If the respiratory system is represented as a one compartment model composed of linear electrical elements, the Minimum Variance Unbiased Estimation (MVUE) is the optimum statistical method to estimate the model parameters. Two well known linear models, RIC and Viscoelastic models were chosen and their parameters were estimated by MVUE. Synthetic data simulations showed that minimum 100 Hz sampling rate is required in order to have minimum variance. Estimation of lung inertance and viscoelastic tissue compliance parameters resulted in very large estimation variance, whereas the rest of the parameters were estimated successfully. Both parameter values and estimator variances have their own characterization in terms of patient discrimination for diagnostic purposes.