Quantile estimation using near optimal unbalanced ranked set sampling

Abstract

Few studies are found in literature on estimation of population quantiles using the method of ranked set sampling (RSS). The optimal RSS strategy is to select observations with at most two fixed rank order statistics from di ff erent ranked sets. In this paper, a near optimal unbalanced RSS model for estimating p th (0 < p < 1) population quantile is proposed. Main advantage of this model is to use each rank order statistics and is distribution-free. The asymptotic relative e ffi ciency (ARE) for balanced RSS, unbalanced optimal and proposed near-optimal methods are computed for di ff erent values of p . We also compared these AREs with respect to simple random sampling. The results show that proposed unbalanced RSS performs uniformly better than balanced RSS for all set sizes and is very close to the optimal RSS for large set sizes. For the practical utility, the near optimal unbalanced RSS is recommended for estimating the quantiles.