In this paper, a new sampling technique is proposed that carries more information than contained in ranked set sample (RSS). The proposed sampling technique is defined by making the use for the idea of visual grouping of population units with respect to a fixed threshold and RSS. We refer to it as RSS-Grouping technique. Under the best informative RSS-Grouping technique, the maximum likelihood estimator (MLE) of the mean of an exponential distribution is derived. This MLE is then compared to various candidate estimators through extensive simulation experiments. Numerical results show that the MLE under the best informative RSS-Grouping scheme is preformed better thanthese estimators. The effects of imperfect sampling on the behavior of the MLE under the proposed scheme is also studied. We conduct a simulation study to assess the finite sample behavior of the MLE under imperfect sampling and imperfect classification of visual grouping. Similarly, the simulation study shows that the MLE is behaved asymptotically unbiased. Additionally, the MLE tends to be at least as efficient as the MLE under RSS regardless of raking errors and the estimation of the threshold has slightly effects on the sampling distribution of the MLE.
Exponential Distribution, Maximum Likelihood, Ranked Set Sampling, Simple Random
Department of Statistics -Yarmouk University - IRBID, Jordan (e-mail:malodat @yu.edu.jo); Department of Mathematics and Statistics - Jordan University of Science and Technology - IRBID, Jordan (e-mail: firstname.lastname@example.org); Department of Mathematics - Jordan University of Science and Technology - IRBID, Jordan (Email: email@example.com
); Department of Mathematics and Statistics - La Trope University - Australia (e-mail:firstname.lastname@example.org).