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.

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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