Joint reconstruction and prediction regions for unobserved exponential lifetimes under doubly Type II censoring

References

• Abd Ellah, A. H., & Sultan, K. S. (2005). Exact Bayesian prediction of exponential lifetime based on fixed and random sample sizes. Quality Technology & Quantitative Management, 2(2), 161–175. https://doi.org/10.1080/16843703.2005.11673091
   Google Scholar
• Aitchison, J. (1964). Two papers on the comparison of Bayesian and frequentist approaches to statistical problems of prediction: Bayesian tolerance regions. Journal of the Royal Statistical Society: Series B (Methodological), 26(2), 161–175. https://doi.org/10.1111/j.2517-6161.1964.tb00550.x
   Web of Science ®Google Scholar
• Aitchison, J., & Sculthorpe, D. (1965). Some problems of statistical prediction. Biometrika, 52(3–4), 469–483. https://doi.org/10.1093/biomet/52.3-4.469
   PubMedGoogle Scholar
• Alizadeh, M., Asgharzadeh, A., & Basiri, E. (2024). Reconstruction regions for unobserved middle order statistics in the exponential distribution. Journal of Computational and Applied Mathematics, 441, 115696. https://doi.org/10.1016/j.cam.2023.115696
   Web of Science ®Google Scholar
• Asgharzadeh, A., Mirzazadeh Ganji, Z., Valiollahi, R., & Ahmadi, J. (2017). Reconstruction of past failure times for left type-II censored data from Weibull model. Journal of Statistical Research of Iran JSRI, 14(1), 31–51. https://doi.org/10.18869/acadpub.jsri.14.1.31
   Google Scholar
• Asgharzadeh, A., Mohammadpour, M., & Ganji, Z. M. (2014). Estimation and reconstruction based on left censored data from Pareto model. Journal of the Iranian Statistical Society, 13(2), 151–175.
   Google Scholar
• Bagheri, S. F., Asgharzadeh, A., Basiri, E., & Fernández, A. J. (2019). One-sample prediction regions for future record intervals. Statistics & Probability Letters, 153, 15–20. https://doi.org/10.1016/j.spl.2019.05.005
   Web of Science ®Google Scholar
• Bagheri, S. F., Asgharzadeh, A., Fernández, A. J., & Pérez-González, C. J. (2021). Joint prediction for future failures times under type-II censoring. IEEE Transactions on Reliability, 71(1), 100–110. https://doi.org/10.1109/TR.2021.3068080
   Web of Science ®Google Scholar
• Balakrishnan, N., Doostparast, M., & Ahmadi, J. (2009). Reconstruction of past records. Metrika, 70(1), 89–109. https://doi.org/10.1007/s00184-008-0181-8
   Web of Science ®Google Scholar
• Barakat, H. M., El-Adll, M. E., & Aly, A. E. (2022). Prediction of future generalized order statistics based on two-parameter exponential distribution for large samples. Quality Technology & Quantitative Management, 19(2), 259–275. https://doi.org/10.1080/16843703.2022.2034261
   Web of Science ®Google Scholar
• Barakat, H. M., Khaled, O. M., & Ghonem, H. A. (2021). New method for prediction of future order statistics. Quality Technology & Quantitative Management, 18(1), 101–116. https://doi.org/10.1080/16843703.2020.1782087
   Web of Science ®Google Scholar
• Basiri, E., Fernández, A. J., Asgharzadeh, A., & Bagheri, S. F. (2020). Best prediction regions for future exponential record intervals. Statistics, 54(5), 969–988. https://doi.org/10.1080/02331888.2020.1825437
   Web of Science ®Google Scholar
• Chhikara, R. S., & Guttman, I. (1982). Prediction limits for the inverse gaussian distribution. Technometrics, 24(4), 319–324. https://doi.org/10.2307/1267827
   Web of Science ®Google Scholar
• David, H. A., & Nagaraja, H. N. (2003). Order statistics (3rd ed.). John Wiley & Sons.
   Google Scholar
• El-Adll, M. E. (2021). Inference for the two-parameter exponential distribution with generalized order statistics. Mathematical Population Studies, 28(1), 1–23. https://doi.org/10.1080/08898480.2019.1681187
   Web of Science ®Google Scholar
• Fernández, A. J. (2000). Bayesian inference from type II doubly censored rayleigh data. Statistics & Probability Letters, 48(4), 393–399. https://doi.org/10.1016/S0167-7152(00)00021-3
   Web of Science ®Google Scholar
• Feroze, N., & Aslam, M. (2012). On posterior analysis of inverse Rayleigh distribution under singly and doubly type II censored data. International Journal of Probability and Statistics, 1(5), 145–152. https://doi.org/10.5923/j.ijps.20120105.01
   Google Scholar
• Harter, H. L., & Moore, A. H. (1968). Maximum-likelihood estimation, from doubly censored samples, of the parameters of the first asymptotic distribution of extreme values. Journal of the American Statistical Association, 63(323), 889–901. https://doi.org/10.1080/01621459.1968.11009317
   Web of Science ®Google Scholar
• Khatib, B., Ahmadi, J., & Razmkhah, M. (2013). Bayesian reconstruction of the missing failure times in exponential distribution. Journal of Statistical Computation and Simulation, 83(3), 501–517. https://doi.org/10.1080/00949655.2011.621123
   Web of Science ®Google Scholar
• Khatib, B., Ahmadi, J., & Razmkhah, M. (2014). Reconstruction of the past lower record values in a proportional reversed hazard rate model. Statistics, 48(2), 421–435. https://doi.org/10.1080/02331888.2012.719518
   Web of Science ®Google Scholar
• Kim, C., & Song, S. (2010). Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples. Statistical Papers, 51(3), 583–597. https://doi.org/10.1007/s00362-008-0142-3
   Web of Science ®Google Scholar
• Lawless, J. F. (1971). A prediction problem concerning samples from the exponential distribution, with application in life testing. Technometrics, 13(4), 725–730. https://doi.org/10.1080/00401706.1971.10488844
   Web of Science ®Google Scholar
• Lawless, J. F. (1977). Prediction intervals for the two parameter exponential distribution. Technometrics, 19(4), 469–472. https://doi.org/10.1080/00401706.1977.10489587
   Web of Science ®Google Scholar
• Lawless, J. F. (1982). Statistical models & methods for lifetime data. Wiley.
   Google Scholar
• Lin, C. T., & Balakrishnan, N. (2003). Exact prediction intervals for exponential distributions based on doubly type-II censored samples. Journal of Applied Statistics, 30(7), 783–801. https://doi.org/10.1080/0266476032000076056
   Web of Science ®Google Scholar
• Lin, C. T., Balakrishnan, N., & Ling, M. H. (2022). Exact tests for outliers in laplace samples. Communications in Statistics-Simulation and Computation, 51(10), 5794–5815. https://doi.org/10.1080/03610918.2020.1780444
   Web of Science ®Google Scholar
• Lin, C. T., Wu, Y. N., Balakrishnan, N., & Ling, M. H. (2022). OTL web interface: Outlier testing in lifetime data. Communications in Statistics–Simulation and Computation, 1–22. https://doi.org/10.1080/03610918.2022.2116748
   Web of Science ®Google Scholar
• Pak, A., Parham, G. A., & Saraj, M. (2013). On estimation of Rayleigh scale parameter under doubly type-II censoring from imprecise data. Journal of Data Science, 11(2), 305–322. https://doi.org/10.6339/JDS.2013.11(2).1144
   Google Scholar
• Razmkhah, M., Khatib, B., & Ahmadi, J. (2010). Reconstruction of order statistics in exponential distribution. Journal of the Iranian Statistical Society, 9(1), 21–40.
   Google Scholar
• Ross, S. M. (2010). Introduction to probability models (10th ed.). Academic.
   Google Scholar
• Sinha, S. K. (1990). On the prediction limits for Rayleigh life distribution. Calcutta Statistical Association Bulletin, 39(1–2), 105–110. https://doi.org/10.1177/0008068319900111
   Google Scholar
• Upadhyay, S. K., & Pandey, M. (1989). Prediction limits for an exponential distribution: A Bayes predictive distribution approach. IEEE Transactions on Reliability, 38(5), 599–602. https://doi.org/10.1109/24.46488
   Web of Science ®Google Scholar
• Volterman, W., Balakrishnan, N., & Cramer, E. (2012). Exact nonparametric meta-analysis for multiple independent doubly type-II censored samples. Computational Statistics & Data Analysis, 56(5), 1243–1255. https://doi.org/10.1016/j.csda.2011.10.012
   Web of Science ®Google Scholar
• Wu, S. F. (2007). Interval estimation for the two-parameter exponential distribution based on the doubly type II censored sample. Quality & Quantity, 41(3), 489–496. https://doi.org/10.1007/s11135-006-9008-8
   Google Scholar
• Wu, S. F. (2008). Interval estimation for a Pareto distribution based on a doubly type II censored sample. Computational Statistics & Data Analysis, 52(7), 3779–3788. https://doi.org/10.1016/j.csda.2007.12.015
   Web of Science ®Google Scholar