On generalized Pólya urn models

Details On generalized Pólya urn models On generalized Pólya urn models

2011-06-21

arxiv.org/abs/1106.4325v1

Mathematics

Probability

15 pages, no figures

Scientific paper

We study an urn model introduced in the paper of Chen and Wei, 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 P\'olya-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.

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