Enhancing the finite population parameter estimation through auxiliary information: Applications in the physical education and radiation safety

This study presents a new estimator based on the exponential-cum-sine function for estimating the CDF of a finite population, with simple random sampling without replacement (SRSWOR). The estimator proposed here combines an auxiliary information mechanism with exponential and sine transformations, which can improve estimation efficiency and precision. The two jointly optimized parameters of the estimator provide greater flexibility and enable efficient use of the relationship between the study and auxiliary variables. Theoretical expressions for the bias and mean squared error (MSE) of the proposed estimator are obtained, and analytical comparisons of efficiency with existing estimators are established using a first-order approximation technique. Empirical and Monte Carlo simulation studies are used to assess the performance of the proposed estimator. The empirical investigation is carried out using actual data from physical education and radiation-related studies, and the simulation study is based on populations of Normal, Gamma, Log-normal, and Exponential distributions with different sample sizes and correlation structures. The results invariably revealed that the proposed estimator has the minimum Mean Square Error (MSE) and Maximum Percentage Relative Efficiency (PRE) in comparison with the usual estimator, sine ratio estimator, product estimator, exponential-cum-sine estimator, Rao-estimator, and the estimator suggested by Yadav et al. (2024). In addition, results show that the efficiency gain of the proposed estimator improves as the degree of positive correlation between the study and auxiliary variables increases. The proposed estimator also shows excellent robustness under various sampling situations and population distributions. Based on this, the study concludes that the proposed exponential-cum-sine-type estimator is a reliable, efficient, and practically useful alternative to the finite-population CDF estimation problems in the fields of survey sampling and other applied statistics