Estimating the Parameters of an Exponentiated Logistic Distribution under Progressive Hybrid Censoring Scheme

As the progressive hybrid censoring scheme (PHCS) and exponentiated logistic distribution (ELD) are widely employed in reliability and survival analysis, it is necessary to infer on ELD parameters under PHCS. The maximum product spacings estimator (MPSE) is effective and authors advocated the use of this method as an alternative to maximum likelihood estimator (MLE), and found that MPSE provides better estimates than MLE in various situations. In this paper, we propose the MPSEs for the parameters of the ELD under PHCS. Also, we derive the approximate MPSEs for the parameters of ELD using Talyor series expansion. And we compare the proposed estimators (MPSEs and approximate MPSEs) in the sense of mean squared error (MSE) under PHCS. The progressive hybrid censored data (PHCD) from the ELD are generated for data size = 25, 30, 35, 40, 45 and various PHCS. Using this generated data, the MSEs and biases of MPSE and approximate MPSE are simulated by the Monte Carlo method based on 1,000 times for = 25, 30, 35, 40, 45 and various PHCD. As a result, approximate MPSEs are better than the corresponding MPSEs. Further, a real data set (strength on GPA for single carbon fibers of 10mm in gauge lengths) has been analyzed.