The non-central negative binomial distribution: Further properties and applications

Seng-Huat Ong, Kian-Kok Toh and Yeh-Ching Low

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 2, 329-344

Abstract: The non-central negative binomial distribution is both a mixed and compound Poisson distribution with applications in photon and neural counting, statistical optics, astronomy and a stochastic reversible counter system. In this paper various important probabilistic properties of the non-central negative binomial distribution in practical applications like log-concavity, discrete self-decomposability, unimodality, asymptotic behavior and tail length of the probability distribution have been derived. The construction as a mixed Poisson process by specifying a joint distribution for the inter-arrival times and its application is illustrated by a fit to real life data set.

Date: 2021
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DOI: 10.1080/03610926.2019.1634817

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