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A new look at q-exponential distributions via excess statistics

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  • Bercher, J.-F.
  • Vignat, C.

Abstract

Q-exponential distributions play an important role in nonextensive statistics. They appear as the canonical distributions, i.e. the maximum generalized q-entropy distributions under mean constraint. Their relevance is also independently justified by their appearance in the theory of superstatistics introduced by Beck and Cohen. In this paper, we provide a third and independent rationale for these distributions. We indicate that q-exponentials are stable by a statistical normalization operation, and that Pickands’ extreme values theorem plays the role of a CLT-like theorem in this context. This suggests that q-exponentials can arise in many contexts if the system at hand or the measurement device introduces some threshold. Moreover we give an asymptotic connection between excess distributions and maximum q-entropy. We also highlight the role of Generalized Pareto Distributions in many applications and present several methods for the practical estimation of q-exponential parameters.

Suggested Citation

  • Bercher, J.-F. & Vignat, C., 2008. "A new look at q-exponential distributions via excess statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5422-5432.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:22:p:5422-5432
    DOI: 10.1016/j.physa.2008.05.038
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    References listed on IDEAS

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    Cited by:

    1. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "On alternative q-Weibull and q-extreme value distributions: Properties and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1171-1190.
    2. Sarabia, José María & Prieto, Faustino, 2009. "The Pareto-positive stable distribution: A new descriptive model for city size data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4179-4191.
    3. Antonopoulos, Chris G. & Michas, George & Vallianatos, Filippos & Bountis, Tassos, 2014. "Evidence of q-exponential statistics in Greek seismicity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 71-77.
    4. Chernyshov, A.A. & Kozelov, B.V. & Mogilevsky, M.M., 2024. "Non-extensive (Tsallis) q-statistics and auroral glow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    5. Hoyos, Isabel & Rodríguez, Boris Anghelo, 2020. "Drawing the complexity of Colombian climate from non-extensive extreme behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    6. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.

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