A Generalised Poisson Mishra Distribution

Abstract

Background: “Mishra distribution" of B. K. Sah (2015) has been obtained in honor of Professor A. Mishra, Department of Statistics, Patna University, Patna (Sah, 2015). A one parameter Poisson-Mishra distribution (PMD) of B. K. Sah (2017) has been obtained by compounding Poisson distribution with Mishra distribution. It has been found that this distribution gives better fit to all the discrete data sets which are negative binomial in nature used by Sankarn (1970) and others. A generalisation of PMD has been obtained by mixing the generalised Poisson distribution of Consul and Jain (1973) with the Mishra distribution.

Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution.

Results: Probability density function and the first four moments about origin of the proposed distribution have been obtained. The estimation of parameters of this distribution has been discussed by using the first moment about origin and the probability mass function at x = 0 . This distribution has been fitted to a number of discrete data-sets to which earlier Poisson-Lindley distribution (PLD) and PMD have been fitted.

Conclusion: P-value of generalised Poisson-Mishra distribution is greater than PLD and PMD. Hence, it provides a better alternative to the PLD of Sankarn and PMD of B. K. Sah.

Nepalese Journal of Statistics, Vol. 2, 27-36