Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation

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 Balakrishnan and Sandhu (Sankhya Series B58 (1995), 1-9). 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 (1995) for progressive Type-II right censored samples. This result is used in order to obtain moments for general progressive Type-IT 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. (C) 1998 Elsevier Science B.V. All rights reserved.