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 Gil, Segura, and Temme, [Numer. Algorithms, 74 (2017), pp. 77-91]) can be utilized to obtain asymptotic representations of these functions and also for their inversion. The performance of the asymptotic inversion methods is illustrated with numerical examples