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

Abstract

In biological and medical research, the cost and collateral damage caused during the collection and measurement of a sample are the reasons behinda compromise on the inference with a fixed and accepted approximation error. The ranked set sampling (RSS) performs better in such scenarios, andthe use of auxiliary information even enhances the performance of the estimators. Inthis study, two generalized classes of estimatorsareproposedto estimate the population variance using RSS and information of auxiliary variable. The bias and mean square errors ofthe proposed classes of estimators are derived up to first order of approximation. Some special cases of one ofthe proposed class ofestimatorsare also considered in the presence of available population parameters. A simulation study was conductedto see the performance of the members of the proposed family by using various sample sizes. The real-life dataapplication 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.