Modified best linear unbiased estimator of the shape parameter of log-logistic distribution

ABSTRACT

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In this article, a modified best linear unbiased estimator of the shape parameter β from log-logistic distribution $\mathrm{LLD}(\alpha ,\beta )$ is considered when scale parameter α is known and when α is unknown under simple random sampling (SRS) and ranked set sampling (RSS). In addition, a modified BLUE of β, when α is known using an RSS version based on the order statistic that maximizes the Fisher information for a fixed set size, will be considered. Theoretical properties of the suggested estimators are compared with its counterpart estimators under SRS. It is found that these estimators under RSS can be real competitors against those under SRS.

KEYWORDS:

• Simple random sampling
• ranked set sampling
• best linear unbiased estimator
• Fisher information number
• simulation study

Acknowledgments

The authors thank the Editor in Chief, an associate editor and reviewers for their valuable comments and suggestions to improve the paper. This research was supported by National Science Foundation of China (Grant No.11901236), Scientific Research Fund of Hunan Provincial Science and Technology Department (Grant No.2019JJ50479), Scientific Research Fund of Hunan Provincial Education Department (Grant No.18B322) and Fundamental Research Fund of Xiangxi Autonomous Prefecture (Grant No.2018SF5026).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by National Science Foundation of China [grant number 11901236], Scientific Research Fund of Hunan Provincial Science and Technology Department [grant number 2019JJ50479], Scientific Research Fund of Hunan Provincial Education Department [grant number 18B322] and Fundamental Research Fund of Xiangxi Autonomous Prefecture [grant number 2018SF5026].