On generalized Pólya urn models
type: Item
instance of: scholarly article
title: On generalized Pólya urn models
zbMATH Open document ID: 0965.60027
DOI: 10.1016/S0167-7152(00)00045-6
author: Samuel Kotz
author: Philippe Robert
author: Hosam M. Mahmoud
published in: Statistics \& Probability Letters
publication date: 2001-08-02T00:00:00Z
review text: The authors consider a two-color urn model characterized by a \(2\times 2\) matrix of nonnegative integers \((\begin{smallmatrix} a & b\\ c & d \end{smallmatrix})\) as follows. The urn process evolves in stages. At each stage a ball is drawn and its color is observed. If a ball of color 1 is drawn at a stage, it is returned to the urn together with \(a\) balls of color 1 and \(b\) balls of color 2. If a ball of color 2 is drawn at a stage, the same manipulation with the matrix row \((c,d)\) is made. Exact distributions of the number of balls of a specific color that appear after \(n\) draws are derived. The variety of essentially different asymptotics that appear for various matrices as \(n\to \infty\) is illustrated by an example, where the authors find an asymptotic mean value.
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 05A05
zbMATH DE Number: 1507149
reviewed by: Ljuben Mutafchiev
MaRDI profile type: Publication
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full work available at URL: s0167-7152(00)00045-6
OpenAlex ID: W1964588325
description: scientific article; zbMATH DE number 1507149