi.org/10.1214/aop/1176996669

Information

Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0285.60005
MathSciNet: MR365668
Digital Object Identifier: 10.1214/aop/1176996669

Subjects:
Primary: 60F05

Keywords: asymptotic distribution , occupancy problem , waiting time

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • June, 1974
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