Ranked set sampling with varied order statistics for skew distributions

Abstract

Ranked Set Sampling (RSS) is a method of sampling that can be advantageous when quantification of all sampling units is costly but when small sets of units can be ranked according to the character under investigation by means of the methods not requiring actual measurements. The units corresponding to each rank are used in RSS and it performs better than simple random sampling (SRS) while estimating the population mean and other population parameters. In this paper, a new RSS procedure (RSSVO) for estimating the population mean of skew distributions is suggested. RSSVO measures only one or two order statistics depending upon the set size. The proposed estimator under RSSVO is then compared with the estimators based on SRS and RSS with equal allocation and Neyman’s optimal allocations. It is shown that the relative precisions of the estimators based on RSSVO are higher than those of the estimators based on SRS and RSS (both equal and Neyman’s optimal allocation) when the distributions under consideration are highly positive skew. Further, it is shown that, the performance of the proposed estimator increases as the skewness increases by using the example of lognormal distribution.