A New Compound Distribution and Its Applications in Over-dispersed Count Data

Every time variance exceeds mean, over-dispersed models are typically employed. This is the reason that over-dispersed models are such an important aspect of statistical modeling. In this work, the parameter of Poisson distribution is assumed to follow a new lifespan distribution called as Chris-Jerry distribution. The resulting compound distribution is an over-dispersed model known as the Poisson-Chris-Jerry distribution. As a result of deriving a general expression for the r th factorial moment, we acquired the moments about origin and the central moments. In addition to this, moment’s related measurements, generating functions, over-dispersion property, reliability characteristics, recurrence relation for probability, and other statistical qualities, have also been described. For the goal of estimating parameter of the suggested model, the maximum likelihood estimation and method of moment estimation have been addressed. The usefulness of maximum likelihood estimates has also been taken into consideration through a simulation study. We employed four real life data sets, examined the goodness-of-fit test, and considered additional standards such as the Akaike’s information criterion and Bayesian information criterion. The outcomes are compared with several potential models. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.