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A new poisson-exponential-gamma distribution for modelling count data with applications

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Abstract

In this paper, a new member of the Poisson family of distributions called the Poisson-Exponential-Gamma (PEG) distribution for modelling count data is proposed by compounding the Poisson with Exponential-Gamma distribution. The first four moments about the origin and the mean of the new PEG distribution were obtained. The expressions for its coefficient of variation, skewness, kurtosis, and index of dispersion were equally derived. The parameters of the PEG distribution were estimated using the Maximum Likelihood Method. Its relative performance based on the Goodness-of-Fit (GoF) criteria was compared with those provided by seven of the existing related distributions (Poisson, Negative-Binomial, Poisson-Exponential, Poisson-Lindley, Poisson-Shanker, Poisson-Shukla, and Poisson Entropy-Based Weighted Exponential distributions) in the literature on three different published real-life count data sets. The GoF assessment of all these distributions was performed based on the values of their loglikelihoods (\({-}2{\text{logLik}}\)), Akaike Information Criteria, Akaike Information Criteria Corrected, and Bayesian Information Criteria. The results showed that the new PEG distribution was relatively more efficient for modelling (over-dispersed) count data than any of the seven existing distributions considered. The new PEG distribution is therefore recommended as a credible alternative for modelling count data whenever relative gain in the model’s efficiency is desired.

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Acknowledgment

The authors acknowledged the anonymous reviewers whose useful comments and observations have helped to improve the first draft of this work.

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Authors and Affiliations

  1. Department of Statistics, University of Ilorin, Ilorin, Nigeria

    Waheed Babatunde Yahya

  2. Department of Statistics, Bayero University, Kano, Nigeria

    Muhammad Adamu Umar

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  1. Waheed Babatunde Yahya
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by both authors. The first draft of the manuscript was written by Muhammad Adamu Umar which was vetted, critically reviewed for appropriate intellectual content by Waheed Babatunde Yahya. Both authors commented on previous versions of the manuscript. Both authors read and approved the final manuscript.

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Correspondence to Waheed Babatunde Yahya.

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Yahya, W.B., Umar, M.A. A new poisson-exponential-gamma distribution for modelling count data with applications. Qual Quant (2024). https://doi.org/10.1007/s11135-024-01894-x

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