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Abstract
In this study, the Poisson (PD) distribution was compounded with a continuous distribution to produce the Poisson XLindley distribution (PXLD). Its raw moments and central moments are acquired as a result of a general expression for its rth factorial moment concerning origin being derived. Additionally, the expressions for its coefficient of variation, skewness, kurtosis and index of dispersion have been provided. For the estimate of its parameters, in particular, the methods of maximum likelihood and moments have been addressed. The applicability of the proposed distribution in modeling real data sets on Nipah virus infection, number of Hemocytometer yeast cell count data, and epileptic seizure counts data is examined by analyzing two real-world data sets.
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