The Kearns–Saul Inequality for Bernoulli and Poisson-Binomial Distributions

Eckhard Schlemm ()
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Eckhard Schlemm: University of Cambridge

Journal of Theoretical Probability, 2016, vol. 29, issue 1, 48-62

Abstract: 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.

Keywords: Bernoulli distribution; Kearns–Saul inequality; Laplace transform; Poisson-binomial distribution; 60E10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-014-0564-x

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