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Recognition of nonextensive statistical distributions by the eigencoordinates method

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  • Nigmatullin, R.R.

Abstract

Nonextensive statistical distributions suggested by Tsallis are studied in the framework of the so-called eigencoordinates (ECs) method which allows to recognize them with high level of authenticity. At first, the possibilities of the ECs method have been demonstrated on model files to exhibit some peculiarities of this new method. Then the amplitude distributions of the real noise tracks before and after earthquakes have been analyzed. It has been shown that this type of noise is fractal and strongly correlated; histograms of the noise amplitudes with high level of reliability are really described by a distribution coming from nonextensive statistics. The possibilities and recommendations for the application of the ECs method to identify theoretical curves claimed for the description of experimental data are discussed.

Suggested Citation

  • Nigmatullin, R.R., 2000. "Recognition of nonextensive statistical distributions by the eigencoordinates method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(3), pages 547-565.
    • Handle: RePEc:eee:phsmap:v:285:y:2000:i:3:p:547-565
    DOI: 10.1016/S0378-4371(00)00237-5
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    Cited by:

    1. Al-Hasan, Mohammed & Nigmatullin, Raoul R., 2003. "Identification of the generalized Weibull distribution in wind speed data by the Eigen-coordinates method," Renewable Energy, Elsevier, vol. 28(1), pages 93-110.
    2. Nigmatullin, Raoul & Sarkar, Samyadip & Biswas, Karabi, 2021. "New class of fractal elements with log-periodic corrections: Confirmation on experimental data," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Raoul Nigmatullin & Semyon Dorokhin & Alexander Ivchenko, 2021. "Generalized Hurst Hypothesis: Description of Time-Series in Communication Systems," Mathematics, MDPI, vol. 9(4), pages 1-11, February.
    4. Touré, Siaka, 2005. "Investigations on the Eigen‐coordinates method for the 2‐parameter weibull distribution of wind speed," Renewable Energy, Elsevier, vol. 30(4), pages 511-521.
    5. Nigmatullin, Raoul R. & Toboev, Vyacheslav A. & Lino, Paolo & Maione, Guido, 2015. "Reduced fractal model for quantitative analysis of averaged micromotions in mesoscale: Characterization of blow-like signals," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 166-181.
    6. Nigmatullin, R.R. & Osokin, S.I. & Toboev, V.A., 2011. "NAFASS: Discrete spectroscopy of random signals," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 226-240.

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