Operational Interpretations of the Chernoff Inequality

TL;DR

This paper extends the Chernoff inequality using operational methods, revealing it as part of a broader continuum of probability bounds and establishing new relations with moment bounds and monotonic functions.

Contribution

It introduces a generalized framework for Chernoff bounds, connecting them to absolute monotonic functions and expanding their theoretical understanding.

Findings

Chernoff bound is part of a continuum of probability bounds

Established a relation between moment bounds and monotonic functions

Generalized Chernoff inequality using operational methods

Abstract

We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability bounds.