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

Abstract

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 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.