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

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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.… Click to show full abstract

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.

Keywords: binomial distribution; negative binomial; non central; distribution properties; central negative; distribution

Journal Title: Communications in Statistics - Theory and Methods
Year Published: 2019

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