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-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.