On conditional moments of progressively censored order statistics with a time constraint.

*(English)*Zbl 1341.62274
Choudhary, Pankaj K. (ed.) et al., Ordered data analysis, modeling and health research methods. In honor of H. N. Nagaraja’s 60th birthday. Selected papers based on the presentations at the international conference, Austin, TX, USA, March 7–9, 2014. Cham: Springer (ISBN 978-3-319-25431-9/hbk; 978-3-319-25433-3/ebook). Springer Proceedings in Mathematics & Statistics 149, 55-71 (2015).

Summary: Different hybrid progressive censoring schemes , which are mixtures of Type-I censoring and Type-II progressively censoring schemes, have been proposed in the literature. These censoring schemes impose a time constraint on the life-testing experiment and the number of progressively censored order statistics observed before this time constraint is recorded. Conditional on the number of progressively censored order statistics being observed before the time constraint, a computational method for the conditional moments of progressively censored order statistics is discussed. Simple computational formulae are presented and these formulae are illustrated with examples when the underlying distributions are uniform and exponential. These results will be useful for the development of estimation methods such as the least squares estimation, best linear unbiased estimation and approximate maximum likelihood estimation methods and for deriving asymptotic distributions of the estimates of model parameters for Type-I hybrid progressively censored data.

For the entire collection see [Zbl 1337.92005].

For the entire collection see [Zbl 1337.92005].

##### Keywords:

approximate maximum likelihood estimation; best linear unbiased estimation; hybrid censoring; type-I censoring; type-II censoring
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\textit{H. K. T. Ng} et al., in: Ordered data analysis, modeling and health research methods. In honor of H. N. Nagaraja's 60th birthday. Selected papers based on the presentations at the international conference, Austin, TX, USA, March 7--9, 2014. Cham: Springer. 55--71 (2015; Zbl 1341.62274)

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