The enhanced estimation of population distribution function within the framework of random sampling: Implementations in AIGC design and radiation science

Assessing the population distribution function (DF) is an elementary issue in survey sampling theory, especially when there is auxiliary information available to increase statistical efficiency. This study proposes an improved estimator for estimating the population DF under simple random sampling using dual auxiliary information. The proposed estimator leverages the correlation between the study variable and the auxiliary variable, yielding higher precision than conventional estimators. Under the first-order approximation, the properties of the estimator, such as bias and mean squared error (MSE), are derived, and conditions under which the proposed estimator is superior to the existing ones are given. Empirical analysis uses with simulated and real data to ensure effectiveness. Moreover, the proposed estimation framework is illustrated through case studies in Artificial Intelligence Generated Content (AIGC) design and radiation science, where accurate distribution estimation is crucial for decision-making, predictive modeling, and uncertainty quantification. The results show that the proposed estimator is more efficient and has less estimation error than traditional estimators that use effective dual auxiliary information, and it can always be applied to achieve the best estimation results. The results illustrate the strong potential of the suggested methodology as a powerful and reliable tool for applying modern methods of statistical inference in interdisciplinary research areas.