Exponential bounds for the hypergeometric distribution

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 ( (2003) 345-354) and Talagrand ( (1994) 28-76). We also extend a convex ordering of Kempe...

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Published inBernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability Vol. 23; no. 3; p. 1911
Main Authors Greene, Evan, Wellner, Jon A
Format Journal Article
LanguageEnglish
Published England 01.08.2017
Subjects
finite sampling correction factor
sampling without replacement
hypergeometric distribution
convex ordering
exponential bound
binomial distribution
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Summary: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 ( (2003) 345-354) and Talagrand ( (1994) 28-76). We also extend a convex ordering of Kemperman's ( (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.
ISSN:1350-7265
DOI:10.3150/15-BEJ800