Bayesian and non-Bayesian inferential approaches under lower-recorded data with application to model COVID-19 data

Rashad M. EL-Sagheer; Mohamed S. Eliwa; Khaled M. Alqahtani; Mahmoud El-Morshedy; Rashad M. EL-Sagheer; Mohamed S. Eliwa; Khaled M. Alqahtani; Mahmoud El-Morshedy

doi:10.3934/math.2022873

AIMS Mathematics

2022, Volume 7, Issue 9: 15965-15981. doi: 10.3934/math.2022873

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Research article

Bayesian and non-Bayesian inferential approaches under lower-recorded data with application to model COVID-19 data

1.
Department of Mathematics, Faculty of Science, Al-Azhar University, Naser city 11884, Cairo, Egypt
2.
High Institute of Computer and Management Information System, First Statement, New Cairo 11865, Cairo, Egypt
3.
Department of Statistics and Operation Research, College of Science, Qassim University, P.O. Box 6644, Buraydah 51482, Saudi Arabia
4.
Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
5.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
6.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 15 March 2022 Revised: 02 June 2022 Accepted: 08 June 2022 Published: 29 June 2022
MSC : 62N05, 62F10

In this article, estimation of the parameters as well as some lifetime parameters such as reliability and hazard rate functions for the Dagum distribution based on record statistics is obtained. Both Bayesian and non-Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. Moreover, approximate confidence intervals for the parameters based on the asymptotic distribution of the maximum likelihood estimators are constructed. Besides, to construct the variances of the reliability and hazard rate functions the delta method is implemented. The Lindley's approximation and Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under both symmetric and asymmetric loss functions. Also, the corresponding highest posterior density credible intervals are constructed. A simulation study is utilized to assay and evaluate the performance of the proposed inferential approaches. Finally, a real data set of COVID-19 mortality rate is analyzed to illustrate the proposed methods of estimation.
- Dagum distribution,
- reliability characteristics,
- record statistics,
- Lindley's and MCMC techniques,
- COVID-19 data
Citation: Rashad M. EL-Sagheer, Mohamed S. Eliwa, Khaled M. Alqahtani, Mahmoud El-Morshedy. Bayesian and non-Bayesian inferential approaches under lower-recorded data with application to model COVID-19 data[J]. AIMS Mathematics, 2022, 7(9): 15965-15981. doi: 10.3934/math.2022873

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Abstract

In this article, estimation of the parameters as well as some lifetime parameters such as reliability and hazard rate functions for the Dagum distribution based on record statistics is obtained. Both Bayesian and non-Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. Moreover, approximate confidence intervals for the parameters based on the asymptotic distribution of the maximum likelihood estimators are constructed. Besides, to construct the variances of the reliability and hazard rate functions the delta method is implemented. The Lindley's approximation and Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under both symmetric and asymmetric loss functions. Also, the corresponding highest posterior density credible intervals are constructed. A simulation study is utilized to assay and evaluate the performance of the proposed inferential approaches. Finally, a real data set of COVID-19 mortality rate is analyzed to illustrate the proposed methods of estimation.

References

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