Parametric Estimationa For Log-logistic Distribution Under Ranked Set Sampling

How to obtain samples with representative and/or contain more population information is an important part of sampling design.In order to achieve the single-objective or bi-objective optimization,a lot of new sampling methods have been devised.Ranked set sampling(RSS)is one of them.RSS further considers the situation that quantification of sampling units is either costly or difficult,but ranking the units in a small set is easy and inexpensive.At present,the parameter research under RSS has been regarded as an important issue,which has attracted wide attention from many scholars.In this work,we focus on the estimation of the scale parameter a and the shape parameter ? for log-logistic distribution under RSS.Maximum likeli-hood estimators(MLE)of ?a and ?,respectively,for the log-logistic distribution will be considered in cases when one parameter is known and when both are unknown.In addition,the MLE of one parameter,when another parameter is known using a RSS version based on the order statistic that maximizes the Fisher information for a fixed set size(RSSF),will be considered.All efficiencies of these MLEs are simulated under both perfect ranking and imperfect ranking.Next,modified best linear unbiased estimator(MBLUE)of? from log-logistic distribution are considered when ? is known or ? is unknown under RSS.when? is known,the MBLUE of ? under RSSF will also be considered.In the last part of the paper,a modification of RSS called moving extremes RSS(MERSS)will be used to estimate ca and ? for the log-logistic distribution.Several tradi-tional estimators and ad hoc estimators(AHEs)will be studied under MERSS.The simulation results show that these estimators under RSS are significantly more efficient than the ones under simple random sampling(SRS).