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

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

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

Ahmad, Peer Bilal; Wani, Mohammad Kafeel
Annals of Data Science , Volume OnlineFirst – Jun 7, 2023
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References (36)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-023-00478-0
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Annals of Data Science – Springer Journals

Published: Jun 7, 2023

Keywords: Count data; Over-dispersion; Poisson distribution; Compounding; Simulation; Goodness-of-fit

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