Poisson-modification of the Quasi Lindley distribution and its zero modification for over-dispersed count data

In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape of the distribution and moments and related measures, are explored. It was noted that the new distribution to be either unimodal or bimodal, and over-dispersed. Further, it has a tendency to accommodate various right tail behaviors and variance-to-mean ratios. A zero-modified version of this distribution is also derived. Its unknown parameter estimation by using the maximum likelihood estimation method is examined by a simulation study based on the asymptotic theory. Finally, three real-world data sets are used to illustrate the flexibility and potentiality of the new distribution.