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

Abstract

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.

Keywords:

• Bernoulli random variable
• Cumulative distribution function
• Poisson approximation
• Non uniform bound
• Stein-Chen method.

Mathematics Subject Classification:

• 60F05
• 60G05.

Funding

This research is supported by the Centre of Excellence in Mathematics, the Commission on Higher Education, Thailand.