A new reduced contagious zero-inflated model: An application to count data

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Published: Aug 23, 2023
DOI: https://doi.org/10.53982/aijnas.2023.0302.01-j
Keywords:
Gamma, Poisson, Model, Contagious, moment I

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Mumini Idowu Adarabioyo
Department of Mathematical and Physical Sciences, Afe Babalola University, Ado-Ekiti, Nigeria
Gafar Matanmi Oyeyemi
Department of Statistics, University of Ilorin, Ilorin, Nigeria

Abstract

In this paper, a reduced one-parameter contagious distribution was developed from the joint distribution of three-parameter gamma and Poisson distributions, on which Lakshmi’s three-parameter gamma distribution is based to model a count data. The distribution properties and some common descriptive measures relating to this contagious distribution are derived. The behavior of the probability mass function with changes in parameters was also studied. The parameter estimation by the maximum likelihood and moment-generating function methods is discussed. A simulation study was carried out with the proposed model to check for consistency and bias. The new model show consistency as the sample size increases. The model was applied to a real-life dataset and was seen to be more flexible in capturing excess zero, under, and over-dispersion in count data and proved to be a useful alternative to some existing zero-inflated models.

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How to Cite
Adarabioyo, M. I., & Oyeyemi, G. M. (2023). A new reduced contagious zero-inflated model: An application to count data. ABUAD International Journal of Natural and Applied Sciences, 3(2), 1-15. https://doi.org/10.53982/aijnas.2023.0302.01-j
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Vol. 3 No. 2 (2023)
Section
Articles
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors hold the copyright of all published articles except otherwise stated.

Author Biography

Gafar Matanmi Oyeyemi, Department of Statistics, University of Ilorin, Ilorin, Nigeria

Professor of Statistics, Department of Statistics, University of Ilorin, Ilorin, Nigeria

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References

1. Famoye, F., & Singh, K. (2006). Zero-inflated generalized Poisson regression model with an Application to Domestic Violence Data. Journal of Data Science. 4(2006), 117-130

2. Felix Famoye, John T. Wulu, Jr and Karan P. Singh (2004); On the Generalized Poisson Regression Model with an Application to Accident Data. Journal of Data Science 2

3. Francisco louzada, Fernaudo Moreira and Mauro Ribeiro (2017). A zero-inflated non-default rate regression model for credit scoring data. Communication in Statistics-Theory and methods
https://doi.org/10.1080/03610962.2017.1346803.

4. Frank badu Osei, Alfred Stein and Veronica Andreo (2022). A zero-inflated mixture spatially varying coefficient modeling of cholera incidences. Spatial Statistics. Volume 48, 100635. https://doi.org/10.1016/.spata.2022.100635

5. Idowu Adarabioyo and Reuben Ipinyomi (2020). Bayesian Modified Zero Hurdle and Zero-Inflated Models with Application to Under-Five Mortality in Nigeria. IEEE explore.wwwonacademic.com/detail/journal_1000049128719599_cfbd.html

6. Ma, Jiaqi and Goulias. K. G (1999). Application of Poisson Regression Models to Activity frequency Analysis and prediction. Journal of the Transportaion Research Board. Volume 1676, issue 1.
https://doi.org/10.3141/1676-11

7. Kazembe LN (2013) A Bayesian Two Part Model Applied to Analyze Risk Factors of Adult Mortality with Application to Data from Namibia. PLoS ONE 8(9):
e73500. https://doi.org/10.1371/journal.pone.0073500

8. Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34, 1-14.
9. Min, Y., Agresti, A. (2004). Random effects models for repeated measures of zero-
Modelling abundance of rare species: Statistical models for counts with extra zeros. Ecological Modelling, 88, 297-308.
10. Mullahy, J. (1986). Specification and testing of some modified count data models. of statistics, 30, 1-16
11. Partha Deb, Murat. K. Munkin and Pravin. K. Trivedi (2006). Bayesian Analysis of the Two-Part model with Endogeneity: Application to Health Care Expenditure; Journal of Applied Econometrics. 21:1081-1099
12. Peer Bllal Ahmead and Mohammad Kafeel Wani (2023). A new compound distribution and its application in over-dispersed count data. Annals of Data Science. https://doi.org/10.1007/s40745-023-00478-0
13. P´erez S´anchez. J. M and G´omez–D´eniz. E (2015). Bayesian analysis of zero-inflated regression models:Journal of Statistical Planning and Science. (136) 1360-1375)
14. R Vani Lakshmi & V S Vaidyanathan (2016) Three-parameter gamma distribution: Estimation using likelihood, spacings and least squares approach, Journal of Statistics and Management Systems, 19:1, 37-53
15. Showkat Ahmad Dar, Anwar Hassan, Peer Bilal Ahmad and Bilal Ahmad Para (2022). A new compound probability model. Application to count data. The Philippine Statistician Vol 70 No. 2, pp. 11-21
16. Welsh, A. H., Cunningham, R. B., Donnelly, C. F., & Lindenmayer, D. B. (1996).
Modelling abundance of rare species; Statistical models for counts with extra zeros. Ecological Modelling, 88, 297-308.
17. Swarup et. al.(2014). Fitting truncated geometric distributions in large scale real world networks: Theoretical Computer Science (551):22-38
18. Zorn, C. J. W. (1996). Evaluating zero-inflated and hurdle Poisson specification. Midwest Political Science Association, 1-16.