New Distribution for Fitting Discrete Data: The Poisson-Gold Distribution and Its Statistical Properties

Abstract

Motivated mainly by lifetime issues, a new lifetime distribution coined ``Discrete Poisson-Gold distribution'' is introduced in this paper. Different structural properties of the new distribution are derived including moment generating function and the $r^{th}$ moment and others are presented. In addition, we discussed various important mathematical properties of the new distribution including estimation procedures for estimating the distribution parameters using the maximum likelihood and method of moments. The usefulness and credibility of the distribution are illustrated by means of two real-data applications to show its superior performance over some other well-known lifetime distributions and to prove its versatility in practical applications.