Frequentist and Bayesian approach for the generalized logistic lifetime model with applications to air-conditioning system failure times under joint progressive censoring data

Mustafa M. Hasaballah; Oluwafemi Samson Balogun; M. E. Bakr; Mustafa M. Hasaballah; Oluwafemi Samson Balogun; M. E. Bakr

doi:10.3934/math.20241422

AIMS Mathematics

2024, Volume 9, Issue 10: 29346-29369. doi: 10.3934/math.20241422

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Frequentist and Bayesian approach for the generalized logistic lifetime model with applications to air-conditioning system failure times under joint progressive censoring data

1.
Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt
2.
Department of Computing, University of Eastern Finland, Kuopio FI-70211, Finland
3.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 31 July 2024 Revised: 19 September 2024 Accepted: 26 September 2024 Published: 16 October 2024
MSC : 62F10, 62N05

Based on joint progressive Type-II censored data, we examined the statistical inference of the generalized logistic distribution with different shape and scale parameters in this research. Wherever possible, we explored maximum likelihood estimators for unknown parameters within the scope of the joint progressive censoring scheme. Bayesian inferences for these parameters were demonstrated using a Gamma prior under the squared error loss function and the linear exponential loss function. It was important to note that obtaining Bayes estimators and the corresponding credible intervals was not straightforward; thus, we recommended using the Markov Chain Monte Carlo method to compute them. We performed real-world data analysis for demonstrative purposes and ran Monte Carlo simulations to compare the performance of all the suggested approaches.
- generalized logistic distribution,
- maximum likelihood estimation,
- loss function,
- Bayesian estimation,
- Markov chain Monte Carlo,
- joint progressive censoring scheme
Citation: Mustafa M. Hasaballah, Oluwafemi Samson Balogun, M. E. Bakr. Frequentist and Bayesian approach for the generalized logistic lifetime model with applications to air-conditioning system failure times under joint progressive censoring data[J]. AIMS Mathematics, 2024, 9(10): 29346-29369. doi: 10.3934/math.20241422

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Abstract

Based on joint progressive Type-II censored data, we examined the statistical inference of the generalized logistic distribution with different shape and scale parameters in this research. Wherever possible, we explored maximum likelihood estimators for unknown parameters within the scope of the joint progressive censoring scheme. Bayesian inferences for these parameters were demonstrated using a Gamma prior under the squared error loss function and the linear exponential loss function. It was important to note that obtaining Bayes estimators and the corresponding credible intervals was not straightforward; thus, we recommended using the Markov Chain Monte Carlo method to compute them. We performed real-world data analysis for demonstrative purposes and ran Monte Carlo simulations to compare the performance of all the suggested approaches.

References

[1]	N. Balakrishnan, M. Y. Leung, Order statistics from the Type I generalized logistic distribution, Comm. Statist. Simulation Comput., 17 (1988), 25–50. https://doi.org/10.1080/03610918808812648 doi: 10.1080/03610918808812648
[2]	N. L. Johnson, S. Kotz, N. Balakrishnan, Continuous univariate distributions, 2 Eds., New York: Wiley and Sons, 1995.
[3]	A. Asgharzadeh, Point and interval estimation for a generalized logistic distribution under progressive type-II censoring, Comm. Statist. Theory Methods, 35 (2006), 1685–1702. https://doi.org/10.1080/03610920600683713 doi: 10.1080/03610920600683713
[4]	M. R. Alkasasbeh, M. Z. Raqab, Estimation of the generalized logistic distribution parameters: Comparative study, Stat. Methodol., 6 (2009), 262–279. https://doi.org/10.1016/j.stamet.2008.10.001 doi: 10.1016/j.stamet.2008.10.001
[5]	R. D. Gupta, D. Kundu, Generalized logistic distributions, J. Appl. Statist. Sci., 18 (2010), 51–66.
[6]	M. Li, L. Yan, Y. Qiao, X. Cai, K. K. Said, Generalized fiducial inference for the stress–strength reliability of generalized logistic distribution, Symmetry, 15 (2023), 1365. https://doi.org/10.3390/sym15071365 doi: 10.3390/sym15071365
[7]	A. Asgharzadeh, R. Valiollahi, Mohammad Z. Raqab, Estimation of the stress-strength reliability for the generalized logistic distribution, Stat. Methodol., 15 (2013), 73–94. https://doi.org/10.1016/j.stamet.2013.05.002 doi: 10.1016/j.stamet.2013.05.002
[8]	N. Balakrishnan, R. Aggarwala, Progressive censoring: Theory, methods, and applications, Birkhäuser Boston, 2000. https://doi.org/10.1007/978-1-4612-1334-5
[9]	A. Rasouli, N. Balakrishnan, Exact likelihood inference for two exponential populations under joint progressive type-II censoring, Commun. Stat. Theory Methods, 39 (2010), 2172–2191. https://doi.org/10.1080/03610920903009418 doi: 10.1080/03610920903009418
[10]	Y. Qiao, W. Gui, Statistical inference of weighted exponential distribution under joint progressive type-II censoring, Symmetry, 14 (2022), 2031. https://doi.org/10.3390/sym14102031 doi: 10.3390/sym14102031
[11]	H. Panahi, Reliability estimation and order-restricted inference based on joint type-II progressive censoring scheme with application to splashing data in atomization process, In: Proceedings of the institution of mechanical engineers, Part O: Journal of risk and reliability, 2024. https://doi.org/10.1177/1748006X241242834
[12]	M. M. Hasaballah, Y. A. Tashkandy, O. S. Balogun, M. E. Bakr, Reliability analysis for two populations Nadarajah-Haghighi distribution under Joint progressive type-II censoring, AIMS Mathematics, 9 (2024), 10333–10352. https://doi.org/10.3934/math.2024505 doi: 10.3934/math.2024505
[13]	M. M. Hasaballah, Yusra A. Tashkandy, Oluwafemi Samson Balogun, M. E. Bakr, Bayesian and classical inference of the process capability index under progressive type-II censoring scheme, Phys. Scr., 99 (2024), 055241. https://doi.org/10.1088/1402-4896/ad398c doi: 10.1088/1402-4896/ad398c
[14]	M. M. Hasaballah, Y. A. Tashkandy, O. S. Balogun, M. E. Bakr, Bayesian inference for the inverse Weibull distribution based on symmetric and asymmetric balanced loss functions with application, Eksploat. Niezawod., 26 (2024), 187158. https://doi.org/10.17531/ein/187158 doi: 10.17531/ein/187158
[15]	M. M. Hasaballah, O. S. Balogun, M. E. Bakr, Point and interval estimation based on joint progressive censoring data from two Rayleigh-Weibull distribution with applications, Phys. Scr., 99 (2024), 085239. http://dx.doi.org/10.1088/1402-4896/ad6107 doi: 10.1088/1402-4896/ad6107
[16]	H. R. Varian, A Bayesian approach to real state assessment, In: Studies in Bayesian econometrics and statistics: In Honor of L. J. Savage, North-Holland Pub. Co., 1975,195–208.
[17]	N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys., 21 (1953), 1087–1092. https://doi.org/10.1063/1.1699114 doi: 10.1063/1.1699114
[18]	W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57 (1970), 97–109. https://doi.org/10.1093/biomet/57.1.97 doi: 10.1093/biomet/57.1.97
[19]	A. Xu, G. Fang, L. Zhuang, C. Gu, A multivariate student-t process model for dependent tail-weighted degradation data, IISE Trans., 2024. https://doi.org/10.1080/24725854.2024.2389538
[20]	L. Zhuang, A. Xu, Y. Wang, Y. Tang, Remaining useful life prediction for two-phase degradation model based on reparameterized inverse Gaussian process, European J. Oper. Res., 319 (2024), 877–890. https://doi.org/10.1016/j.ejor.2024.06.032 doi: 10.1016/j.ejor.2024.06.032
[21]	F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics, 5 (1963), 375–383. https://doi.org/10.2307/1266340 doi: 10.2307/1266340

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