Weighted Ranked Set Sampling for Skewed Distributions

Abstract

Ranked set sampling (RSS) is a useful technique for improving the estimator of a population mean when the sampling units in a study can be more easily ranked than the actual measurement. RSS performs better than simple random sampling (SRS) when the mean of units corresponding to each rank is used. The performance of RSS can be increased further by assigning weights to the ranked observations. In this paper, we propose weighted RSS procedures to estimate the population mean of positively skewed distributions. It is shown that the gains in the relative precisions of the population mean for chosen distributions are uniformly higher than those based on RSS. The gains in relative precisions are substantially high. Further, the relative precisions of our estimator are slightly higher than the ones based on Neyman’s optimal allocation model for small sample sizes. Moreover, it is shown that the performance of the proposed estimator increases as the skewness increases by using the example of the lognormal family of distributions.

Keywords

• ordered observations
• Neyman’s allocation
• relative precision
• skewness
• unbiased estimator
• weight