Development of an alternative ranked set sampling estimators

Abstract

Ranked Set Sampling (RSS) is a well-established technique that improves estimation efficiency by incorporating ranking information before selecting a sample. Conventional RSS estimators such as the Mean RSS estimator, is not appropriate when observations are measured in rates or are periodical and in the presence of skewed or heavy-tailed distributions. This study develops credible-alternative Ranked Set Sampling (RSS) estimators, namely the Harmonic Mean RSS (HMRSS), Geometric Mean RSS (GMRSS), and Trimmed Mean RSS (TMRSS) estimators that are robust to data measured in rate, period and less sensitive to extreme values. The proposed RSS estimators were validated with artificial datasets with varying values of ,  and . Percentage relative efficiency,  was used as a criterion to judge the efficiency of the proposed  estimators against the orthodox estimators. A  indicates efficiency of the proposed estimator over the existing ones. Variances of MRSS, HMRSS, GMRSS and TMRSS were 0.0333, 0.00078, 0.0033, and 0.0370 respectively, when ,  and . Results when  and  were  and  respectively, and  and  for  and . The results indicate that both HMRSS and GMRSS outperform the orthodox MRSS in terms of efficiency, particularly when dealing with skewed or heavy-tailed distributions. However, the TMRSS estimator, despite its robustness against outliers, showed mixed performance and less efficient to MRSS estimator.