A new analytical tool with properties and theoretical insights: Its implementations in logistic management and radiation sector

The importance of applying auxiliary information has been most significant in increasing the efficiency of population parameter estimation. From this perspective, the present research paper provides a useful approach to the analysis of the finite population distribution function, yielding theoretical and practical insights. It was proposed to derive the estimator within the framework of auxiliary-variable-based sampling to achieve higher accuracy than existing techniques. Approximate expressions for bias and mean squared error are derived, and the estimator’s optimal mean squared error is obtained analytically. The tool is used in two significant areas to demonstrate its practical applicability, namely logistics management and the radiation industry. This is supported by its performance, as shown in a large-scale numerical study that found the proposed estimator superior to the classical alternatives across all scenarios considered, evidenced by significant improvements in percent relative efficiencies. Such empirical observations determine the estimator’s power and its ability to optimize predictive performance, operational decision-making, and risk assessment in uncertain environments. We show that this work is a theoretically well-grounded and practically versatile analytical instrument that makes a substantial contribution to the identification of the roles of population distribution and clearly demonstrates its applicability in logistics management and the radiation industry.