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.
