Exponential bounds for the hypergeometric distribution

TL;DR

This paper derives exponential bounds for the hypergeometric distribution, incorporating a finite sampling correction, and compares it to binomial bounds, providing insights into sampling without replacement.

Contribution

It introduces new exponential bounds for the hypergeometric distribution with a finite sampling correction factor, extending existing binomial bounds to sampling without replacement.

Findings

Established exponential bounds for hypergeometric distribution

Included finite sampling correction factor in bounds

Proved convex ordering for sampling without replacement

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 Le\'on and Perron (2003) and Talagrand (1994). We also establish a convex ordering 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.