An innovative data analysis toolkit with mathematical and theoretical frameworks: Its implications in higher education and the radiation sector

This paper introduces a new statistical estimator that is based on a sound mathematical and theoretical framework. The new estimator is designed to facilitate accurate estimation of population proportions, which is critically important of radiation science and education. The proposed methodology advances beyond traditional ratio and regression-based estimators by integrating optimized strategies for weighting, bias reduction, and rigorous statistical adjustments. Analytical representations of bias, mean squared error, and relative efficiency are established to ascertain the theoretical superiority of the proposed estimator. These theoretical findings are confirmed by a comprehensive real-world datasets. Empirical evidence indicates that the suggested estimator is consistently superior to traditional population-proportion estimators, with significantly lower MSE and greater stability, especially when measurement noise is present. In addition to its practical importance in radiation science, the proposed estimator is also evaluated using higher education data. Its combination of applied data analysis and mathematical theory could serve as an important resource in further teaching of statistics, data science, applied mathematics. Collectively, the proposed data analysis toolkit offers a consistent and versatile framework that facilitates more precise and resilient estimations with considerable implications for radiation protection, policy development, environmental monitoring, and advanced statistical analysis.