A NEW EXPONENTIATED DISCRETE LINDLEY DISTRIBUTION FOR ANALYZING COUNT DATA

Abstract

In this article, a new discrete distribution called the exponentiated discrete Lindley distribution is derived. The usefulness of this distribution is supported by its ability to analyze different types of count data (over-, under-, equi-dispersed, positively, and negatively skewed). Also, with two parameters, it possesses a bathtub-shaped hazard rate function, which is not the case for well-known discrete distributions. We also discuss some of its important properties with numerical illustrations. Subsequently, the point and interval estimation of the parameters are performed under the classical and Bayesian paradigms. A simulation study is carried out to showcase the numerical illustration of the discussed estimation procedures. To examine the practical applicability, four real datasets are fitted, and the results are fairly compared with other well-known existing discrete models.