The moment bound is tighter than chernoff’s bound for positive tail probabilities

Abstract

Chemoff’s bound on P[X ≥ t] is used almost universally when a tight bound on tail probabilities is required. In this article we show that for all positive t and for all distributions, the moment bound is tighter than Chemoff’s bound. By way of example, we demonstrate that the improvement is often substantial. © Taylor & Francis Group, LLC.