Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

Manal M. Yousef, Amal S. Hassan, Abdullah H. Al-Nefaie, Ehab M. Almetwally () and Hisham M. Almongy
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Manal M. Yousef: Department of Mathematics, Faculty of Science, New Valley University, EL-Khargah 72511, Egypt
Amal S. Hassan: Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
Abdullah H. Al-Nefaie: Quantitative Methods Department, School of Business, King Faisal University, Al Ahsa 31982, Saudi Arabia
Ehab M. Almetwally: Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
Hisham M. Almongy: Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2022, vol. 10, issue 17, 1-26

Abstract: The current work focuses on ranked set sampling and a simple random sample as sampling approaches for determining stress–strength reliability from the inverted Topp–Leone distribution. Asymptotic confidence intervals are established, along with a maximum likelihood estimator of the parameters and stress–strength reliability. The reliability of such a system is assessed using the Bayesian approach under symmetric and asymmetric loss functions. The highest posterior density credible interval is constructed successively. The results are extracted using Monte Carlo simulation to compare the proposed estimators performance with different sample sizes. Finally, by looking at waiting time data and failure times of insulating fluid, the usefulness of the suggested technique is demonstrated.

Keywords: stress–strength reliability; inverted Topp Leone distribution; ranked set sampling method; Bayesian inference; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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