Abstract
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the use of the Poisson binomial machinery. Some open questions of approximating rational fractions of the Poisson binomial are presented.
Funding Statement
The first author was supported by NSF Grant DMS-2113779 and a start-up grant at Columbia University.
Acknowledgments
We thank Tom Liggett, Jim Pitman and Terry Tao for helpful discussions. We thank Yuting Ye for providing Example 2, and C.-H. Zhang for the simple proof in Example 1(3). We also thank an anonymous Associate Editor and the Editors for suggestions that greatly improve the presentation of the paper.
Citation
Wenpin Tang. Fengmin Tang. "The Poisson Binomial Distribution— Old & New." Statist. Sci. 38 (1) 108 - 119, February 2023. https://doi.org/10.1214/22-STS852
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