Advances in Urn Models during the Past Two Decades

This paper surveys some key developments that have occurred pertaining to urn models in probabilistic, statistical and biological literatures during the past two decades. It should be regarded as a compact sequel to the book Urn Models and Their Applications by Johnson and Kotz (1977) and as a natural companion to the two chapters in the book Discrete Multivariate Distributions by Johnson, Kotz and Balakrishnan (1997) dealing with multivariate Pólya-Eggenberger distributions and multivariate Ewens distributions, respectively.