A generalized exponential-type estimator for population mean using auxiliary attributes.

Sohail Ahmad,Aamna Khan,Muhammad Arslan,Javid Shabbir,Feng Chen

doi:10.1371/journal.pone.0246947

Abstract

In this paper, we propose a generalized class of exponential type estimators for estimating the finite population mean using two auxiliary attributes under simple random sampling and stratified random sampling. The bias and mean squared error (MSE) of the proposed class of estimators are derived up to first order of approximation. Both empirical study and theoretical comparisons are discussed. Four populations are used to support the theoretical findings. It is observed that the proposed class of estimators perform better as compared to all other considered estimator in simple and stratified random sampling.

Highlights

In survey sampling, we generally use the auxiliary information to increase precision of the estimators by taking the advantages of correlation between the study variable y and the auxiliary variable x
Several authors have used the auxiliary variables and auxiliary attributes at estimation stage to increase the efficiency of the estimators
To estimate the mean time-based compensations earned by the individuals, the auxiliary attribute can be utilized in type of the education and martial status etc

Summary

Introduction

We generally use the auxiliary information to increase precision of the estimators by taking the advantages of correlation between the study variable y and the auxiliary variable x. Auxiliary information can be quantified in the form of auxiliary proportions to get better precision For this reason, several authors have used one or more auxiliary proportions at the estimation stage to increase the efficiency of the estimators. These mixed estimators outperformed than the individual estimators For this reason, several authors have used the auxiliary variables and auxiliary attributes at estimation stage to increase the efficiency of the estimators. Naik and Gupta [3] introduced the idea of point bi-serial correlation coefficient Using this idea, many authors have used the information on the auxiliary attribute for improving the precision of the estimators. Solanki and Singh [4] suggested a class of estimators for population mean of the study variable using known population proportion of the auxiliary attribute. Syp Sy Sp1 be point bi-serial correlation co-efficient between the study variable y and the auxiliary attribute p1. It is well known that the yR and yP are more precise than usual mean estimator y0 when

Cp1 2 Cy and ryp1

À f ryp1 CyCp1 þ ryp2 CyCp2 À

C R2 2 y yp1p2

C R 2 2 yh yhp1hp2h

Conclusion