IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i19p4141-d1251857.html
   My bibliography  Save this article

New Monotonicity and Infinite Divisibility Properties for the Mittag-Leffler Function and for Stable Distributions

Author

Listed:
  • Nuha Altaymani

    (Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Wissem Jedidi

    (Department of Statistics & OR, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

Abstract

Hyperbolic complete monotonicity property ( HCM ) is a way to check if a distribution is a generalized gamma ( GGC ), hence is infinitely divisible. In this work, we illustrate to which extent the Mittag-Leffler functions E α , α ∈ ( 0 , 2 ] , enjoy the HCM property, and then intervene deeply in the probabilistic context. We prove that for suitable α and complex numbers z , the real and imaginary part of the functions x ↦ E α z x , are tightly linked to the stable distributions and to the generalized Cauchy kernel.

Suggested Citation

  • Nuha Altaymani & Wissem Jedidi, 2023. "New Monotonicity and Infinite Divisibility Properties for the Mittag-Leffler Function and for Stable Distributions," Mathematics, MDPI, vol. 11(19), pages 1-26, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4141-:d:1251857
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/19/4141/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/19/4141/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lennart Bondesson, 2015. "A Class of Probability Distributions that is Closed with Respect to Addition as Well as Multiplication of Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 28(3), pages 1063-1081, September.
    Full references (including those not matched with items on IDEAS)

    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. Anthony G. Pakes, 2020. "Self-Decomposable Laws from Continuous Branching Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 361-395, March.
    2. Higbee, Joshua D. & McDonald, James B., 2024. "A comparison of the GB2 and skewed generalized log-t distributions with an application in finance," Journal of Econometrics, Elsevier, vol. 240(2).

    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:gam:jmathe:v:11:y:2023:i:19:p:4141-:d:1251857. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.