A Reversion of the Chernoff Bound

2005/01/22 by Ted Theodosopoulos, Theodosopoulos, Ted
Computer Science · Physics and Astronomy · #60E10 #60F10 #60J50 #62E17 #Chaos, Complexity, and Education #FOS: Mathematics #Probability (math.PR) #Scientific Research and Discoveries #Statistical Mechanics and Entropy #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.math/0501360

openalex publication_date 2005/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are tighter and more broadly applicable than existing tail approximations.

Citations

• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
• Saddlepoint Approximations in Statistics

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• Halving the bounds for the Markov, Chebyshev, and Chernoff Inequalities using smoothing
• General upper and lower tail estimates using Malliavin calculus and Stein's equations
• Nearly tight universal bounds for the binomial tail probabilities
• A Note on the Chernoff Bound for Random Variables in the Unit Interval