A Poisson approximation in an urn model with indistinguishable balls
type: Item
instance of: scholarly article
title: A Poisson approximation in an urn model with indistinguishable balls
zbMATH Open document ID: 0715.60033
DOI: 10.1016/0378-3758(90)90098-F
author: V. V. Menon
author: N. K. Indira
published in: Journal of Statistical Planning and Inference
publication date: 1990-01-01T00:00:00Z
review text: It is considered the distribution of n indistinguishable balls into m urns when the possible arrangements are equally probable. Let \(M_ k\) be the number of urns containing exactly k balls. The probability \(P(M_ k=r)\) is approximated by the term \(p(r;\mu)=e^{-\mu}\mu^ r/r!\), where \(\mu =m^ 2n^ k/(m+n)^{k+1}\) and \(\mu\), m and n are chosen such that \(\mu^ 2/m\) and \(\mu^ 2/n\) tend to 0 as m and n tend to infinity. The remainder term is developed so that the rate of convergence can be estimated. The approximation of \(P(M_ k\leq r)\) is given in the same way. The used method is elementary.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 4178231
zbMATH Keywords: Bose-Einstein statistics
zbMATH Keywords: indistinguishable balls
zbMATH Keywords: rate of convergence
MaRDI profile type: Publication
cites work: Q5538132
cites work: A unified approach to limit theorems for urn models
cites work: On some generalized farlie-gumbel-morgenstern distributions-II regression, correlation and further generalizations
cites work: On the maximum of Stirling numbers of the second kind
cites work: Q4122535
full work available at URL: 0378-3758(90)90098-f
OpenAlex ID: W1977236207
description: scientific article; zbMATH DE number 4178231