A DISCRETE ANALOGUE OF THE CONTINUOUS POWER LINDLEY DISTRIBUTION AND ITS APPLICATIONS

Abstract

Methods to generate a discrete analogue of a continuous distribution have been widely considered in recent decades. In general, the discretization procedure comprises in transform continuous attributes into discrete attributes generating new probability distributions that could be an alternative to the traditional  discrete models, such as Poisson and Binomial models, commonly used in analysis of count data. It also  avoids the use of continuous in the analysis of strictly discrete data. In this paper, using the discretization  method based on the survival function, it is introduced a discrete analogue of power Lindley distribution. Some mathematical properties are studied. The maximum likelihood theory is considered for estimation and asymptotic inference concerns. A simulation study is also carried out in order to evaluate some properties of the maximum likelihood estimators of the proposed model. The usefulness and accurate of the proposed model are evaluated using real datasets provided by the literature.