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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 5, Pages 717-728

A refinement of normal approximation to Poisson binomial

Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

Received 8 August 2004; Revised 6 December 2004

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let X1,X2,,Xn be independent Bernoulli random variables with P(Xj=1)=1P(Xj=0)=pj and let Sn:=X1+X2++Xn. Sn is called a Poisson binomial random variable and it is well known that the distribution of a Poisson binomial random variable can be approximated by the standard normal distribution. In this paper, we use Taylor's formula to improve the approximation by adding some correction terms. Our result is better than before and is of order 1/n in the case p1=p2==pn.