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

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.