Ranked set sampling with lowest order statistics for Pareto distribution

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 visual inspection or other methods not requiring actual measurements. RSS performs better than simple random sampling (SRS) to estimate the population mean. In original RSS procedure, the units corresponding to each rank are used. In this article, we propose to use RSS method with lowest order statistics from each sample to estimate the population mean of Pareto distribution which is highly positively skew. The Pareto distribution is chosen due to its application in social and scientific phenomenon including the distribution of wealth in a society. The estimator based on lowest order statistics with bias correction term has been proposed. Two cases, known and unknown scale parameter, have been considered. The simulation-based methods have also been included. It is shown that the gains in the relative precisions of population mean based on our proposed method are uniformly higher than those based upon the RSS and extreme RSS procedures. The proposed method with bias correction term is recommended for real applications.

Keywords:

• Ordered observations
• Pareto distribution
• Scale and shape parameters
• Unbiased estimator