Bounding Means of Discrete Distributions

TL;DR

This paper presents new methods for bounding the mean of discrete distributions using sample data, especially effective for small samples and categorical data, providing tighter bounds than traditional inequalities.

Contribution

It introduces novel techniques to compute mean bounds for discrete distributions leveraging known value sets, improving accuracy for small sample sizes.

Findings

Stronger bounds for small sample sizes compared to standard inequalities

Applicable to categorical data with known categories

Methods outperform traditional bounds in discrete settings

Abstract

We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with known category-based values. For small sample sizes, we show how to leverage the knowledge of the set of possible values to compute bounds that are stronger than for general random variables such as standard concentration inequalities.