A New Three-Parameter Poisson-Lindley Distribution for Modelling Over-dispersed Count Data

In this paper, a new Three-parameter Poisson-Lindley distribution (NTPPLD), of which Shanker and Mishra's [17] Two-parameter Poisson-Lindley distribution and Sankaran's [10] One-parameter Poisson-Lindley distribution are particular cases, is proposed.Distributional properties and common descriptive measures pertaining to this mixed distribution are derived.The behaviour of the probability mass function with variations in the parameters is also studied.Estimation of parameters by the method of maximum likelihood and method of moments are discussed and a simulation study is carried out to check the consistency of the maximum likelihood estimates.Finally, the proposed distribution is applied to real-data sets and it is seen that this distribution is a flexible model that may be a useful alternative to known distributions like Poisson, Poisson Lindley, Two-parameter Poisson Lindley and many others for count data analysis.