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

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  • Xu, Wei
  • Chen, Wen
  • Liang, Yingjie

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, Lévy 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. Lévy 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 Lévy 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%.

Suggested Citation

  • Xu, Wei & Chen, Wen & Liang, Yingjie, 2018. "Feasibility study on the least square method for fitting non-Gaussian noise data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1917-1930.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:1917-1930
    DOI: 10.1016/j.physa.2017.11.108
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    Cited by:

    1. Xu, Wei & Liang, Yingjie & Chen, Wen & Wang, Fajie, 2020. "Recent advances of stretched Gaussian distribution underlying Hausdorff fractal distance and its applications in fitting stretched Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    2. Marouani, H. & Fouad, Y., 2019. "Particle swarm optimization performance for fitting of Lévy noise data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 708-714.

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