Journal of Applied Probability

On generalized Pólya urn models

May-Ru Chen and Markus Kuba

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Abstract

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.

Article information

Source
J. Appl. Probab., Volume 50, Number 4 (2013), 1169-1186.

Dates
First available in Project Euclid: 10 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1389370106

Digital Object Identifier
doi:10.1239/jap/1389370106

Mathematical Reviews number (MathSciNet)
MR3161380

Zentralblatt MATH identifier
1290.60009

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05C05: Trees

Keywords
Urn model limiting distribution

Citation

Chen, May-Ru; Kuba, Markus. On generalized Pólya urn models. J. Appl. Probab. 50 (2013), no. 4, 1169--1186. doi:10.1239/jap/1389370106. https://projecteuclid.org/euclid.jap/1389370106


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References

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