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.
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John J. Bartko (1966) studied this question.
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