  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.
