Computing the effect of measurement errors on ranked set sampling estimators of the population mean

Abstract

Summary The effect of measurement errors shows the seriousness of the estimators or the estimation procedures and cannot be avoided in sensitive cases because “a miss is as good as a mile.” In this article, we have proposed the very first ranked set estimators like unbiased, ratio, product, difference, ratio exponential, and product exponential estimators under both correlated and uncorrelated measurement errors. The expressions for bias and mean square error of the proposed estimators are obtained up to the first order of approximation. The proposed ranked set estimators have been compared through relative efficiencies over unbiased estimators and the effect of measurement errors has been given through percentage computation of measurement errors. The theoretical conditions are obtained under which the proposed estimator has performed better. The performance of the proposed ranked set estimators under measurement errors are shown by efficiency comparisons, Monte‐Carlo simulation study, and real data study.

Computing the population mean on the use of auxiliary information under ranked set sampling

“…Koyuncu and Al-Omari [25] developed generalized robust-regression-type estimators under di erent RSS. Vishwakarma and Singh [26,27] computed the e ect of measurement errors on RSS estimators of the population mean and gave some applications to solar energy data.…”