A new data analysis tool with theoretical foundations and statistical properties: Its implementations in sports and radiation sciences

The paper is a new data analysis program that was created to estimate the means and distribution functions of a finite population with the help of auxiliary information, under simple random sampling. The proposed estimator has a theoretical basis since it combines the advantages of ratio, product, and exponential-type estimators in one framework and overcomes their methodological shortcomings. Analytical results also indicate that the new estimator is unbiased in the first order of approximation, and has a lower mean squared error than the existing ones, which are strong statistical properties and theoretical reliability. The practical usefulness of this tool is proved by its usage in various scientific fields, especially in the field of sports and radiation sciences where effective methods of estimation are very important to make decisions and interpret data. The findings point at the idea that the tool can be used to increase accuracy, to improve efficiency, to decrease the cost of the survey, and to bring other credible inferences in the cases when the complete enumeration of the population is not possible. The paper has theoretical as well as practical value, and the proposed estimator has a chance to become an effective data analysis tool of contemporary statistical practice.