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Inspired by previous research on the promising internal model-based impedance control (IMBIC) scheme, it was implemented and experiments were undertaken to determine the stochastic estimation of human arm impedance. A 2-DOF selective compliant assembly robot arm (SCARA) robot with significant nonlinear frictions was used in the experiments in order to test the accuracy and reliability of the estimation under nonlinear frictions, with the IMBIC and with a proportional derivative (PD) control, respectively. After the stochastic estimation method with the SCARA robot and the IMBIC was validated using a spring array, the method was applied to the estimation of human arm impedance. The experimental results demonstrated that the stochastic estimation using the IMBIC yields accurate and reliable estimations even under substantial frictions: the multiple coherence functions exceeded 0.95 throughout the frequency range investigated and the estimated magnitudes and phases matched well with a second-order best-fit model. Furthermore, the best-fit model demonstrated reasonable agreement with the results of previous research. The stochastic estimation using the IMBIC has also demonstrated effectiveness in the estimation of human arm impedance using conventional robots.