A new statistical method with properties: Its empirical exploration in art education and radiation sector

Proper estimation of population distribution function is very important in statistical inferences, planning of policies and decision making in various applications. In this article we establish a new estimator for estimating the population distribution function using auxiliary information. The estimator is proposed with a theoretical framework of finite population distribution function, and its theoretical properties are obtained, such as bias, mean squared error (MSE), and consistency. Analytical comparisons indicate that the new estimator is better in realistic regularity conditions than the traditional existing estimators. Conditions of superiority are clearly laid out, and the efficiency gains are demonstrated to be positive when there is a good correlation between the study and the auxiliary variables. In order to determine the useful applicability, empirical investigation of the estimator is done through real-world data of art education and the radiation industry. In the case of art education, the approach helps to improve distributional assessment of student performance indicators with the help of institutional auxiliary records. It is used to improve the distribution estimation of exposure-related measurements in the radiation sector through the use of appropriate auxiliary measurements. The results of the empirical studies prove the high efficiency improvements in comparison with the current methods. The findings confirm that the distribution function estimation with the help of the suggested framework and the integration of auxiliary information is greatly increased. The research work adds to the survey sampling theory, and it has a practical contribution to researchers and other policy makers who need distributional estimation reliability in complicated data settings. 62D05.