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Truncated Mittag-Leffler distribution and superstatistics

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  • Agahi, Hamzeh
  • Khalili, Monavar

Abstract

The Mittag-Leffler stochastic process is an important tool in practical applications. In this paper, we first focus on some claims of Burr type-XII as a superstatistical stationary distribution (Sánchez, 2019). Then, we present the capabilities of the Mittag-Leffler distribution and introduce truncated Mittag-Leffler distributions. Finally, in the oil price analysis of time series real data, we show that the truncated Mittag-Leffler distribution performs better than other nominated distributions, especially the Burr distribution.

Suggested Citation

  • Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120303022
    DOI: 10.1016/j.physa.2020.124620
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    References listed on IDEAS

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    1. Sulaiman, Tukur Abdulkadir & Yavuz, Mehmet & Bulut, Hasan & Baskonus, Haci Mehmet, 2019. "Investigation of the fractional coupled viscous Burgers’ equation involving Mittag-Leffler kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    2. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    3. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    4. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    5. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
    6. dos Santos, Maike A.F., 2020. "Mittag-Leffler functions in superstatistics," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    Cited by:

    1. dos Santos, M.A.F. & Menon, L. & Cius, D., 2022. "Superstatistical approach of the anomalous exponent for scaled Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. dos Santos, Maike A.F. & Junior, Luiz Menon, 2021. "Random diffusivity models for scaled Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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