Generalized class of estimators for finite population mean when study variable is qualitative in nature

TL;DR

This paper introduces a new generalized class of estimators for the population mean of qualitative variables in simple random sampling, improving efficiency over existing methods by utilizing auxiliary information.

Contribution

It develops a generalized estimator class with asymptotic bias and MSE expressions, and demonstrates its superior efficiency through theoretical analysis and empirical validation.

Findings

Proposed estimators are more efficient than existing ones for qualitative variables.

Asymptotic bias and MSE expressions derived for the estimators.

Empirical study confirms the theoretical superiority of the proposed estimators.

Abstract

This paper suggests a generalized class of estimators for population mean of the qualitative study variable in simple random sampling using information on an auxiliary variable. Asymptotic expressions of bias and mean square error of the proposed class of estimators have been obtained. Asymptotic optimum estimator has been investigated along with its approximate mean square error. It has been shown that proposed generalized class of estimators are more efficient than all the estimators considered by Singh et al. (2010) in case of qualitative study variable. In addition theoretical findings are supported by an empirical study based on real population to show the superiority of the constructed estimators over others.