Limit Laws for a Class of Diminishing Urn Models. Limit Laws for a Class of Diminishing Urn Models
نویسندگان
چکیده
In this work we analyze a class of diminishing 2 × 2 Pólya-Eggenberger urn models with ball replacement matrix M given by M = ` −a 0 c −d´, a, d ∈ N and c ∈ N0. We obtain limit laws for this class of 2 × 2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which corresponds to the special case a = c = d = 1. Furthermore, we also obtain limit laws for the well known sampling without replacement urn, a = d = 1 and c = 0, and corresponding generalizations, a, d ∈ N and c = 0.
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