Improved estimators in simple random sampling when study variable is an attribute

TL;DR

This paper develops and compares new estimators for estimating population means in simple random sampling when the study variable is qualitative, demonstrating their improved performance over traditional methods through theoretical bias and MSE analysis and empirical validation.

Contribution

It introduces novel estimators tailored for qualitative study variables and provides their bias and MSE expressions, showing their superiority over existing estimators.

Findings

New estimators have lower bias and MSE than traditional ones.

Theoretical results are supported by empirical evidence.

Constructed estimators outperform others in practical applications.

Abstract

This article addresses the problem of estimating the population mean in the presence of auxiliary information when study variable itself is qualitative in nature. Bias and mean squared error (MSE) expressions of the class of estimators are derived up to the first order of approximation. The suggested estimators have been compared with the traditional estimator and several other estimators considered by Singh (2010). In addition, we support this theoretical result by an empirical study to show the superiority of the constructed estimator over others.