Development of Robust Exponential Estimators for Population Mean Estimation Under PPS ‎Sampling: Applications In Medical, Agricultural, And Displacement Contexts in The USA

Abstract

The main objective of this research is to explore the effective use of auxiliary variables to enhance the estimation of the population mean of ‎the study variable under consideration. The proposed generalized estimators demonstrate superior performance compared to existing methods, particularly in terms of reduced mean squared error (MSE), which is used as the primary measure of precision. Using first-order approximation techniques, the study examines important statistical properties of the proposed estimators, with a specific focus on their bias ‎and MSE under the Probability Proportional to Size (PPS) sampling framework. PPS sampling assigns higher inclusion probabilities to ‎units with larger size measures, making it highly efficient for heterogeneous populations. A new generalized class of estimators is developed ‎by incorporating auxiliary information to improve the accuracy of population mean estimation under PPS sampling. The methodology is ‎applied to a real-world radiation science dataset, where average ambient radiation levels are recorded across different geographical regions ‎selected based on area size and population distribution. In addition, a simulation study is conducted using artificially generated datasets to ‎validate the performance of the proposed estimators under controlled conditions. Graphical analysis and comparative charts are also pre-‎pared using both simulated and real datasets to visually demonstrate the superiority of the proposed estimators. The results clearly indicate ‎that the suggested estimators achieve lower MSE compared to existing approaches, making them highly suitable for radiological risk as-‎assessment and environmental health monitoring applications‎.