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New Non-uniform Bounds on Poisson Approximation for Dependent Bernoulli Trials

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Abstract

The aim of this article is a use of the Stein–Chen method to obtain new non-uniform bounds on the error of the distribution of sums of dependent Bernoulli random variables and the Poisson distribution. The bounds obtained in this study are improved to be more appropriate for measuring the accuracy of Poisson approximation. Examples are provided to illustrate applications of the obtained results.

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Acknowledgments

This research is supported by the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand. The author would like to thank the referees for their useful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Burapha University, Chonburi, 20131, Thailand

    K. Teerapabolarn

  2. Centre of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok, 10400, Thailand

    K. Teerapabolarn

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  1. K. Teerapabolarn
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Correspondence to K. Teerapabolarn.

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Communicated by Ataharul M. Islam.

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Teerapabolarn, K. New Non-uniform Bounds on Poisson Approximation for Dependent Bernoulli Trials. Bull. Malays. Math. Sci. Soc. 38, 231–248 (2015). https://doi.org/10.1007/s40840-014-0014-z

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  • DOI: https://doi.org/10.1007/s40840-014-0014-z

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