A Poisson XLindley Distribution with Applications

Abstract In this paper, a Poisson XLindley distribution (PXLD) has been obtained by compounding Poisson (PD) distribution with a continuous distribution. A general expression for its rth factorial moment about origin has been derived and hence its raw moments and central moments are obtained. The expressions for its coefficient of variation, skewness, kurtosis and index of dispersion have also been given. In particular, the method of maximum likelihood and the method of moments for the estimation of its parameters have been discussed. Finally, two real-life data sets are analyzed to investigate the suitability of the proposed distribution in modeling a real data set on Nipah virus infection, number of Hemocytometer yeast cell count data and epileptic seizure counts data.