Based on a Gaussian distribution for the subgap states of amorphous InGaZnO transistors, a new methodology is developed for the extraction of the electrical parameters of the transistors. The calculated non-linear Y-function is transformed to a linear one, adopting a mobility model that fits the classical methodology of Y-function traditionally used in MOSFETs. The efficiency of the new Y-function is verified in experimental data, for the extraction of the electrical parameters of the transistor as the threshold voltage, the on-voltage, the mobility, and the characteristic decay energies of the exponential distributions used to simulate the Gaussian distribution. All the transfer characteristics are reconstructed using only the transfer characteristic for V d =0.1V and the extracted electrical parameters of the transistor.