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

TL;DR

This paper introduces a stretched least square method based on Hausdorff calculus to more accurately fit stretched Gaussian noise, which is common in science and engineering, outperforming traditional least squares in numerical experiments.

Contribution

The paper develops a novel stretched least square method utilizing Hausdorff fractal distance to improve fitting of stretched Gaussian noise.

Findings

Stretched least square method outperforms traditional least squares in accuracy.

Numerical experiments confirm the effectiveness of the proposed method.

Method is specifically tailored for non-Gaussian, stretched Gaussian noise.

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.