Journal of Mathematics and Statistics

The Uniform Truncated Negative Binomial Distribution and its Properties

Bahady I. Kamel, Shaban E. Abo Youssef and Mohamed G. Sief

DOI : 10.3844/jmssp.2016.290.301

Journal of Mathematics and Statistics

Volume 12, Issue 4

Pages 290-301


A new three parameters continuous distribution which is named the Uniform Truncated Negative Binomial (UTNB) distribution is introduced. It has the uniform and the Marshall-Olkin extended uniform distributions as sub-models. Some reliability and statistical properties of the new distribution are derived, including the shape behavior of the density and hazard rate functions, the mean residual life, moments and moment generating function, quantiles and related measures. The limiting distributions of the sample extremes, stochastic orderings, entropies and stress-strength reliability are derived. Maximum likelihood estimation is performed. Application to censored data illustrate the potentiality of the proposed distribution is provided.


© 2016 Bahady I. Kamel, Shaban E. Abo Youssef and Mohamed G. Sief. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.