On pointwise binomial approximation for independent binomial random variables

摘要

We use Stein's method and the binomial w-functions to give a uni-form bound for the point metric between the distribution of a sumof n independent binomial random variables, each with parameters niand pi, by a binomial distribution with parameters m =Pni=1 ni andp = 1mPni=1 nipi. When all pi are small or all pi are close to p, theresult of the study gives a good binomial approximation.