Abstract
In this paper, a general exponential form of the underlying distribution and a general conjugate prior are used to discuss the maximum likelihood and Bayesian estimation based on an adaptive progressive censored sample. A general procedure for deriving the point and interval Bayesian prediction of the future progressive censored from the same sample as well as that from an unobserved future sample is also developed. The Weibull, Pareto, and Burr Type-XII distributions are then used as illustrative examples. Finally, two numerical examples are presented for illustrating all the inferential procedures developed here.
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References
Abdel-Aty Y, Franz J, Mahmoud MAW (2007) Bayesian prediction based on generalized order statistics using multiply type-II censoring. Statistics 41(6):495–504
Aggarwala R, Balakrishnan N (1998) Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. J Stat Plan Inference 70(1):35–49
Al-Hussaini EK (1999) Predicting observables from a general class of distributions. J Stat Plan Inference 79(1):79–91
AL-Hussaini EK, Abd EBA (2003) On Bayesian predictive distributions of generalized order statistics. Metrika 57(2):165–176
Al-Hussaini EK, Al-Awadhi F (2010) Bayes two-sample prediction of generalized order statistics with fixed and random sample size. J Stat Comput Simul 80(1):13–28
Al-Hussaini EK, Jaheen ZF (1992) Bayesian estimation of the parameters, reliability and failure rate functions of the Burr type XII failure model. J Stat Comput Simul 41(1–2):31–40
Ali Mousa MAM (2001) Inference and prediction for Pareto progressively censored data. J Stat Comput Simul 71(2):163–181
Arnold BC, Press SJ (1989) Bayesian estimation and prediction for Pareto data. J Am Stat Assoc 84(408):1079–1084
Balakrishnan N, Cohen AC (2014) Order statistics and inference: estimation methods. Academic Press, Boston
Balakrishnan N, Sandhu RA (1995) A simple simulational algorithm for generating progressive Type-II censored samples. Am Stat 49(2):229–230
Balakrishnan N, Shafay AR (2012) One-and two-sample bayesian prediction intervals based on Type-II hybrid censored data. Commun Stat Theory Methods 41(9):1511–1531
Balakrishnan N, Childs A, Chandrasekar B (2002) An efficient computational method for moments of order statistics under progressive censoring. Stat Probab Lett 60(4):359–365
Basak I, Basak P, Balakrishnan N (2006) On some predictors of times to failure of censored items in progressively censored samples. Comput Stat Data Anal 50(5):1313–1337
Cramer E, Iliopoulos G (2010) Adaptive progressive Type-II ensoring. Test 19(2):342–358
David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, New York
Dunsmore IR (1974) The Bayesian predictive distribution in life testing models. Technometrics 16(3):455–460
Lwin T (1972) Estimation of the tail of the Paretian law. Scand Actuar J 55(2):170–178
Mohie El-Din MM, Abdel-Aty Y, Shafay AR (2012) Two-sample Bayesian prediction intervals of generalized order statistics based on multiply Type II censored data. Commun Stat Theory Methods 41(3):381–392
Mohie El-Din MM, Shafay AR (2013) One-and two-sample Bayesian prediction intervals based on progressively Type-II censored data. Stat Pap 54(2):287–307
Mohie El-Din MM, Sadek A, Nagy M (2016) Bayesian estimation and two-sample prediction based on unified hybrid censored sample. J Stat Appl Prob 5(3):1–10
Nelson W (1982) Applied life data analysis. Wiley, New York
Ng HKT, Chan PS (2007) Comments on: Progressive censoring methodology: an appraisal. Test 16(2):287–289
Ng HKT, Kundu D, Chan PS (2009) Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme. Nav Res Logist (NRL) 56(8):687–698
Nigm AM, Hamdy HI (1987) Bayesian prediction bounds for the Pareto lifetime model. Commun Stat Theory Methods 16(6):1761–1772
Raqab MZ, Asgharzadeh A, Valiollahi R (2010) Prediction for Pareto distribution based on progressively Type-II censored samples. Comput Stat Data Anal 54(7):1732–1743
Shafay AR, Balakrishnan N (2012) One-and two-sample Bayesian prediction intervals based on Type-I hybrid censored data. Commun Stat Theory Methods 41(1):65–88
Viveros R, Balakrishnan N (1994) Interval estimation of parameters of life from progressively censored data. Technometrics 36(1):84–91
Ye ZS, Chan PS, Xie M, Ng HKT (2014) Statistical inference for the extreme value distribution under adaptive Type-II progressive censoring schemes. J Stat Comput Simul 84(5):1099–1114
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The authors would like to thank the editor, associate editor and two anonymous referees for their thorough review of the paper and their valuable suggestions that improved the original version of the manuscript.
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Mohie El-Din, M.M., Shafay, A.R. & Nagy, M. Statistical inference under adaptive progressive censoring scheme. Comput Stat 33, 31–74 (2018). https://doi.org/10.1007/s00180-017-0745-z
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DOI: https://doi.org/10.1007/s00180-017-0745-z