POISSON APPROXIMATION FOR INDEPENDENT BINOMIAL RANDOM VARIABLES

Abstract

This paper gives a bound for the total variation distance between the distribution of a sum of independent binomial random variables and an appropriate Poisson distribution with mean n i=1 m i p i , where m i and p i = 1q i are parameters of each binomial distribution.With this bound, it is indicated that the distribution of the sum can be approximated by the Poisson distribution when each m i p i is small.