A new improved difference-cum-exponential ratio type estimator in systematic sampling two auxiliary variables

J Shabbir,S Masood,S Gupta

doi:10.4038/jnsfsr.v48i1.9931

Abstract

A difference-cum-exponential ratio type estimator was proposed for estimating the finite population mean using two auxiliary variables under systematic sampling. Expressions for the biases and mean square errors (MSEs) were derived up to first order of approximation. It was observed that the proposed estimator is more efficient than the usual sample mean estimator, traditional ratio estimator, exponential-ratio estimator and many other recently proposed difference type estimators in terms of MSEs. Four datasets were used for efficiency comparisons.

Highlights

Intelligence coefficient (IQ) level of the students (z)
A difference-cum-exponential ratio type estimator on the number of study hours used by students (x) and was proposed for estimating the finite population mean using two auxiliary variables under systematic sampling
It was observed that the proposed estimator is more efficient than the usual sample mean estimator, traditional ratio estimator, exponential-ratio estimator and many other recently proposed difference type estimators in terms of mean square errors (MSEs)

Summary

INTRODUCTION

(2017), Tailor and Mishra (2018), Qureshi et al (2018) and Mishra et al (2018). The main objective of this study. (v) Tailor and Mishra (2018) suggested the exponential where δi (i = 1, 2) are constants and byx and byz are the ratio-product type estimator, which is given by sample regression coefficients and YRPE. Mishra et al (2018) derived the bias and minimum MSE of YMSS up to first order of approximation as: where v1 and v2 are constants and α is the scalar quantity, which takes values (0, −1, +1). CxzSoρlvx∗iρnz∗g equation (33), MSE of estimator YMSS the correct expressions of bias and to first order of approximation are:. Motivated by Khan (2016) and Riaz et al (2017), the following difference-cum-exponential ratio type estimator is proposed for the population mean under systematic sampling:. (+D2DA,1QA2KYHX Φ), MρSx*SC(x2c−),CPryx) asρ:*y ρ (i) By equations (2) and (43), MSE(YPr )min < Var(Y0 ) if

A1A2YX Φ

RESULTS AND DISCUSSION

CONCLUSION