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Robust Bayesian analysis for exponential parameters under generalized type-II progressive hybrid censoring. (English) Zbl 1392.62077
Summary: The Type-II progressive hybrid censoring scheme has received wide attention, but it has a disadvantage in that long time may be required to complete the life test. The generalized progressive Type-II hybrid censoring scheme has recently been proposed to solve this problem. Under the censoring scheme, the time on test does not exceed a predetermined time. In this paper, we propose a robust Bayesian approach based on a hierarchical structure when the generalized progressive Type-II hybrid censored sample has a two-parameter exponential distribution. For unknown parameters, marginal posterior distributions are provided in closed forms, and their statistical properties are discussed. To examine the robustness of the proposed method, Monte Carlo simulations are conducted and a real data set is analyzed. Further, the quality and adequacy of the proposed model are evaluated in an analysis based on the real data.

62F15 Bayesian inference
62N02 Estimation in survival analysis and censored data
Full Text: DOI
[1] Balakrishnan and Cramer. 2014. The art of progressive censoring. New York: Springer-Verlag. · Zbl 1365.62001
[2] Berger, J. O.1984. The robust Bayesian viewpoint (with discussion). In Robustness of Bayesian analysis, ed. J. Kadane. Amsterdam: North-Holland.
[3] Berger, J. O.1985. Statistical decision theory and Bayesian analysis. New York: Springer-Verlag. · Zbl 0572.62008
[4] Beger, J. O., and J. M. Bernardo. 1989. Estimating a product of means: Bayesian analysis with reference priors. Journal of the American Statistical Association 84:200-7.
[5] Chandrasekar, B., A. Childs, and N. Balakrishnan. 2004. Exact likelihood inference for the exponential distribution under generalized Type-I and Type-II hybrid censoring. Naval Research Logistics 51:994-1004. · Zbl 1162.62317
[6] Chen, M. H., and Q. M. Shao. 1998. Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics 8:69-92.
[7] Cho, Y., H. Sun, and K. Lee. 2015. Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme. Statistical Methodology 23:18-34. · Zbl 07035600
[8] Cohen, A. C.1963. Progressively censored sample in life testing. Technometrics 5:327-39. · Zbl 0124.35401
[9] Cramer, E., and N. Balakrishnan. 2013. On some exact distributional results based on Type-I progressively hybrid censored data from exponential distributions. Statistical Methodology 10:128-50. · Zbl 1365.62061
[10] Devroye, L.1984. A simple algorithm for generating random variates with a log-concave density. Computing 33:247-57. · Zbl 0561.65004
[11] Górny, J., and E. Cramer. 2016. Exact likelihood inference for exponential distributions under generalized progressive hybrid censoring schemes. Statistical Methodology 29:70-94. · Zbl 07035799
[12] Górny, J., and E. Cramer. 2017. From Bspline representations to gamma representations in hybrid censoring. Statistical Papers. doi:10.1007/s0036201608664.
[13] Han, M.1997. The structure of hierarchical prior distribution and its applications. Chinese Operations Research and Management Science 6:31-40.
[14] Jeffreys, H.1961. Theory of probability and inference. 3rd ed. London: Cambridge Univ. Press. · Zbl 0116.34904
[15] Kundu, D., and A. Joarder. 2006. Analysis of Type-II progressively hybrid censored data. Computational Statistics and Data Analysis 50:2509-28. · Zbl 1284.62605
[16] Lee, K., H. Sun, and Y. Cho. 2016. Exact likelihood inference of the exponential parameter under generalized Type II progressive hybrid censoring. Journal of the Korean Statistical Society 45:123-36. · Zbl 1330.62363
[17] Nelson, W.1982. Applied life data analysis. New York: Wiley. · Zbl 0579.62089
[18] Spiegelhalter, D., N. G. Best, B. Carlin, and A. van der Linde. 2002. Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society, Series B 64:583-640. · Zbl 1067.62010
[19] Viveros, R., and N. Balakrishnan. 1994. Interval estimation of parameters of life from progressively censored data. Technometrics 36:84-91. · Zbl 0800.62623
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