Improved estimator of population variance using information on auxiliary attribute in simple random sampling

TL;DR

This paper introduces new estimators for population variance in simple random sampling that leverage auxiliary attribute information, demonstrating improved efficiency over previous methods through theoretical analysis and numerical validation.

Contribution

It proposes a new family of variance estimators using auxiliary attributes, extending prior methods and deriving their mean square errors for enhanced efficiency.

Findings

Proposed estimators are more efficient than previous Singh and Kumar (2011) estimators.

Derived mean square errors for the new estimators.

Numerical example confirms theoretical efficiency improvements.

Abstract

Singh and Kumar (2011) suggested estimators for calculating population variance using auxiliary attributes. This paper proposes a family of estimators based on an adaptation of the estimators presented by Kadilar and Cingi (2004) and Singh et al. (2007), and introduces a new family of estimators using auxiliary attributes. The expressions of the mean square errors (MSEs) of the adapted and proposed families are derived. It is shown that adapted estimators and suggested estimators are more efficient than Singh and Kumar (2011) estimators. The theoretical findings are supported by a numerical example.