A simulation based optimization of factor-type exponential estimators in sample surveys with coefficients of variation and kurtosis

Abstract

In the context of sample surveys, this article presents factor-type exponential ratio estimators as a technique for estimating population means. These estimators use supplementary information for an auxiliary variable, such as coefficients of variation and coefficients of kurtosis. The research includes a range of alpha values from −1 to +1 to improve estimate.Following that, the study rigorously develops formulas for both bias and mean square error for the suggested estimators. Up to the first degree of large sample approximation, these formulas are produced. The empirical findings we present are renowned in that they show that the suggested estimators consistently beat existing exponential estimators with significantly lower mean squared errors.We calculate the suggested estimator’s percent relative efficiency in comparison to the traditional mean estimator to put a number on how effective it is. We show persuasive proof of the significant improvement offered by our estimators over existing exponential estimators by a complete numerical illustration and a rigorously conducted simulations exercise. Summary:We present factor-type exponential ratio estimators for estimating population means in sample surveys. Key points:We take into account auxiliary information, different alpha values, and various correlation circumstances. Objective:We want to improve population mean estimation precision. Method:To assess our estimators, we use numerical examples and simulations. Results:Our estimators typically outperform competitors, with smaller mean squared errors. Advantage:We demonstrate their robustness and efficiency in improving population mean estimate through rigorous simulations.