BAYESIAN PREDICTION OF PROGRESSIVELY FIRST-FAILURE-CENSORED ORDER STATISTICS BASED ON k-RECORD VALUES FROM WEIBULL DISTRIBUTION

Abstract

Prediction on the basis of censored data has an important role in lifetime studies. This paper discusses Bayesian two-sample prediction of progressively firrst-failure-censored order statistics coming from a future sample based on observed k-record values from two-parameter Weibull distribution. Bayesian interval predictions are obtained based on a continuous-discrete joint prior for the unknown two parameters. Moreover, Bayesian point predictors are investigated under symmetric and asymmetric loss functions. Finally, the estimated risks of various point predictors obtained are compared using the Monte Carlo method.

Keywords

• Bayesian prediction,k-record,Progressive first-failure censoring,Weibull distribution

References

1. Ahmadi, J., MirMostafaee, S.M.T.K. and Balakrishnan, N. (2011). Bayesian Prediction of order statistics based on k-record values from exponential distribution. Statistics, 45, 375-387.
2. Ahmadi, J., MirMostafaee, S.M.T.K. and Balakrishnan, N. (2012). Bayesian Prediction of k-record values based on progressively censored data from exponential distribution. Journal of Statistical Computation and Simulation, 82, 51-62.
3. Ali Mousa, M.A.M. and Jaheen, Z.F. (2002). Bayesian prediction for progressively censored data from the Burr model. Statistical Papers, 43, 587-593.
4. Ali Mousa, M.A.M. and Al-Sagheer, S.A. (2005). Bayesian prediction for progressively Type-II censored data from the Rayleigh model. Communications in Statistics - Theory and Methods, 34, 2353-2361.
5. Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998). Records, John Wiley & Sons, New York. [6] Balakrishnan, N. (2007). Progressive censoring methodology: an appraisal. Test, 16, 211-256.‌
6. Balakrishnan, N. and Aggarwala, R. (2000). Progressive Censoring: Theory, Methods and Applications, Birkh¨auser, Boston.
7. Balakrishnan, N. and Cramer, E. (2014). The Art of Progressive Censoring: Applications to Reliability and Quality, Birkh¨auser, New York.
8. Balakrishnan, N. and Shafay, R.A. (2012). One- and two-sample Bayesian prediction intervals based on Type-II hybrid censored data. Communications in Statistics - Theory and Methods, 41, 1511-1531.

9. Calabria, R. and Pulcini, G. (1996). Point estimation under asymmetric loss functions for left-truncated exponential samples. Communications in Statistics - Theory and Methods, 25, 585-600.
10. Doostparast, M. (2009). A note on estimation based on record data. Metrika, 69, 69-80.
11. Dunsmore, I.R. (1983). The future occurrence of records. Annals of the Institute of Statistical Mathe- matics, 35, 267-277.
12. Dziubdziela, W. and Kopocinski, B. (1976). Limiting properties of the k-th record values. Zastosowania Matematyki, 15, 187-190.
13. Ghafoori, S., Habibi Rad, A. and Doostparast, M. (2011). Bayesian two-sample prediction with progres- sively Type-II censored data for some lifetime models. Journal of Iranian Statistical Society, 10, 63-86.
14. Huang, S.R. and Wu, S.J. (2012). Bayesian estimation and prediction for Weibull model with progressive censoring. Journal of Statistical Computation and Simulation, 82, 1607-1620.
15. Kamps, U. (1995). A concept of generalized order statistics, Teubner, Stuttgart.
16. Kamps, U. (1995). A concept of generalized order statistics. Journal of Statistical Planning and Infer- ence, 48, 1-23.
17. Kundu, D. and Howlader, H. (2010). Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data. Computational Statistics and Data Analysis, 54, 1547-1558.
18. Lawless, J.F. (1982). Statistical Models and Methods for Lifetime Data, John Wiley & Sons, New York. [20] Madi, M.T. and Raqab, M.Z. (2004). Bayesian prediction of temperature records using the Pareto model.‌ Environmetrics, 15, 701-710.
19. Murthy, D.N.P., Xie, M. and Jiang, R. (2004). Weibull Models, John Wiley & Sons, New York.
20. Nevzorov, V. (2001). Records: Mathematical Theory, Translation of Mathematical Monographs No. 194, American Mathematical Society, Providence, RI.
21. Raqab, M.Z., Asgharzadeh, A. and Valiollahi, R. (2010). Prediction for Pareto distribution based on progressively Type-II censored samples. Computational Statistics and Data Analysis, 54, 1732-1743.
22. Saeidi, A. R., Akbari, M. G. and Doostparast, M. (2014). Hypotheses testing with the two-parameter Pareto distribution on the basis of records in fuzzy environment. Kybernetika, 50, 744-757.
23. Shafay, R.A., Balakrishnan, N. and Sultan, K.S. (2014). Two-sample Bayesian prediction for sequential order statistics from exponential distribution based on multiply Type-II censored samples. Journal of Statistical Computation and Simulation, 83, 526-544.
24. Soland, R. M. (1969). Bayesian analysis of the Weibull process with unknown scale and shape parame- ters. IEEE Transactions on Reliability Analysis, 18, 181-184.
25. Soliman, A.A., Al-Hossain, A.Y. and Al-Harbi, M.M. (2011). Predicting observables from Weibull model based on general progressive censored data with asymmetric loss. Statistical Methodology, 8, 451-461.
26. Soman, K.P. and Misra, K.B. (1992). A least square estimation of three parameters of a Weibull distri- bution. Microelectronics Reliability, 32, 303-305.
27. Varian, H.R. (1975). A Bayesian Approach to Real Estate Assessment, Studies in Bayesian econometrics and statistics in honor of Leonard J. Savage, 195-208.
28. Wu, S.J. and Ku¸s, C. (2009). On estimation based on progressive first failure censored sampling. Com- putational Statistics and Data Analysis, 53, 3659-3670.