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On Generalized Pólya Urn Models

Part of: Limit theorems Graph theory Combinatorics

Published online by Cambridge University Press:  30 January 2018

May-Ru Chen  and
Markus Kuba
May-Ru Chen*
Affiliation:
National Sun Yat-sen University
Markus Kuba*
Affiliation:
Technische Universität Wien
*
∗ Postal address: Department of Applied Math., National Sun Yat-sen University, 70 Lien-hai Road, Kaohsiung 804, Taiwan, R.O.C. Email address: mayru@faculty.nsysu.edu.tw
∗∗ Postal address: Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria, HTL Wien 5 Spengergasse, Spengergasse 20, 1050 Wien, Austria. Email address: kuba@dmg.tuwien.ac.at
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Abstract

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We study an urn model introduced in the paper of Chen and Wei (2005), where at each discrete time step m balls are drawn at random from the urn containing colors white and black. Balls are added to the urn according to the inspected colors, generalizing the well known Pólya-Eggenberger urn model, case m = 1. We provide exact expressions for the expectation and the variance of the number of white balls after n draws, and determine the structure of higher moments. Moreover, we discuss extensions to more than two colors. Furthermore, we introduce and discuss a new urn model where the sampling of the m balls is carried out in a step-by-step fashion, and also introduce a generalized Friedman's urn model.

Keywords

Urn modellimiting distribution

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 05A15: Exact enumeration problems, generating functions 05C05: Trees
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 4 , December 2013 , pp. 1169 - 1186
Copyright
© Applied Probability Trust 

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