Classical and Bayesian inference for the discrete Poisson Ramos-Louzada distribution with application to COVID-19 data

Ibrahim Alkhairy; Ibrahim Alkhairy

doi:10.3934/mbe.2023628

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14061-14080. doi: 10.3934/mbe.2023628

Previous Article Next Article

Research article Special Issues

Classical and Bayesian inference for the discrete Poisson Ramos-Louzada distribution with application to COVID-19 data

Ibrahim Alkhairy ^,

Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia

Academic Editor: Yang Kuang

Received: 27 February 2023 Revised: 27 May 2023 Accepted: 12 June 2023 Published: 25 June 2023

The present study is based on the derivation of a new extension of the Poisson distribution using the Ramos-Louzada distribution. Several statistical properties of the new distribution are derived including, factorial moments, moment-generating function, probability moments, skewness, kurtosis, and dispersion index. Some reliability properties are also derived. The model parameter is estimated using different classical estimation techniques. A comprehensive simulation study was used to identify the best estimation method. Bayesian estimation with a gamma prior is also utilized to estimate the parameter. Three examples were used to demonstrate the utility of the proposed model. These applications revealed that the PRL-based model outperforms certain existing competing one-parameter discrete models such as the discrete Rayleigh, Poisson, discrete inverted Topp-Leone, discrete Pareto and discrete Burr-Hatke distributions.
- Ramos-Louzada distribution,
- poisson mixture, estimation,
- Markov Chain Monte Carlo,
- COVID-19,
- data analysis
Citation: Ibrahim Alkhairy. Classical and Bayesian inference for the discrete Poisson Ramos-Louzada distribution with application to COVID-19 data[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14061-14080. doi: 10.3934/mbe.2023628

Related Papers:

Abstract

The present study is based on the derivation of a new extension of the Poisson distribution using the Ramos-Louzada distribution. Several statistical properties of the new distribution are derived including, factorial moments, moment-generating function, probability moments, skewness, kurtosis, and dispersion index. Some reliability properties are also derived. The model parameter is estimated using different classical estimation techniques. A comprehensive simulation study was used to identify the best estimation method. Bayesian estimation with a gamma prior is also utilized to estimate the parameter. Three examples were used to demonstrate the utility of the proposed model. These applications revealed that the PRL-based model outperforms certain existing competing one-parameter discrete models such as the discrete Rayleigh, Poisson, discrete inverted Topp-Leone, discrete Pareto and discrete Burr-Hatke distributions.

References

[1]	M. Shoukri, M. H. Asyali, R. VanDorp, D. Kelton, The Poisson inverse Gaussian regression model in the analysis of clustered counts data, J. Data Sci., 2 (2004), 17–32. https://doi.org/10.6339/JDS.2004.02(1).135 doi: 10.6339/JDS.2004.02(1).135
[2]	G. Shmueli, T. P. Minka, J. B. Kadane, S. Borle, P. Boatwright, A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution, J. R. Stat. Soc. Ser. C., 54 (2005), 127–142. https://doi.org/10.1111/j.1467-9876.2005.00474.x doi: 10.1111/j.1467-9876.2005.00474.x
[3]	E. Mahmoudi, H. Zakerzadeh, Generalized poisson–lindley distribution, Commun. Stat. Methods, 39 (2010), 1785–1798. https://doi.org/10.1080/03610920902898514 doi: 10.1080/03610920902898514
[4]	L. Cheng, S. R. Geedipally, D. Lord, The Poisson–Weibull generalized linear model for analyzing motor vehicle crash data, Saf. Sci., 54 (2013), 38–42. https://doi.org/10.1016/j.ssci.2012.11.002 doi: 10.1016/j.ssci.2012.11.002
[5]	H. Hassan, S. A. Dar, P. B. Ahmad, Poisson Ishita distribution: A new compounding probability model, IOSR J. Eng., 9 (2019), 38–46.
[6]	E. Altun, A new model for over-dispersed count data: Poisson quasi-Lindley regression model, Math. Sci., 13 (2019), 241–247. https://doi.org/10.1007/s40096-019-0293-5 doi: 10.1007/s40096-019-0293-5
[7]	B. A. Para, T. R. Jan, H. S. Bakouch, Poisson Xgamma distribution: A discrete model for count data analysis, Model Assist. Stat. Appl., 15 (2020), 139–151. https://doi.org/10.3233/MAS-200484 doi: 10.3233/MAS-200484
[8]	E. Altun, G. M. Cordeiro, M. M. Ristić, An one-parameter compounding discrete distribution, J. Appl. Stat., 49 (2022), 1935–1956. https://doi.org/10.1080/02664763.2021.1884846 doi: 10.1080/02664763.2021.1884846
[9]	M. Ahsan-ul-Haq, A. Al-bossly, M, El-morshedy, M. S. Eliwa, Poisson XLindley distribution for count data : Statistical and reliability properties with estimation techniques and inference, Comput. Intell. Neurosci., 2022 (2022). https://doi.org/10.1155/2022/6503670 doi: 10.1155/2022/6503670
[10]	M. Ahsan-ul-Haq, On poisson moment exponential distribution with applications, Ann. Data Sci., 2022. https://doi.org/10.1007/s40745-022-00400-0 doi: 10.1007/s40745-022-00400-0
[11]	P. L. Ramos, F. Louzada, A Distribution for instantaneous failures, Stats, 2 (2019), 247–258. https://doi.org/10.3390/stats2020019 doi: 10.3390/stats2020019
[12]	D. Roy, Discrete rayleigh distribution, IEEE Trans. Reliab., 53 (2004), 255–260. https://doi.org/10.1109/TR.2004.829161 doi: 10.1109/TR.2004.829161
[13]	H. Krishna, P. S. Pundir, Discrete Burr and discrete Pareto distributions, Stat. Methodol., 6 (2009), 177–188. https://doi.org/10.1016/j.stamet.2008.07.001 doi: 10.1016/j.stamet.2008.07.001
[14]	M. El-Morshedy, M. S. Eliwa, E. Altun, Discrete Burr-Hatke distribution with properties, estimation methods and regression model, IEEE Access, 8 (2020), 74359–74370. https://doi.org/10.1109/ACCESS.2020.2988431 doi: 10.1109/ACCESS.2020.2988431
[15]	A. S. Eldeeb, M. Ahsan-ul-Haq, A. Babar, A discrete analog of inverted Topp-Leone distribution: Properties, estimation and applications. Int. J. Anal. Appl., 19 (2021), 695–708. https://doi.org/10.28924/2291-8639-19-2021-695 doi: 10.28924/2291-8639-19-2021-695
[16]	J. F. Lawless, Statistical models and methods for lifetime data, John Wiley & Sons, 2011.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)