A Characterization of Hypergeometric Distributions

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Abstract
A theorem, that mixtures with binomial mixing distribution which are themselves binomial characterize the hypergeometric family of distributions, is displayed in various forms (the theorem and three equivalent restatements). These exhibit the fact that the property in question is related in a fundamental way to properties of moment sequences for distributions on the unit interval and is in fact equivalent to an identity on the space of the first N moments for distributions on the unit interval where N is the sample size parameter of the binomial mixing distributions.

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