Binomial approximation for a sum of independent binomial random variables

Abstract

This paper uses Stein’s method and the binomial w-functions to determine a bound for approximating the distribution of a sum of n independent binomial random variables, each with parameters ni and pi, by a binomial distribution with parameters m = P n=1 ni and p = 1 m P n i=1 nipi. When all pi are small or all pi are close to p, the result of the study gives an accurate approximation. Mathematics Subject Classication: 60F05, 60G50