Regression cum exponential type estimator for population proportion using auxiliary attributes: Application on radiation data and simulation study

In numerous instances, incorporating an auxiliary attributes enhances the precision of population parameter estimate. This study enhances the knowledge of survey sampling by offering an improved estimator for determining the population proportion in simple random sampling that incorporates an auxiliary attribute. We find out the expression of the bias and mean square error (MSEs) for both the existing and new estimators up to the first order of approximation. We determined the theoretical optimum values and then computed the least MSE of the estimator that was initially recommended. The performance of the estimators was evaluated using three real-world datasets from the radiation sciences, and their reliability was confirmed by a simulation analysis. An empirical study showed that the proposed estimator has a greater percentage relative efficiency PREs than the considered existing estimators. In light of this, it may be important to investigate the proposed estimator's dominating characteristics of its practical applications.