Bayesian prediction intervals for the exponential-type distributions under multiply Type-II censoring data
*Mohammed S. KotbCorresponding authormsakotb1712@yahoo.comAffiliation 1Department of MathematicsFaculty of ScienceAl-Azhar UniversityNasr City, Cairo, 11884, EgyptAffiliation 2Department of MathematicsAl-Baha UniversityAl-Baha, Saudi ArabiaView full profile → , Yahia Abdel-Atyyahia1970@yahoo.comAffiliation 1Department of MathematicsFaculty of ScienceAl-Azhar UniversityNasr City, Cairo, 11884, EgyptAffiliation 2Department of MathematicsTaibah UniversityAl-Madinah, Saudi ArabiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 07 Dec 2021
- Accepted:
- 09 Aug 2022
- Published Online:
- 30 Nov 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JSMS-1014
- Pages:
- 1261–1275
Abstract
Keywords
Subject Classifications
References
[1] Y. Abd El-Aty, J. Franz, and M. A. W. Mahmoud, “Bayesian prediction based on generalized order statistics using multiply Type-II censoring,” Statistics, vol. 41, no. 6, pp. 495-504 (2007).
[2] N. Balakrishnan, “On the maximum likelihood estimation of the location and scale parameters of the exponential distribution based on multiply Type-II censored samples,” Journal of Applied Statistics, vol. 17, pp. 55-61 (1990).
[3] K. Balasubramanian and N. Balakrishnan, “Estimation for one and two-parameter exponential distributions under multiple Type-II censoring,” Statistical Papers, vol. 33, pp. 203-216 (1992).
[4] S. B. Kang, “Approximate MLE for exponential distribution under multiple Type-II censoring,” Journal of Korean Data & Information Science Society, vol. 14, pp. 983-988 (2003).
[5] N. Balakrishnan, D. Kundu, H. K. T. Ng, and N. Kannan, “Point and interval estimation for a simple step-stress model with Type-II censoring,” Journal of Quality Technology, vol. 39, pp. 35-47 (2007).
[6] S.B. Kang, Y.S. Cho, J.T. Han, J. Kim, An estimation of the entropy for a double exponential distribution based on multiply Type-II censored samples, Entropy 14, 161-173 (2012).
[7] S.B. Kang, S.K. Lee, AMLEs for the exponential distribution based on multiple Type-II censored samples, The Korean Communications in Statistics 12, 603-613 (2005).
[8] M.M. Mohie-El-Din, Y. Abd El-Aty, A.R. Shafay, Two-sample Bayesian prediction intervals of generalized order statistics based on multiply Type-II censored data, Communications in Statistics-Theory and Methods 41, 381-392 (2012).
[9] M.Z. Raqab, Approximate maximum likelihood predictors of future failure times of shifted exponential distributions under multiple Type-II censoring, Statistical Methods & Applications 13, 41-52 (2004).
[10] C. Kim, S. Song, Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples, Statistical Papers 51, 583-597 (2010).
[11] M.S. Kotb, M.Z. Raqab, Inference and prediction for modified Weibull distribution based on doubly censored samples, Mathematics and Computers in Simulation 132, 195-207 (2017).
[12] M.Z. Raqab, M.T. Madi, Bayesian prediction of the total time on test using doubly censored Rayleigh data, Journal of Statistical Computation and Simulation 72, 781-789 (2002).
[13] D. Kundu, H. Howlader, Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data, Computational Statistics and Data Analysis 54, 1547-1558 (2010).
[14] M.S. Kotb, Bayesian inference and prediction for modified Weibull distribution under generalized order statistics, Journal of Statistics & Management Systems 17(5&6), 547-578 (2014).
[15] M.S. Kotb, Bayesian prediction bounds for the exponential-type distribution based on generalized progressive hybrid censoring scheme, Stochastics and Quality Control 33(2), 93-101 (2018).
[16] M.M. Mohie El-Din, M.S. Kotb, E.F. Abd-Elfattah, H.A. Newer, Bayesian inference and prediction of the Pareto distribution based on ordered ranked set sampling, Communications in Statistics - Theory and Methods 46(13), 6264-6279 (2017).
[17] E.K. Al-Hussaini, Predicting observables from a general class of distributions, Journal of Statistical Planning and Inference 79, 79- 91 (1999).
[18] B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, A First Course in Order Statistics, New York: Wiley (1994).
[19] M. S. Kotb and M. Z. Raqab, “Statistical inference for modified Weibull distribution based on progressively Type-II censored data,” Mathematics and Computers in Simulation, vol. 162, pp. 233-248 (2019).
[20] L. Rayleigh, “On the resultant of a large number of vibrations of the same pitch and of arbitrary phase,” Philosophical Magazine, vol. 10, pp. 73-78 (1980).
[21] L. Rayleigh, “On waves propagated along the plane surface of an elastic solid,” Proceedings of the London Mathematical Society, vol. 17, pp. 1-4 (1985).
[22] A. J. Fernández, “Bayesian inference from Type-II censored Rayleigh data,” Statistics and Probability Letters, vol. 48, pp. 393-399 (2000).
[23] D. Sun and J. O. Berger, “Bayesian sequential reliability for Weibull and related distribution,” Annals of the Institute of Statistical Mathematics, vol. 46, no. 2, pp. 221-249 (1994).
[24] T. Lwin, “Estimating the tail of the Paretian law,” Skandinavisk Aktuarietidskruft, vol. 55, pp. 170-178 (1972).
[25] B. C. Arnold and S. J. Press, “Bayesian estimation and prediction for Pareto data,” Journal of the American Statistical Association, vol. 84, pp. 1079-1084 (1989).
[26] F. Proschan, “Theoretical explanation of observed decreasing failure rate,” Technometrics, vol. 5, pp. 375-383 (1963).
[27] E. T. Lee and J. W. Wang, Statistical Methods for Survival Data Analysis, 3rd ed. New York: John Wiley (2003).
[28] J. S. Maritz and T. Lwin, Empirical Bayes Methods, 2nd ed. London: Chapman and Hall (1989).
[29] S. Geisser, “On hierarchical Bayes procedures for predicting simple exponential survival,” Biometrics, vol. 46, pp. 225-230 (1990).
[30] J. M. Bernardo and A. F. M. Smith, Bayesian Theory, 1st ed. New York: John Wiley and Sons Inc. (1994).




