Estimation of population variance under ranked set sampling method by using the ratio of supplementary information with study variable

In biological and medical research, the cost and collateral damage caused during the collection and measurement of a sample are the reasons behind a compromise on the inference with a fixed and accepted approximation error. The ranked set sampling (RSS) performs better in such scenarios, and the use of auxiliary information even enhances the performance of the estimators. In this study, two generalized classes of estimators are proposed to estimate the population variance using RSS and information of auxiliary variable. The bias and mean square errors of the proposed classes of estimators are derived up to first order of approximation. Some special cases of one of the proposed class of estimators are also considered in the presence of available population parameters. A simulation study was conducted to see the performance of the members of the proposed family by using various sample sizes. The real-life data application is done to estimate the variance of gestational age of fetuses with supplementary information. The results showed that RSS design is a more accurate method than simple random sampling, to determine the population variance of hard-to-measure or destructive sampling units.