Feasibility study on the least square method for fitting non-Gaussian noise data

摘要

This study is to investigate the feasibility of least square method infitting non-Gaussian noise data. We add different levels of the two typicalnon-Gaussian noises, L\'evy and stretched Gaussian noises, to exact value ofthe selected functions including linear equations, polynomial and exponentialequations, and the maximum absolute and the mean square errors are calculatedfor the different cases. L\'evy and stretched Gaussian distributions have manyapplications in fractional and fractal calculus. It is observed that thenon-Gaussian noises are less accurately fitted than the Gaussian noise, but thestretched Gaussian cases appear to perform better than the L\'evy noise cases.It is stressed that the least-squares method is inapplicable to thenon-Gaussian noise cases when the noise level is larger than 5%.