A new estimator with Monte Carlo simulation and theoretical framework: Its implementations in the sports and radiation sciences

The primary aim of survey sampling is to develop reliable estimators for population parameters, particularly the population mean. Complete population data in practical areas such as sports and radiation sciences are seldom accessible due to time, cost, and availability constraints. Consequently, robust statistical methods are essential to ensure that the information derived from a sample accurately represents the underlying population. Previous research has shown that incorporating auxiliary information can substantially enhance the precision of estimations. The existing techniques, such as ratio, regression, and product, fail to leverage distributional properties, particularly the cumulative distribution function (CDF) of auxiliary variables. To address this limitation, the present research paper introduces a novel statistical approach within a theoretical framework that utilizes two auxiliary pieces of information, specifically sample means and the CDF values of auxiliary variables in simple random sampling. This dual integration provides a two-dimensional analytical advantage by capturing both the location and distributional features of the auxiliary data. The theoretical properties of the proposed estimators, including bias and mean squared error (MSE), are rigorously derived, and comparative analyses show that they significantly outperform conventional approaches. Thus, the framework provides a robust, adaptable foundation in sports and radiation to enable precise estimates and improve analysis.