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Exact likelihood inference based on type-I and type-II hybrid censored samples from the exponential distribution. (English) Zbl 1049.62021
Summary: S.-M. Chen and G. K. Bhattacharyya [Commun. Stat., Theory Methods 17, No. 6, 1857–1870 (1988; Zbl 0644.62101)] derived the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution and an exact lower confidence bound for the mean based on a hybrid censored sample. In this paper, an alternative simple form for the distribution is obtained and is shown to be equivalent to that of Chen and Bhattacharyya. Noting that this scheme, which would guarantee the experiment to terminate by a fixed time $$T$$, may result in few failures, we propose a new hybrid censoring scheme which guarantees at least a fixed number of failures in a life testing experiment. The exact distribution of the MLE as well as an exact lower confidence bound for the mean is also obtained for this case. Finally, three examples are presented to illustrate all the results developed here.

##### MSC:
 62F10 Point estimation 62N01 Censored data models 62N05 Reliability and life testing 62N02 Estimation in survival analysis and censored data