Large deviation inequalities for sums of indicator variables

TL;DR

This paper surveys Chernoff-type bounds for tail probabilities of sums of indicator variables, highlighting known inequalities, comparisons, and a recently rediscovered inequality of particular interest.

Contribution

It compiles and reviews existing Chernoff bounds for sums of indicator variables, including a newly highlighted inequality not previously published.

Findings

Most bounds are previously known

Comparisons between different bounds are provided

A recently rediscovered inequality is emphasized

Abstract

A survey is given of some Chernoff type bounds for the tail probabilities P(X-EX > a) and P(X-EX < a) when X is a random variable that can be written as a sum of indicator variables that are either independent or negatively related. Most bounds are previously known and some comparisons are made. This paper was written in 1994, but was never published because I had overlooked some existing papers containing some of the inequalities. Because of some recent interest in one of the inequalities, which does not seem to be published anywhere else, it has now been lightly edited and made available here.