Asian Journal of Probability and Statistics

The Poisson-Pratibha distribution is derived by compounding the Poisson distribution with the Pratibha distribution and the proposed distribution has the capability to capture the skewness and the over-dispersion of the dataset. The distribution has a tendency to accommodate the right tail and tends to zero at faster rate. A general expression for the r th factorial moment of Poisson-Pratibha distribution has been obtained and hence its first four moments about origin and central moments have been derived. The proposed distribution is unimodal, has increasing hazard rate and over-dispersed. Moments based descriptive measures have been derived and studied. The reliability properties including hazard function, reverse hazard function, cumulative hazard function, second rate of failure and Mills ratio of the proposed probability model have been discussed. A simulation study has been done to test the performance of maximum likelihood estimates. Finally, the goodness of fit of the proposed distribution and its comparison with other one parameter over-dispersed discrete distributions including Poisson-Lindley distribution (PLD), Poisson-Garima distribution(PGD) and Poisson-Sujatha distribution (PSD) on two datasets are discussed and presented. The result shows that the PPD has greater flexibility and applicability in modeling real over-dispersed count data and thus provides its suitability for practical applications.