zbMATH — the first resource for mathematics

Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme. (English) Zbl 07035600
Summary: Recently, progressive hybrid censoring schemes have become quite popular in a life-testing problem and reliability analysis. However, the limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time \(T\). In this article, we propose a generalized progressive hybrid censoring scheme, which allows us to observe a pre-specified number of failures. So, the certain number of failures and their survival times are provided all the time. We also derive the exact distribution of the maximum likelihood estimator (MLE) as well as exact confidence interval (CI) for the parameter of the exponential distribution under the generalized progressive hybrid censoring scheme. The results of simulation studies and real-life data analysis are included to illustrate the proposed method.

62-XX Statistics
Full Text: DOI
[1] Ahmed, E. A., Bayesian estimation based on progressive type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach, J. Appl. Stat., 41, 752-768, (2014)
[2] Balakrishnan, N.; Aggarwala, R., Progressive censoring: theory, methods and applications, (2000), Birkhäuser Boston
[3] Balakrishnan, N.; Childs, A.; Chandrasekar, B., An efficient computational method for moments of order statistics under progressive censoring, Statist. Probab. Lett., 60, 359-365, (2002) · Zbl 1045.62042
[4] Balakrishnan, N.; Kundu, D., Hybrid censoring models, inferential results and applications, Comput. Statist. Data Anal., 57, 166-209, (2013) · Zbl 1365.62364
[5] Childs, A.; Chandrasekar, B.; Balakrishnan, N., Exact likelihood inference for an exponential parameter under progressive hybrid schemes, (Vonta, F. Nikulin; etal., Statistical Models and Methods for Biomedical and Technical Systems, (2007), Birkhäuser Boston), 319-330 · Zbl 1049.62021
[6] Dube, S.; Pradhan, B.; Kundu, D., Parameter estimation of the hybrid censored log-normal distribution, J. Stat. Comput. Simul., 81, 275-287, (2011) · Zbl 1221.62137
[7] Dyer, D. D.; Whisenand, C. W., Best linear estimator of the parameter of the Rayleigh distribution—part I: small sample theory for censored order statistics, IEEE Trans. Reliab., 22, 27-34, (1973)
[8] Epstein, B., Truncated life-tests in the exponential case, Ann. Math. Statist., 25, 555-564, (1954) · Zbl 0058.35104
[9] Hemmati, F.; Khorram, E., Statistical analysis of the log-normal distribution under type-II progressive hybrid censoring schemes, Comm. Statist. Simulation Comput., 42, 52-75, (2013) · Zbl 1327.62487
[10] Huang, S. R.; Wu, S. J., Bayesian estimation and prediction for Weibull model with progressive censoring, J. Stat. Comput. Simul., 82, 1607-1620, (2012) · Zbl 1431.62440
[11] Kundu, D., On hybrid censored Weibull distribution, J. Statist. Plann. Inference, 137, 2127-2142, (2007) · Zbl 1120.62081
[12] Kundu, D.; Joarder, A., Analysis of type II progressively hybrid censored data, Comput. Statist. Data Anal., 50, 2509-2528, (2006) · Zbl 1284.62605
[13] Lin, C. T.; Chou, C. C.; Huang, Y. L., Inference for the Weibull distribution with progressive hybrid censoring, Comput. Statist. Data Anal., 56, 451-467, (2012) · Zbl 1316.62042
[14] Lin, C. T.; Huang, Y. L., On progressive hybrid censored exponential distribution, J. Stat. Comput. Simul., 82, 689-709, (2012) · Zbl 1432.62332
[15] Lin, C. T.; Huang, Y. L.; Balakrishnan, N., Exact Bayesian variable sampling plans for the exponential distribution with progressive hybrid censoring, J. Stat. Comput. Simul., 83, 402-404, (2013) · Zbl 1348.62019
[16] Rastogi, M. K.; Tripathi, Y. M., Estimating the parameters of a burr distribution under progressive type II censoring, Stat. Methodol., 9, 381-391, (2012) · Zbl 1365.62368
[17] Viveros, R.; Balakrishnan, N., Interval estimation of parameters of life from progressively censored data, Technometrics, 36, 84-91, (1994) · Zbl 0800.62623
[18] Wu, S. J., Estimation of the two parameter bathtub-shaped lifetime distribution with progressive censoring, J. Appl. Stat., 35, 1139-1150, (2008) · Zbl 1253.62012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.