• Bernoulli
  • Volume 23, Number 3 (2017), 1911-1950.

Exponential bounds for the hypergeometric distribution

Evan Greene and Jon A. Wellner

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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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Bernoulli Volume 23, Number 3 (2017), 1911-1950.

Received: July 2015
Revised: December 2015
First available in Project Euclid: 17 March 2017

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binomial distribution convex ordering exponential bound finite sampling correction factor hypergeometric distribution sampling without replacement


Greene, Evan; Wellner, Jon A. Exponential bounds for the hypergeometric distribution. Bernoulli 23 (2017), no. 3, 1911--1950. doi:10.3150/15-BEJ800.

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