A Class of Modified Ratio Estimators Using Linear Combination of Quartile Deviation and Median of Auxiliary Variable under Rank Set Sampling

M Iqbal Jeelani,S.A.Mir M.S.Pukhta

doi:10.13189/ujam.2014.020602

Abstract

In this paper we suggest a new modified ratio estimator of population mean of the study variable using the linear combination of known values of Quartile deviation and Median of the auxiliary variable under Rank set sampling. Mean squared error up to the first degree of approximation are derived and compared with modified ratio estimators given by Kadilar and Chingi (1) based on simple random sampling. The proposed modified ratio estimators under rank set sampling perform better than the ratio estimators given by Kadilar. The simulated study has been carried out in support of the results.

Highlights

Most of the times in sample surveys, along with the variable of interest YY, information on auxiliary variable XX, which is highly correlated with YY is collected
Ratio method of estimation is one such example which utilizes the information on auxiliary variable XX, which is positively correlated with the variable of interest YY, in order to improve the precision of the estimate of population mean
The procedure of ratio estimation under rank set sampling given by Samawi and Muttlak[3]are as under: Let Y be the variable if interest and X be a suitable concomitant variable which is correlated to Y and easy to rank

Summary

Introduction

Most of the times in sample surveys, along with the variable of interest YY, information on auxiliary variable XX, which is highly correlated with YY is collected. This information on auxiliary variable may well be utilized to obtain a more efficient estimator of population mean. Ratio method of estimation is one such example which utilizes the information on auxiliary variable XX , which is positively correlated with the variable of interest YY, in order to improve the precision of the estimate of population mean. Some extension is done by Swami [3] utilized both the rank and the measure of the concomitant variable and considered ratio estimation using RSS. The ratio estimation based on RSS is more efficient compared with the SRS ratio estimate

Ratio Estimation under Simple Random Sampling

Ratio Estimation under Rank Set Sampling

Proposed Ratio Estimators under Rank Set Sampling

Bias and Mean Square Estimation of Proposed Estimators

Efficiency Comparison and Numerical Illustration

Conclusions