Negative binomial approximation for independent negative binomial variables

摘要

This paper uses Stein's method and the negative binomial w-functionsto determine a bound for the total variation distance between the dis-tribution of a sum of independent negative binomial random variables,each with parameters ni and pi = 1??qi, and a negative binomial distri-bution with parameters m =Pni=1 ni and p = mm+Pni=1niqipi. The resultof this study gives an accurate approximation when all qi are small orall qi are close to q.