A new tail bound for the sum of bounded independent random variables

Jackson Loper; Jeffrey Regier

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arXiv · 2503.17594

A new tail bound for the sum of bounded independent random variables

Jackson Loper·Jeffrey Regier

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Abstract

We construct a new tail bound for the sum of independent random variables for situations in which the expected value of the sum is known and each random variable lies within a specified interval, which may be different for each variable. This new bound can be computed by solving a two-dimensional convex optimization problem. Simulations demonstrate that the new bound is often substantially tighter than Hoeffding's inequality for cases in which both bounds are applicable.

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Jackson Loper, Jeffrey Regier. 2025-03-22. A new tail bound for the sum of bounded independent random variables. https://arxiv.org/abs/2503.17594

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