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In this paper, the variation characteristics of low-temperature polycrystalline silicon (LTPS) thin-film transistors (TFTs) are investigated with a statistical approach. A special layout is proposed to investigate the device variation with respect to various devices distances. Two non-Gaussian equations are proposed to fit the device parameter distributions, whose the coefficients of determination (R2) are both near 0.9, reflecting the validity of the model. Two benchmark circuits are used to compare the difference between the proposed model and the conventional Gaussian distribution for the device parameter distribution. The output behaviors of the digital and analog circuits show that the variation in the short range would greatly affect the performance of the analog circuits and would instead be averaged in the digital circuits.