IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v541y2020ics0378437119320497.html
   My bibliography  Save this article

Tsallis–Mittag-Leffler distribution and its applications in gas prices

Author

Listed:
  • Agahi, Hamzeh
  • Alipour, Mohsen

Abstract

The theory of Mittag-Leffler process is a fundamental concept in probability and stochastic process. This paper introduces the class of Tsallis–Mittag-Leffler distributions. In special case, our results include a new Tsallis q-Weibull distribution, one-parametric Mittag-Leffler distribution and some other well-known distributions. Finally, to illustrate the applicability of our distribution, a real data set on gas prices in time series data based on 100 days moving average is analyzed.

Suggested Citation

  • Agahi, Hamzeh & Alipour, Mohsen, 2020. "Tsallis–Mittag-Leffler distribution and its applications in gas prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119320497
    DOI: 10.1016/j.physa.2019.123675
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119320497
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123675?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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).
    3. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "Information geometry on the curved q-exponential family with application to survival data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 788-802.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    2. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    3. Zhang, Zhehao, 2018. "Renewal sums under mixtures of exponentials," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 281-301.
    4. Emad-Eldin Aly & Nadjib Bouzar, 2000. "On Geometric Infinite Divisibility and Stability," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 790-799, December.
    5. Levy, Edmond, 2021. "On the density for sums of independent Mittag-Leffler variates with common order," Statistics & Probability Letters, Elsevier, vol. 179(C).
    6. Kozubowski, Tomasz J., 2005. "A note on self-decomposability of stable process subordinated to self-decomposable subordinator," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 89-91, August.
    7. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    8. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.
    9. Sánchez, Ewin, 2019. "Burr type-XII as a superstatistical stationary distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 443-446.
    10. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
    11. Kozubowski, Tomasz J., 1998. "Mixture representation of Linnik distribution revisited," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 157-160, June.
    12. Kozubowski, Tomasz J., 2005. "A note on self-decomposability of stable process subordinated to self-decomposable subordinator," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 343-345, July.
    13. Cho, Soobin & Kim, Panki, 2021. "Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 229-279.
    14. 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.
    15. Pillai, R. N. & Jayakumar, K., 1995. "Discrete Mittag-Leffler distributions," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 271-274, May.
    16. Tomasz Kozubowski, 2000. "Exponential Mixture Representation of Geometric Stable Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 231-238, June.
    17. Agahi, Hamzeh & Alipour, Mohsen, 2019. "Mittag-Leffler-Gaussian distribution: Theory and application to real data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 227-235.
    18. O. E. Barndorff-Nielsen & N. N. Leonenko, 2005. "Spectral Properties of Uperpositions of Ornstein-Uhlenbeck Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 335-352, September.
    19. Mirko D’Ovidio & Federico Polito, 2014. "Discussion on the paper “On simulation and properties of the stable law” by L. Devroye and L. James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 359-363, August.
    20. Chunsheng Ma, 2013. "Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 941-958, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119320497. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.