International Journal of Mathematics and Mathematical Sciences
Volume 2005 (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 K. Neammanee. 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 be independent Bernoulli random variables with and let . 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 in the case .