Normal Approximation In An Urn Model With Indist Inguishable Balls

Abstract

For the Bose-Einstein Statistics, where n indistinguishable balls are distributed in m urns such that all the arrangements are equally likely, define the random variables Mk= number of urns containing exactly k balls each; Nk= number of urns containing at least k balls each. We consider the approximation of the distributions of Mkand Nkby suitable normal distributions, for large butfinite m. Estimates are found for the error in the approximation to both the probability mass function and the distribution function in each case. These results apply also to the alternative model where no urn is allowed to be empty. The results are illustrated by some numerical examples. © 1988, Taylor & Francis Group, LLC. All rights reserved.