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Abstract:
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We consider a Polya urn model with two labels, a model which corresponds to sampling methods and many classical probability problems. Keeping in mind that the key interest is the composition of the urns and the stochastic path leading to this long term description, we find moment generating functions for special cases of urn processes that fall into the categories of the forward and backward diagonal urns, Friedman's urn, Bagchi-Pal's urn, the generalized Ehrenfest urn, and Smythe's urn. We present these results and give the restrictions of the values of the urn repopulation rules to find these solutions and to guarantee tenability for negative values. For the generalized Ehrenfest urn and Smythe's urn, which have some negative repopulation values, we present the necessary conditions and examples for the initial urn populations and replacement schemes for tenable schemes.
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