A non-uniform bound on binomial approximation to the beta binomial cumulative distribution function

Abstract

This paper uses Stein’s method and the characterization of beta binomial random variable to determine a non-uniform bound for the distance between the beta binomial cumulative distribution function with parameters n  N, 0  and   0 and the binomial cumulative distribution function with parameters n and    . Some numerical examples are given to illustrate the obtained result.

Keywords

• beta binomial cumulative distribution function
• binomial approximation
• characterization of the beta binomial random variable
• non-uniform bound
• Stein’s method