An Inequality for the Sum of Independent Bounded Random Variables
Christopher R. Dance
TL;DR
This paper presents a new inequality for the sum of independent bounded random variables, improving upon Hoeffding's inequality in specific cases and achieving optimality as the sum approaches a Poisson distribution.
Contribution
It introduces a simple, improved inequality that is optimal in the Poisson limit, enhancing existing bounds for bounded sums.
Findings
The new inequality outperforms Hoeffding's bound in certain cases.
It is proven to be optimal as the sum tends to a Poisson distribution.
The inequality simplifies the analysis of sums of bounded independent variables.
Abstract
We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.
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Taxonomy
TopicsProbability and Risk Models