On pointwise binomial approximation for independent binomial random variables

Abstract

We use Stein's method and the binomial w-functions to give a uniform bound for the point metric between the distribution of a sum of n independent binomial random variables, each with parameters n i and p i , by a binomial distribution with parameters m = n i=1 n i and p = 1 m n i=1 n i p i .When all p i are small or all p i are close to p, the result of the study gives a good binomial approximation.