Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling

Mursala Khan,Rajesh Singh

doi:10.1155/2015/248374

Abstract

A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

Highlights

Introduction and Literature ReviewIncorporating the knowledge of the auxiliary variables is very important for the construction of efficient estimators for the estimation of population parameters and increasing the efficiency of the estimators in different sampling design
Using the knowledge of the auxiliary variables, several authors have proposed different estimation technique for the finite population mean of the study variable; Cochran [1], Tripathy [2], Kadilar and Cingi [3, 4], Singh et al [5], Khan and Arunachalam [6], Lone and Tailor [7], Khan [8], Khan and Hussain [9], and Khan et al [10] have worked on the estimation of population parameters using auxiliary information
We will work on the estimation of population mean using the knowledge of the auxiliary variables under systematic sampling

Summary

Introduction and Literature Review

Incorporating the knowledge of the auxiliary variables is very important for the construction of efficient estimators for the estimation of population parameters and increasing the efficiency of the estimators in different sampling design. We will work on the estimation of population mean using the knowledge of the auxiliary variables under systematic sampling. The mean square errors of the estimators, to the first order of approximation, are given as follows: MSE (t1) = λY2 [ρy∗Cy2 + ρx∗Cx2 (1 − 2k√ρ∗∗)] ,. Utilizing the known knowledge of the auxiliary variable, Singh et al [20] suggested the following ratio and product type exponential estimators: t4. The mean square errors of the estimators up to first order of approximation are given by MSE (t4). The mean square error of the estimator t6, up to first order of approximation, is given by MSE (t6) = λY2 [ρy∗Cy2 + ρx∗Cx2 (1 − 2k√ρ∗∗).

Proposed Estimator

Comparison

Numerical Comparison

Conclusion