Abstract
In this paper, we proposed an improved family of estimators for finite population mean under stratified random sampling, which needed a helping variable on the sample mean and rank of the auxiliary variable. The expression of the bias and mean square error of the proposed and existing estimators are computed up to the first-order approximation. The estimators proposed in different situations were investigated and provided a minimum mean square error relative to all other estimators considered. Four actual data sets and simulation studies are carried out to observe the performance of the estimators. For simulation study, R software is used. The mean square errors of all four data sets are minimum and percent relative efficiencies are more than a hundred percent higher than the other existing estimators, which indicated the importance of the newly proposed family of estimators. From the simulation study, it is concluded that the suggested family of estimators achieved better results. We demonstrate theoretically and numerically that the proposed estimator produces efficient results compared to all other contend estimators in entire situations. Overall, we conclude that the performance of the family of suggested estimators is better than all existing estimators.
Highlights
In the literature of survey sampling, the use of auxiliary variables was discussed by many researchers to improve the efficiency of their developed estimators, for estimating some usual parameters, such as mean, median, variance, and standard deviation
We propose a new family of estimators for estimating the mean using the information on the mean and ranks of the auxiliary variable based on stratified random sampling. e remaining document is set as follows
By taking motivation from Hussain et al [2], we developed a new family of estimators of Y which needed a helping variable on the sample mean and rank of the auxiliary variable
Summary
In the literature of survey sampling, the use of auxiliary variables was discussed by many researchers to improve the efficiency of their developed estimators, for estimating some usual parameters, such as mean, median, variance, and standard deviation. In such situations, traditional ratio, product, and regression estimators give efficient outcomes of the unspecified parameters. We propose a new family of estimators for estimating the mean using the information on the mean and ranks of the auxiliary variable based on stratified random sampling.
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