A new data fitting method for stretched Gaussian noise: stretched least square method

Abstract

Stretched Gaussian distribution is the fundamental solution of the Hausdorff derivative diffusion equation and its corresponding stretched Gaussian noise is a widely encountered non-Gaussian noise in science and engineering. The least square method is a standard regression approach to fit Gaussian noisy data, but has distinct limits for non-Gaussian noise. Based on the Hausdorff calculus, this study develops a stretched least square method to fit stretched Gaussian noise by using the Hausdorff fractal distance as the horizontal coordinate. To better compare with the least square method, different high levels of stretched Gaussian noise are added to real values. Numerical experiments show the stretched least square method is more accurate specific in fitting stretched Gaussian noise than the least square method.