A New Class of Logarithmic Estimators using Subsidiary Information: Real-World Applications and Simulation Insights

In sampling, mean estimate is crucial because it gives a succinct overview of the population’s central tendency, facilitating comparisons and guiding choices in a variety of domains, including environmental studies, economics, and health. The population mean has been estimated in this article by using the logarithmic relationship between the study and auxiliary variable. Even though there are many logarithmic estimators available in the literature, there is still a constant search for more reliable and effective estimators. In keeping with this, we have developed a new and effective class of logarithmic estimators that clearly perform better than their predecessors and provide more accuracy and dependability when estimating parameters. To evaluate and compare the performance of the proposed estimators with the existing ones, we calculated their Mean Square Error (MSE) and Bias up to the first level of approximation. Through extensive theoretical investigation, we proved that the proposed estimators consistently perform better than the existing estimators discussed in this study. Furthermore, by carrying out an extensive simulation study, we empirically supported these findings. The outcomes of this simulation study unequivocally show how much better the proposed estimators are than the existing techniques, indicating their higher accuracy and reliability.