An Alternative Mean Estimator for Ranked Set Sample

Aims: We introduce a new estimator for population mean by using coefficient of variation as prior information in ranked set sampling (RSS). Then we compare it with the estimator of the mean in RSS, the estimator of the mean in simple random sampling (SRS) in the sense of mean square error (MSE). We conclude that the proposed RSS mean estimator is more efficient than the aforementioned estimators.

Study Design: This was rank set sampling, improved estimation study.

Place and Duration of Study: Dokuz Eylul University Department of Statistics between December 2014 and June 2015.

Methodology: In this study, We introduce a new estimator for population mean by using coefficient of variation as prior information in Ranked Set Sampling (RSS). The performance of this estimator is compared in the sense of mean square error (MSE).

Results: When we compared the improved RSS mean estimator, SRS mean estimator and traditional RSS mean estimator in the sense of mean square error. We conclude that the proposed RSS mean estimator is more efficient than the aforementioned estimators.

Conclusion: We have shown that a biased estimator with a smaller MSE can be obtained by using a priori information which is the coefficient of variation. To compare the efficiencies of the mean estimators with each other, we evaluate the relative efficiencies of each estimator using MSE. It is shown that the proposed mean estimator for RSS is more efficient than the conventional estimators. In particular the better efficiencies are obtained for small sample sizes.