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Exponential bounds for the hypergeometric distribution
1Department of Statistics, University of Washington, Seattle, WA 98195-4322, USA.
Abstract:
We establish exponential bounds for the hypergeometric distribution which include a finite sampling correction factor, but are otherwise analogous to bounds for the binomial distribution due to León and Perron (Statist. Probab. Lett.62 (2003) 345-354) and Talagrand (Ann. Probab.22 (1994) 28-76). We also extend a convex ordering of Kemperman's (Nederl. Akad. Wetensch. Proc. Ser. A6 = Indag. Math.35 (1973) 149-164) for sampling without replacement from populations of real numbers between zero and one: a population of all zeros or ones (and hence yielding a hypergeometric distribution in the upper bound) gives the extreme case.
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