Novel Statistical Inference by Developing a Generalized Class for Population Proportion Using Two Auxiliary Attributes: Application on Real Life Data and Simulation Analysis

Estimation of population proportion is a significant problem in survey sampling and has wide application in social sciences, economics, agriculture, medicine, and public health. The accuracy of estimators can be significantly improved by effectively using auxiliary information. This study proposes an improved generalized class of estimators for estimating the population proportion using two auxiliary attributes. First-order approximation of the mathematical property is obtained for the proposed class, including the expressions for the bias and mean square error (MSE). Theoretical comparisons are made with the traditional sample proportion estimator and some existing estimators that are available in the literature. Analytical conditions under which the proposed generalized class performs better than the other estimators are also determined. In order to analyze the practical performance of the proposed methodology, numerical and simulation studies are carried out on the real and artificially generated population. The results of the experiments confirm that the proposed generalized class consistently yields lower MSE and higher PRE than the traditional estimators. It is concluded that the proposed generalized class is a reliable and efficient alternative to the population proportion estimation for practical survey sampling applications having appropriate auxiliary attributes.