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

## TL;DR

This paper evaluates the effectiveness of the least squares method in fitting data contaminated with non-Gaussian noises, specifically Lévý and stretched Gaussian noises, revealing limitations at higher noise levels.

## Contribution

It provides a systematic analysis of least squares fitting performance on non-Gaussian noise data, highlighting its limitations and comparative performance between different noise types.

## Key findings

- Least squares fitting is less accurate with non-Gaussian noise.
- Stretched Gaussian noise is fitted better than Lévý noise.
- The method fails when noise exceeds 5% level.

## Abstract

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