Estimation Based on Ranked Set Sampling for the Two-Parameter Log-Logistic Distribution

Abstract

Ranked set sampling (RSS) is an efficient method for estimating parameters when exact measurement of observation is difficult and/or expensive. Many modification based on RSS have been developed to improve precision. Such of these modification are: median ranked set sampling (MRSS), and extreme ranked set sampling (ERSS). In this thesis, the effectiveness of simple random sampling (SRS), RSS, MRSS, and ERSS in estimating the scale α and shape β parameters concerning log-logistic distribution is investigated. The estimators of α and β are obtained using the maximum likelihood estimation. The obtained estimators based on RSS, MRSS and ERSS are compared with their conventional counterpart in SRS. The comparison is carried out in terms of biases, mean square errors, relative efficiencies with different set and cycle sizes. Monte Carlo simulation study is performed by using R software with 10000 repetitions. The results revealed that the RSS estimators are more efficient than their competitors using other sampling scheme when both parameters are unknown, MRSS estimators are more efficient than their competitors using other sampling scheme for estimating α in which β is known, ERSS estimators are more efficient than their competitors using other sampling scheme for estimating β in which α is known. Finally, some real data applications are included to highlight the importance of these sampling schemes in estimating population parameters, and in particular the parameters of the log-logistic distribution.