Two-fold Auxiliary Information for Efficient Estimation of Population Distribution Function under Sample Surveys

Accepted March 2026

Abstract

In survey sampling, the use of auxiliary information plays a significant role in enhancing the efficiency of population parameter estimates. This manuscript introduces two new classes of estimators for the population distribution function (DF) that effectively utilizes two-fold auxiliary information such as auxiliary variable and the rank of auxiliary variable, to enhance the efficiency. The bias and mean square error (MSE) expressions of the proposed estimators are derived under simple random sampling (SRS) up to the first-order approximation. The optimum conditions for minimum MSE are obtained, and theoretical efficiency comparisons are made with the existing estimators. A simulation study and an empirical application utilizing real datasets demonstrate that the proposed two-fold auxiliary information-based estimators consistently outperform the conventional estimators in terms of efficiency. The results confirm that integrating dual auxiliary information provides a substantial gain in accuracy for estimating the population DF under sample surveys.