A new statistical estimator with theoretical foundation and Monte Carlo simulation: Its applications in safety management and radiation sciences

The paper presents a new, statistically efficient estimator of the finite-population cumulative distribution function (CDF) for simple random sampling, with specific reference to safety management and radiation science applications. The rationale for adopting a distribution-function-based framework is the need to examine probabilistic behavior, variability, and risk traits that conventional estimators, such as means and proportions, fail to account for. The suggested estimator is formulated on a solid theoretical framework that unites two sources of auxiliary information: known auxiliary CDF values and rank information about the auxiliary variable. Closed-form expressions for the bias and mean squared error (MSE) are obtained to first order, and optimality conditions are provided to illustrate the theoretical superiority of the proposed estimator over available CDF estimators. To confirm the analytical results, a detailed Monte Carlo simulation study is performed to examine the estimator’s behavior across different sample sizes, correlation structures, and degrees of non-response. Also, the practical applicability of the offered methodology is illustrated by real data applications of radiation experiments and studies related to the safety management. Simulation and empirical results are both strong on the point of significant efficiency improvement, as indicated by reduced MSE and percentage relative efficiency relative to equivalent estimation using other techniques. The paper concludes that the available estimator will be a valid, sound, practically applicable, and easily usable tool for distributional analysis in safety and radiation-related studies, where the complete population distribution is required to make sound decisions and conduct risk analysis.