Generalized Exponential Truncated Negative Binomial Distribution

SYNOPTIC ABSTRACT: Nadarajah, Jayakumar, and Ristić (2013) introduced a family of life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall–Olkin family of distributions. In this article, we introduce Generalized Exponential Truncated Negative Binomial (GETNB) distribution using the same approach. The GETNB distribution is a generalization of the Marshall–Olkin Generalized Exponential (MOGE) distribution studied in Ristić and Kundu (2015) and Exponential Truncated Negative Binomial (ETNB) distribution studied in Nadarajah et al. (2013). The shape properties of density function and the hazard rate of GETNB distribution are discussed. The expressions for moments, order statistics, and entropy are obtained. The parameters of GETNB distribution are estimated using the method of maximum likelihood. An application to a real data set is also presented. © 2017 Taylor & Francis Group, LLC.