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Exact likelihood inference based on an unified hybrid censored sample from the exponential distribution. (English) Zbl 1274.62667
Summary: Recently, exact confidence bounds and exact likelihood inference have been developed based on hybrid censored samples by S.-M. Chen and G. K. Bhattacharyya [Commun. Stat., Theory Methods 17, No. 6, 1857–1870 (1988; Zbl 0644.62101)], A. Childs et al. [Ann. Inst. Stat. Math. 55, No. 2, 319–330 (2003; Zbl 1049.62021)], and B. Chandrasekar et al. [Nav. Res. Logist. 51, No. 7, 994–1004 (2004; Zbl 1162.62317)] for the case of the exponential distribution. In this article, we propose an unified hybrid censoring scheme (HCS) which includes many cases considered earlier as special cases. We then derive the exact distribution of the maximum likelihood estimator as well as exact confidence intervals for the mean of the exponential distribution under this general unified HCS. Finally, we present some examples to illustrate all the methods of inference developed here.

MSC:
62N05 Reliability and life testing
62F25 Parametric tolerance and confidence regions
62E15 Exact distribution theory in statistics
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