Abstract: In this study modified estimation methods based on the maximum entropy median for fitting unreplicated functional model to data were proposed. Two types of modification were considered, modified Wald-type estimators and modified Theil-type estimators. Also, a coefficient of determination to estimate the proportion of variation when both variables are measured with error is proposed. A Monte Carlo experiment were used to study the performance of the proposed estimators, the simulation results showed that the proposed estimators are more efficient than the classical estimators when the data contains outliers. A real data analysis for fitting the relationships between the unemployment rate and the human development index in the Arab’s states also included. The data analysis showed that there is a negative relationship between both variables and suggested that the Arab’s states should change their economical, educational and social policies to improve the life quality in these states.