Zero-modified Poisson-Modification of Quasi Lindley distribution and its application
Zero-modified Poisson-Modification of Quasi Lindley distribution and its application

Summary/Abstract: The Poisson-Modification of Quasi Lindley (PMQL) distribution is a newly introduced mixedPoisson distribution for over-dispersed count data. The aim of this article is to introduce theZero-modified PMQL (ZMPMQL) distribution as an alternative to the PMQL distributionin order to accommodate zero inflation/deflation. The method of obtaining the ZMPMQLdistribution jointly with some of its important properties, namely the probability mass anddistribution functions, mean, variance, index of dispersion, and quantile function are presented. Furthermore, some of its special cases are discussed. The maximum likelihood(ML) estimation method is used for the unknown parameter estimation. A simulation studyis conducted in order to evaluate the asymptotic theory of the ML estimation method andto show the superiority of the ML method over the method of moments estimation. Theapplicability of the introduced distribution is illustrated by using a real-world data set.

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