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Binomial approximation to the Poisson binomial distribution

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  • Ehm, Werner

Abstract

Upper and lower bounds are given for the total variation distance between the distribution of a sum S of n independent, non-identically distributed 0-1 random variables and the binomial distribution (n, p) having the same expectation as S. The proof uses the Stein--Chen technique. Equivalence of the total variation and the Kolmogorov distance is established, and an application to sampling with and without replacement is presented.

Suggested Citation

  • Ehm, Werner, 1991. "Binomial approximation to the Poisson binomial distribution," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 7-16, January.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:1:p:7-16
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    Cited by:

    1. Róbert Pethes & Levente Kovács, 2023. "An Exact and an Approximation Method to Compute the Degree Distribution of Inhomogeneous Random Graph Using Poisson Binomial Distribution," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    2. Li Zhang & Ying-Ying Zhang, 2022. "The Bayesian Posterior and Marginal Densities of the Hierarchical Gamma–Gamma, Gamma–Inverse Gamma, Inverse Gamma–Gamma, and Inverse Gamma–Inverse Gamma Models with Conjugate Priors," Mathematics, MDPI, vol. 10(21), pages 1-27, October.
    3. Arun Chandrasekhar & Robert Townsend & Juan Pablo Pablo Xandri, 2019. "Financial Centrality and the Value of Key Players," Working Papers 2019-26, Princeton University. Economics Department..
    4. Biscarri, William & Zhao, Sihai Dave & Brunner, Robert J., 2018. "A simple and fast method for computing the Poisson binomial distribution function," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 92-100.
    5. Christophe Ley & Gesine Reinert & Yvik Swan, 2014. "Approximate Computation of Expectations: the Canonical Stein Operator," Working Papers ECARES ECARES 2014-36, ULB -- Universite Libre de Bruxelles.
    6. Vydas Čekanavičius & Bero Roos, 2006. "Compound Binomial Approximations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 187-210, March.
    7. Arun G. Chandrasekhar & Robert Townsend & Juan Pablo Xandri, 2018. "Financial Centrality and Liquidity Provision," NBER Working Papers 24406, National Bureau of Economic Research, Inc.
    8. David M. Phillippo & Sofia Dias & A. E. Ades & Mark Belger & Alan Brnabic & Alexander Schacht & Daniel Saure & Zbigniew Kadziola & Nicky J. Welton, 2020. "Multilevel network meta‐regression for population‐adjusted treatment comparisons," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1189-1210, June.
    9. Zhang, Yazhe, 2016. "Binomial approximation for sum of indicators with dependent neighborhoods," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 146-154.
    10. López, Fernando & Matilla-García, Mariano & Mur, Jesús & Marín, Manuel Ruiz, 2010. "A non-parametric spatial independence test using symbolic entropy," Regional Science and Urban Economics, Elsevier, vol. 40(2-3), pages 106-115, May.
    11. Marie Ernst & Yvik Swan, 2022. "Distances Between Distributions Via Stein’s Method," Journal of Theoretical Probability, Springer, vol. 35(2), pages 949-987, June.
    12. Greene, Evan & Wellner, Jon A., 2016. "Finite sampling inequalities: An application to two-sample Kolmogorov–Smirnov statistics," Stochastic Processes and their Applications, Elsevier, vol. 126(12), pages 3701-3715.
    13. Aihua Xia & Fuxi Zhang, 2009. "Polynomial Birth–Death Distribution Approximation in the Wasserstein Distance," Journal of Theoretical Probability, Springer, vol. 22(2), pages 294-310, June.

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