Asymptotic inversion of the binomial and negative binomial cumulative distribution functions

The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in [2]) can be used to obtain asymptotic representations of these functions, and also for their inversion. The performance of the asymptotic inversion methods is illustrated with numerical examples.