Volume 30 • Number 2 • 2007   • Bounds on Random Infinite Urn Model S. Boonta and K. Neammanee Abstract. Let N(n) be a Poisson random variable with parameter n. An infinite urn model is defined as follows: N(n) balls are independently placed in an infinite set of urns and each ball has probability pk > 0 of being assigned to the k-th urn. We assume that pk ≥ pk+1 for all k and ∑k=1∞ pk=1. Let Un be the number of occupied urns after N(n) balls have been thrown. Dutko showed in 1989 that under the condition limn → ∞ Var(Un)= ∞ we have [(Un - E(Un))/( √ {Var(Un)})] → dN(0,1)  as  n → ∞ where N(0,1) is the standard normal random variable. However, Dutko did not give a bound of his approximation. So in this paper, we give uniform and non-uniform bounds of the approximation. 2000 Mathematics Subject Classification: 60F05, 60G50 Full text: PDF