A novel statistical outlet with reliability characteristics: Its implementations in the human capital resilience and radiation sector

The purpose of the study is to enhance the estimation of the finite population mean in Probability Proportional to Size (PPS) sampling with the aid of auxiliary information. The proposal is to develop a new modified estimator in the generalized framework to achieve efficiency and reliability. Theoretical properties of the estimator, such as bias and mean squared error (MSE), are derived and compared with those of existing estimators. A thorough simulation study is conducted to confirm its performance under varying distributions and correlation levels. The findings indicate that the proposed estimator always has a smaller MSE and a greater percentage relative efficiency (PRE) than the traditional estimators. These results underscore the performance and strengths of the suggested method in managing a heterogeneous population, and, therefore, it is a valuable instrument in practical survey studies.