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Statistical inferences based on INID progressively type II censored order statistics. (English) Zbl 1416.62556
The progressive type II censoring model for independent and nonidentical distributed random variables was introduced by N. Balakrishnan and E. Cramer [Ann. Inst. Stat. Math. 60, No. 1, 151–171 (2008; Zbl 1184.62071)]. In this model, a system of heterogeneous independent units are subjected to a statistical lifetime test, such that at each failure time of an unit, a given number of surviving units are randomly removed from the experiment. The present paper develops this theme by starting with the study of the distribution of the censored order statistics. These random variables are associated with a progressive censoring plan. Inference and Fisher information properties are highlighted for the proportional hazard rate model. In particular, the authors refer to the exponential and Weibull distributions. In the exponential case, explicit log-likelihood function and Fisher information matrix formulas (associated with the regression coefficient) are obtained. Numerical examples and concluding remarks are finally stated.

MSC:
62N01 Censored data models
62N05 Reliability and life testing
62N03 Testing in survival analysis and censored data
62G30 Order statistics; empirical distribution functions
62B10 Statistical aspects of information-theoretic topics
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