Poisson approximation io the distribution of empiy 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 1-p. A Poisson limit is known for M_o when (n/m)→∞. We find a corresponding approximation to the distribution of M_o when m is large but finite, Ihe method is elementary, and yields the rate of convergence to the limit law. Ihe results are new for the classical case (p = 1) as well.

Keywords:

• classical occupancy problem
• randomized occupancy model
• empty cells
• Poisson approximation
• rate of convergence