Volume 52, pp. 270-280, 2020.

Asymptotic inversion of the binomial and negative binomial cumulative distribution functions

A. Gil, J. Segura, and N. M. Temme

Abstract

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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Key words

binomial cumulative distribution function, negative binomial cumulative distribution function, asymptotic representation, asymptotic inversion methods

AMS subject classifications

33B20, 41A60

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