Application to radiation data sets by suggesting an improved mean estimator under probability proportional to size sampling

The performance of estimators was established through applications to three real-world datasets from the radiation sciences, and their reliability was confirmed by using simulation study, which demonstrated to be more effective in fitting data than conventional estimators, when investigated with the mean square error metrics, suggesting it could serve as a valuable complementary tool for researchers studying sampling theory and general statistical estimating. Finding out how well microwave and gamma irradiation work against the drugstore beetle was the driving force for this research. In this research, radiation data is put through to a new estimator for population mean estimate under PPS sampling. By using the sampling strategy in a symmetrical fashion across the population, we may eliminate bias and ensure that the sample more accurately represents the whole population. The proposed estimator was evaluated using a comprehensive numerical analysis and simulation research. When compared to existing estimators, the numerical result clearly shows that the proposed estimator works better when estimating the population mean.