Exact likelihood inference of the exponential parameter under generalized type II progressive hybrid censoring. (English) Zbl 1330.62363
Summary: Type II progressive hybrid censoring schemes (PHCS) have become quite popular in reliability and lifetime-testing studies. However, the drawback of the Type II PHCS is that it might take a very long time in order to complete the life test. In this article, we propose generalized Type II PHCS which provide a guarantee of the time to complete the life test. Also, we consider both exact and approximate inferential procedures based on generalized Type II PHCS when the lifetime distribution of the test items follows an independent and identically distributed (iid) exponential distribution. Given by the exact conditional first moment, bias adjusted MLE is proposed and its distribution is discussed. The results of simulation studies and real data analysis were conducted to evaluate the performance of the proposed method.
Keywords:
confidence interval; exact conditional distribution; exponential distribution; generalized type II progressive hybrid censoring; maximum likelihood estimatorSoftware:
SPLIDAReferences:
| [1] | Balakrishnan, N.; Aggarwala, R., Progressive censoring: theory, methods and applications (2000), Birkhäuser: Birkhäuser Boston |
| [2] | Balakrishnan, N.; Childs, A.; Chandrasekar, B., An efficient computational method for moments of order statistics under progressive censoring, Statistics & Probability Letters, 60, 359-365 (2002) · Zbl 1045.62042 |
| [4] | Chen, S.; Bhattacharyya, G. K., Exact confidence bounds for an exponential parameter under hybrid censoring, Communications in Statistics. Theory and Methods, 17, 1857-1870 (1988) · Zbl 0644.62101 |
| [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: Birkhäuser Boston), 319-330 · Zbl 1049.62021 |
| [6] | Cho, Y.; Sun, H.; Lee, K., Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring, Entropy, 17, 101-122 (2015) |
| [7] | Cho, Y.; Sun, H.; Lee, K., Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme, Statistical Methodology, 23, 18-34 (2015) · Zbl 1486.62257 |
| [8] | Dube, S.; Pradhan, B.; Kundu, D., Parameter estimation of the hybrid censored log-normal distribution, Journal of Statistical Computation and Simulation, 81, 275-287 (2011) · Zbl 1221.62137 |
| [9] | Hemmati, F.; Khorram, E., Statistical analysis of the log-normal distribution under type-II progressive hybrid censoring schemes, Communications in Statistics—Simulation and Computation, 42, 52-75 (2013) · Zbl 1327.62487 |
| [10] | Kundu, D., Bayesian inference and life testing plan for Weibull distribution in presence of progressive censoring, Technometrics, 50, 144-154 (2008) |
| [11] | Kundu, D.; Joarder, A., Analysis of Type II progressively hybrid censored data, Computational Statistics and Data Analysis, 50, 2509-2528 (2006) · Zbl 1284.62605 |
| [12] | Lawless, J., Statistical models and methods for lifetime data (1982), Wiley: Wiley New York · Zbl 0541.62081 |
| [13] | Lin, C. T.; Chou, C. C.; Huang, Y. L., Inference for the Weibull distribution with progressive hybrid censoring, Computational Statistics and Data Analysis, 56, 451-467 (2012) · Zbl 1316.62042 |
| [14] | Lin, C. T.; Huang, Y. L., On progressive hybrid censored exponential distribution, Journal of Statistical Computation and Simulation, 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, Journal of Statistical Computation and Simulation, 83, 402-404 (2013) · Zbl 1348.62019 |
| [16] | Meeker, W. Q.; Escobar, L. A., Statistical methods for reliability data (1998), Wiley: Wiley New York · Zbl 0949.62086 |
| [17] | Ng, H. K.T.; Kundu, D.; Chan, P. S., Statistical analysis of exponential lifetimes under an adaptive Type-II progressively censoring scheme, Naval Research Logistics, 56, 687-698 (2009) · Zbl 1178.62111 |
| [18] | Wu, M.; Shi, Y.; Sun, Y., Inference for accelerated competing failure models from Weibull distribution under Type-I progressive hybrid censoring, Journal of Computational and Applied Mathematics, 263, 423-431 (2014) · Zbl 1381.62267 |
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