This paper proposes improved estimators for a finite population proportion based on auxiliary information, using the simple random sampling (SRS) framework. The main aim is to improve the estimate accuracy by using auxiliary variables correlated with the study attribute. First-order approximations are used to obtain the statistical properties of the proposed estimators, and their performance is analyzed based on bias and mean squared error (MSE). Moreover, Percent Relative Efficiency (PRE) is also used as a comparative measure to evaluate how efficient the proposed estimators are relative to the current classical estimators. A large-scale numerical experiment is conducted to investigate the actual performance of the proposed estimators under various distributional conditions, sample sizes, and levels of correlation between the study and auxiliary variables. The simulation results remain consistent in showing that the proposed estimators yield smaller MSE values and larger PRE than the common, ratio, product, regression, and Rao estimators across diverse situations. These findings support the theoretical benefits of the estimated estimators and show that they perform well across various population structures. The proposed estimators are also applied to actual data sets to demonstrate their practical use. The empirical results support the simulation ones and indicate that the proposed estimators yield more accurate estimates of the population proportion. In general, the work offers an effective estimation model that enhances the precision of population proportion estimation and can be employed in various practical settings with auxiliary information.
Wang et al. (Tue,) studied this question.