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An Improvement of Poisson Approximation for Sums of Dependent Bernoulli Random Variables

This article uses the Stein-Chen method to obtain new non uniform bounds on the error of the cumulative distribution function of sums of dependent Bernoulli random variables and the Poisson cumulative distribution function. The bounds obtained in the present study are sharper than those reported in Teerapabolarn and Neammanee (2006). Examples are provided to illustrate applications of the obtained results.