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November 2000 A bound for the distribution of the sum of discrete associated or negatively associated random variables
Michael V. Boutsikas, Markos V. Koutras
Ann. Appl. Probab. 10(4): 1137-1150 (November 2000). DOI: 10.1214/aoap/1019487610

Abstract

Let $X_1, X_2,\dots, X_n$ be a sequence of integer-valued random variables that are either associated or negatively associated.We present a simple upper bound for the distance between the distribution of the sumof $X_i$ and a sum of $n$ independent randomvariables with the same marginals as $X_i$. An upper bound useful for establishing a compound Poisson approximation for $\Sigma_{i=1}^nX_i$ is also provided. The new bounds are of the same order as the much acclaimed Stein–Chen bound.

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Michael V. Boutsikas. Markos V. Koutras. "A bound for the distribution of the sum of discrete associated or negatively associated random variables." Ann. Appl. Probab. 10 (4) 1137 - 1150, November 2000. https://doi.org/10.1214/aoap/1019487610

Information

Published: November 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1073.60507
MathSciNet: MR1810868
Digital Object Identifier: 10.1214/aoap/1019487610

Subjects:
Primary: 60E15
Secondary: 60G50 , 62E17

Keywords: association , compound Poisson approximation , negative association , positive-negative dependence , probability metrics , rate of convergence

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 4 • November 2000
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