Weighted geometric distribution with new characterizations of geometric distribution

Abstract

ABSTRACTIn this article, we derive a new generalized geometric distribution through a weight function, which can also be viewed as a discrete analog of weighted exponential distribution introduced by Gupta and Kundu (2009). We derive some distributional properties like moments, generating functions, hazard function, and infinite divisibility followed by different estimation methods to estimate the parameters. New characterizations of the geometric distribution are presented using the proposed generalized geometric distribution. The superiority of the proposed distribution to other competing models is demonstrated with the help of two real count datasets.