Abstract
The primary purpose of this article is to examine the issue of estimating the finite population distribution function from auxiliary information, such as population mean and rank of the auxiliary variables, that are already known. In order to better estimate the distribution function (DF) of a finite population, two improved estimators are developed. The bias and mean squared error of the suggested and existing estimators are derived up to the first order of approximation. To improve the efficiency of an estimators, we compare the suggested estimators with existing counterpart. Based on the numerical outcomes, it is to be noted that the suggested classes of estimators perform well using six actual data sets. The strength and generalization of the suggested estimators are also verified using a simulation analysis. Based on the result of actual data sets and a simulation study, we observe that the suggested estimator outperforms as compared to all existing estimators which is compared in this study.