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Improved Chen‒Stein bounds on the probability of a union

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  09 December 2016

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of Southern California
*
* Postal address: Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA 90089, USA. Email address: smross@usc.edu
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Abstract

We improve the Chen‒Stein bounds when applied to the probability of a union. When the probability is small, the improvement in the distance from the lower to the upper bound is roughly a factor of 2. Further improvements are determined when the events of the union are either negatively or positively dependent.

Keywords

Chen‒Stein Poisson approximationimproved bounds on unionsnegative and positive dependencies

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60E99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1265 - 1270
Copyright
Copyright © Applied Probability Trust 2016 

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