Abstract
Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.
Highlights
Survey sampling is a process to collect information on the subject under study from population by choosing and analyzing true subset from it [1]. e national and international agencies regularly present estimates for different indicators like family income, retail prices, poverty, inflation, and wages of employees
Khan and Shabbir [17] utilized the aforementioned theory of two auxiliary variables and suggested generalized exponential-type ratio-cum-ratio estimator to estimate population mean of study variable under stratified ranked set sampling (StRSS) scheme. ey compared the proposed estimator with some existing estimators with the help of relative bias (RB), relative mean square error (RMSE), and percentage relative efficiency (PRE). ey concluded that the proposed estimator performs efficiently when study variable and auxiliary variables follow trivariate normal distribution
To compare the percent relative efficiencies (PREs) of proposed estimator and existing estimator under StRSS, a real-life data set given by Bierens and Ginther [19] has been utilized
Summary
Survey sampling is a process to collect information on the subject under study from population by choosing and analyzing true subset from it [1]. e national and international agencies regularly present estimates for different indicators like family income, retail prices, poverty, inflation, and wages of employees. Neyman [2] introduced stratified random sampling (StRS) for efficient estimation of the population parameters in heterogeneous environment. Neyman [3] proposed the procedure of estimating population parameters by utilizing auxiliary information in stratified random sampling. Samawi [8] introduced stratified ranked set sampling (StRSS) for obtaining unbiased and efficient estimates of population mean. Ali et al [13] introduced stratified extreme-cum-median ranked set sampling (StEMRSS) for estimation of mean of heterogeneous populations in the presence of outliers. Erefore, there is a need to utilize two auxiliary variables in the construction of generalized estimators under RSS design to increase their efficiency. Khan and Shabbir [17] utilized the aforementioned theory of two auxiliary variables and suggested generalized exponential-type ratio-cum-ratio estimator to estimate population mean of study variable under StRSS scheme. (Wyz(1)h+ Wyz(2mh)h) + (Wyz( mh)h + Wyz(mh+1)h)} ] V(yz(E) stemrss), E(e1(E)(stemrss)e2(E)( stemrss))
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