Approximating the Negative Binomial

This paper presents the results of a numerical investigation of six approximations to the cumulative negative binomial distribution. The approximations studied include two Poissons, Poisson Gram-Charlier, Normal, Normal Gram-Charlier and the Camp-Paulson. Two approximations were found to be extremely good: the Poisson Gram-Charlier when the probability p is large, and the Camp-Paulson almost everywhere.