Central Binomial Tail Bounds

TL;DR

This paper introduces new bounds for the central binomial tail, offering alternative proofs and connections to classical Chernoff and Slud bounds, enhancing understanding of tail probability estimates.

Contribution

It presents an alternative form for the binomial tail that leads to new bounds and links to existing Chernoff and Slud bounds, providing both novel bounds and proofs.

Findings

New bounds for the central binomial tail

Connections to Chernoff and Slud bounds

Alternative proofs for classical bounds

Abstract

An alternate form for the binomial tail is presented, which leads to a variety of bounds for the central tail. A few can be weakened into the corresponding Chernoff and Slud bounds, which not only demonstrates the quality of the presented bounds, but also provides alternate proofs for the classical bounds.