POISSON APPROXIMATION FOR INDEPENDENT NEGATIVE BINOMIAL RANDOM VARIABLES

Abstract

We give a bound for the total variation distance between the distribution of a sum of independent negative binomial random variables and an appropriate Poisson distribution with mean n i=1 r i q i p i , where r i and p i = 1q i are parameters of each negative binomial distribution.It is indicated that the distribution of the sum can be approximated by the Poisson distribution with this mean when each r i q i is small.