New bounds on Poisson approximation to the distribution of a sum of negative binomial random variables

The Stein-Chen method is usedto give new bounds, non-uniform bounds, for the distances between the distribution of a sum of independent negative binomial random variables and a Poisson distribution with mean, where ri and pi = 1-qi are parameters of each negative binomial distribution. Results of this study are superior than those presented in Teerapabolarn (2014) and Hung and Giang (2016)