Open Access
August 2017 Exponential bounds for the hypergeometric distribution
Evan Greene, Jon A. Wellner
Bernoulli 23(3): 1911-1950 (August 2017). DOI: 10.3150/15-BEJ800


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. A 76 = 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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Evan Greene. Jon A. Wellner. "Exponential bounds for the hypergeometric distribution." Bernoulli 23 (3) 1911 - 1950, August 2017.


Received: 1 July 2015; Revised: 1 December 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714323
MathSciNet: MR3624882
Digital Object Identifier: 10.3150/15-BEJ800

Keywords: Binomial distribution , Convex ordering , exponential bound , finite sampling correction factor , hypergeometric distribution , sampling without replacement

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 3 • August 2017
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