Journal of Theoretical Probability

, Volume 29, Issue 1, pp 48–62 | Cite as

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



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.


Bernoulli distribution Kearns–Saul inequality Laplace transform Poisson-binomial distribution 

Mathematics Subject Classification (2010)



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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Wolfson CollegeUniversity of CambridgeCambridgeUK

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