The Kearns--Saul inequality for Bernoulli and Poisson-binomial distributions

Abstract

We give a direct rigorous proof of the Kearns--Saul inequality which bounds the Laplace transform of a generalised Bernoulli random variable. We extend the arguments to generalised Poisson-binomial distributions and characterise the set of parameters such that an analogous inequality holds for the sum of two generalised Bernoulli random variables.

arXiv comment11 pages, 3 figures; to appear in Journal of Theoretical Probability

References in corpus (1)

• Large Deviation Methods for Approximate Probabilistic Inference

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