Relations for Moments of Progressively Type-II Censored Order Statistics from Log-Logistic Distribution with Applications to Inference

Abstract

In this article, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a log-logistic distribution. The use of these relations in a systematic recursive manner would enable the computation of all the means, variances and covariances of progressively Type-II right censored order statistics from the log-logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R ₁,…, R _m ). The results established here generalize the corresponding results for the usual order statistics due to Balakrishnan and Malik (1987) and Balakrishnan et al. (1987). The moments so determined are then utilized to derive best linear unbiased estimators for the scale- and location-scale log-logistic distributions. A comparison of these estimates with the maximum likelihood estimates is made through Monte Carlo simulation. The best linear unbiased predictors of progressively censored failure times is then discussed briefly. Finally, a numerical example is presented to illustrate all the methods of inference developed here.

Keywords:

• Best linear unbiased estimators (BLUEs)
• Best linear unbiased predictors (BLUPs)
• Log-logistic distribution
• Maximum likelihood estimators (MLEs)
• Product moments
• Progressive Type-II right-censored order statistics
• Recurrence relations
• Single moments

Mathematics Subject Classification:

• Primary 62G30, 62F10
• Secondary 62M20, 62N05

Acknowledgment

We express our sincere thanks to the anonymous referees whose comments and suggestions led to a considerable improvement in this article.