Statistical Formulation for Average Parameter Determination via Quantile-Linked Auxiliary Characteristics

This article suggests a brief and integrated methodology for enhancing the mean estimation in a finite population using the pre-specified median of the target variable in conjunction with quantile-related auxiliary measurements. Although a number of conventional ratio and regression estimators are reliant on the average of the auxiliary variable, the current study presents new exponential-type families that combine the variable’s known median under investigation with the dispersion-related characteristics of supplementary information. The estimators are constructed and analyzed theoretically, under Simple Random Sampling Without Replacement (SRSWOR), and the minimum expression of the MSE under optimal conditions is obtained. The results are confirmed using simulated Kumaraswamy–Gamma populations and through several real-world datasets, such as those on education, wheat production, U.S. cereal consumption, and solar radiation data (HI-SEAS weather station, September–December 2016). The findings consistently demonstrate that the developed estimators provide a substantially lower MSE and greater percentage relative efficiency (PRE) relative to conventional estimators. These applications indicate that the median-based unified framework can be used to give more precise and efficient mean estimation in several fields, comprising agriculture, nutrition, and education, as well as meteorological and environmental research.