Journal of Applied Probability

On generalized Pólya urn models

May-Ru Chen and Markus Kuba

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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.

Article information

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

First available in Project Euclid: 10 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Urn model limiting distribution


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

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