Abstract

The Poisson-Komal distribution is derived by compounding the Poisson distribution with the Komal distribution. 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 about origin of Poisson-Komal 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. Various descriptive measures based on moments have been studied. Some interesting and useful statistical properties including unimodality and increasing hazard rate 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 and Poisson-Garima distribution on two datasets from biological sciences are discussed and presented. The result shows that the proposed distribution provides greater flexibility in modeling real over-dispersed count data.

Keywords

komal distribution, compounding, moments, statistical properties, maximum likelihood estimation, simulation, goodness of fit