Modified regression-cum-exponential estimators of population mean under ranked set sampling approached

Abstract

This research work modified regression – cum – exponential estimators of population mean under ranked set sampling approach. The proposed estimators are functions of unknown parameters of the study variables which limits their applicability although these unknown parameters of the study variable can be estimated but larger sample is required to achieve this and this will leads to additional cost for a survey. The estimators proposed are function of known parameters of auxiliary variable which are sensitive to extreme values or outliers. This will drastically reducing the efficiency of the estimators. The estimators proposed is a ratio based estimator which is only efficient when the correlation between the study and auxiliary variable is positive. Then we estimators address key limitations of the existing methods by eliminating their dependence on unknown parameters and reducing their sensitivity to outliers. This is achieved by integrating robust regression techniques and robust measures of dispersion. The properties of the propose estimators are derived, and both theoretical and empirical analyses demonstrate that they achievea lower Mean Squared Error (MSE) and higher efficiency compared to the current estimators: (MSE: 4034.046, PRE 133.6946), (MSE: 5084.461, PRE 106.0742), (MSE: 3398.236, PRE 120.9747), (MSE: 3937.292, PRE: 104.412), (MSE: 6926.666, PRE: 132.3065), (MSE:8677.438, PRE: 105.612). The research recommended for practical use, especially when auxiliary variable information is available and data may contain extreme values or outlier.