Abstract

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.Keywords and PhrasesUrn modelsPólya-Eggenberger distributionsMultivariate Ewens distributionsClassical occupancy modelsEhrenfest urn modelsPólya urn model with a continuum of colorsUrn models with random drawingsUrn models with indistinguishable ballsCompartmental urn modelsApplication

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