Enhanced estimation for distribution function using auxiliary variable: Application with radiation data

In order to get the best possible results from survey sampling, auxiliary information is essential for estimating population parameters like mean, variance, distribution function, and so on. In this article we develop an improved estimator for estimation of population distribution function (DF). The newly developed estimator leverage auxiliary information under simple random sampling method. The proposed estimators have been thoroughly evaluated using metrics such as percentage relative efficiency and mean square error, which show that they are useful in the estimating process. Empirical validation is accomplished using radiation datasets. We compared our developed estimator with ratio, product, traditional regression estimators, and other well-known estimators that have been investigated in the existing literature. Based on the numerical results, it is demonstrated that our proposed estimator perform better in terms of minimum mea squared error and higher PREs. The findings have important implications for both the evolution of survey sampling techniques and mathematical modeling classified radiation data sets.