Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference

In this paper, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a half-logistic distribution. The use of these relations in a systematic recursive manner would enable one to compute all the means, variances and covariances of progressively Type-II right censored order statistics from the half-logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R1,…,Rm). The results established here generalize the corresponding results for the usual order statistics due to Balakrishnan (1985). These moments are then utilized to derive best linear unbiased estimators of the scale and location-scale parameters of the half-logistic distribution. A comparison of these estimators with the maximum likelihood estimates is then made. The best linear unbiased predictors of censored failure times is then discussed briefly. Finally, two numerical examples are presented to illustrate all the inferential methods developed here.