Study of some improved ratio type estimators using information on auxiliary attributes under second order approximation

TL;DR

This paper evaluates the second order biases and mean square errors of improved ratio type estimators that utilize auxiliary attribute information, enhancing the accuracy of population mean estimation.

Contribution

It introduces second order bias and MSE calculations for existing estimators using auxiliary attribute data, providing a deeper accuracy analysis.

Findings

Second order biases and MSEs are derived for the estimators.

Numerical illustration compares estimator performances.

Improved estimators show better accuracy over first order approximations.

Abstract

Chakrabarty, Khoshnevisan, Sahai and Ray, Solanki suggested some estimators to estimate unknown population mean of the study variable. These authors discussed the estimators along with their first order biases and mean square errors(MSEs). In this paper, we have tried to found out the second order biases and mean square errors of some estimators using information on auxiliary attribute. We have compared the performance of the estimators with the help of a numerical illustration.