Poisson approximation to the distribution of empty cells in randomized occupancy

Abstract

Let M o denote the number of empty cells when n balls are dropped independently and at random in m cells such that each ball stays in its cell with probability p and falls through with probability l-p. A Poisson limit is known for Mo when (n/m)°. We find a corresponding approximation to the distribution of M when m is large but finite. The method is elementary, and yields the rate of convergence to the limit law,. The results are new for the classical case (p = 1) as well. © 1985, Taylor & Francis Group, LLC. All rights reserved.