The Poisson-Rama distribution with properties and applications to model over-dispersed count data

The discrete data available in any fields of knowledge is influenced by several known and unknown factors and the factors which affect the discrete data are stochastic in nature. The stochastic nature of discrete data is really a challenge for statistician to model and analyse with the existing discrete distributions. In the present paper, Poisson-Rama distribution, a Poisson mixture of Rama distribution, has been proposed to model over-dispersed data. Distributional properties, estimation of parameter using maximum likelihood method, and applications of the proposed distributions have been discussed. The simulation study has been carried out to know the consistency of maximum likelihood estimates of parameter. It is observed that the proposed distribution gives much closure fit than several over-dispersed one parameter discrete distributions including Poisson-Lindley distribution, Poisson-Akash distribution and Poisson-Ishita distribution.