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.

Asymptotic inversion methods, Asymptotic representation, Binomial cumulative distribution function, Negative binomial cumulative distribution function
dx.doi.org/10.1553/ETNA_VOL52S270
Electronic Transactions on Numerical Analysis
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Gil, A, Segura, J, & Temme, N.M. (2020). Asymptotic inversion of the binomial and negative binomial cumulative distribution functions. Electronic Transactions on Numerical Analysis, 52, 270–280. doi:10.1553/ETNA_VOL52S270