Hypergeometric Distribution Revisited: Tail Inequalities, Confidence Bounds and Sample Sizes

TL;DR

This paper refines tail inequalities and confidence bounds for the hypergeometric distribution, providing simplified, practical formulas for sample size determination and confidence interval computation, with a unified notation for better understanding.

Contribution

It offers a unified, simplified approach to tail inequalities and confidence bounds for hypergeometric distributions, enhancing practical usability and clarity.

Findings

Simplified bounds for tail probabilities

Explicit formulas for confidence intervals

Sample size calculations for hypergeometric sampling

Abstract

We revisit and refine known tail inequalities and confidence bounds for the hypergeometric distribution, i.e., for the setting where we sample without replacement from a fixed population with binary values or properties. The results are presented in a unified notation in order to increase understanding and facilitate comparisons. We focus on the usability of the results in practice and thus on simple bounds. Further, we make the computation of confidence intervals and necessary sample sizes explicit in our results and demonstrate their use in an extended example.