an:06279834
Zbl 1290.60009
Chen, May-Ru; Kuba, Markus
On generalized P??lya urn models
EN
J. Appl. Probab. 50, No. 4, 1169-1186 (2013).
00329136
2013
j
60C05 60F05 05A15
urn model; limiting distribution
Summary: We study an urn model introduced in the paper of \textit{M. Chen} and \textit{C. Wei} [J. Appl. Probab. 42, No. 4, 964--976 (2005; Zbl 1093.60007)], 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??lya-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.
Zbl 1093.60007