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Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. (English) Zbl 1067.62538
Summary: In this paper, we first establish three properties of progressive Type-II censored order statistics from arbitrary continuous distributions. These properties are then used to develop an algorithm to simulate general progressive Type-II censored order statistics from any continuous distribution, by generalizing the algorithm given recently by N. Balakrishnan and R.A. Sandhu [Sankhya Ser. B 58, No. 1, 1–9 (1995; Zbl 0873.62025)]. We then establish an independence result for general progressive Type-II censored samples from the uniform (0,1) population, which generalizes a result given by Balakrishnan and Sandhu for progressive Type-II right censored samples. This result is used in order to obtain moments for general progressive Type-II censored order statistics from the uniform (0,1) distribution. This independence result also gives rise to a second algorithm for the generation of general progressive Type-II censored order statistics from any continuous distribution. Finally, best linear unbiased estimators (BLUEs) for the parameters of one- and two-parameter uniform distributions are derived, and the problem of maximum-likelihood estimation is discussed.

##### MSC:
 62G30 Order statistics; empirical distribution functions 65C60 Computational problems in statistics (MSC2010) 62F10 Point estimation
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##### References:
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