IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i5p818-d1602825.html
   My bibliography  Save this article

On T -Transformation of Probability Measures

Author

Listed:
  • Shokrya S. Alshqaq

    (Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia)

  • Ohud A. Alqasem

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Raouf Fakhfakh

    (Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72311, Saudi Arabia)

Abstract

The concept of the ( T = ( s , t ) ) -transformation of probability measures, introduced for s > 0 and t ∈ R , is examined in this work from the perspective of Cauchy–Stieltjes kernel (CSK) families and their related variance functions (VFs). We calculate the VF formula under the T -transformation of measures. Furthermore, the stability of the free Meixner family ( FMF ) of probability measures under the ( T = ( s , t ) ) -transformation is significantly shown based on this formula. Additionally, the Wigner’s semicircle CSK family is given a novel characterization based on the ( 1 , t ) -transformation of probability measures.

Suggested Citation

  • Shokrya S. Alshqaq & Ohud A. Alqasem & Raouf Fakhfakh, 2025. "On T -Transformation of Probability Measures," Mathematics, MDPI, vol. 13(5), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:818-:d:1602825
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/5/818/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/5/818/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Włodzimierz Bryc & Abdelhamid Hassairi, 2011. "One-Sided Cauchy–Stieltjes Kernel Families," Journal of Theoretical Probability, Springer, vol. 24(2), pages 577-594, June.
    2. Bryc, Włodek & Fakhfakh, Raouf & Hassairi, Abdelhamid, 2014. "On Cauchy–Stieltjes kernel families," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 295-312.
    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. Fakhfakh, Raouf, 2017. "The mean of the reciprocal in a Cauchy–Stieltjes family," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 1-11.
    2. Raouf Fakhfakh, 2021. "On some properties of Cauchy-Stieltjes Kernel families," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(4), pages 1186-1200, December.
    3. Fakhfakh, Raouf, 2022. "A characterization of the Marchenko–Pastur probability measure," Statistics & Probability Letters, Elsevier, vol. 191(C).
    4. Ayed. R. A. Alanzi & Ohud A. Alqasem & Maysaa Elmahi Abd Elwahab & Raouf Fakhfakh, 2024. "Studies on the Marchenko–Pastur Law," Mathematics, MDPI, vol. 12(13), pages 1-10, July.
    5. Fakhfakh, Raouf, 2020. "Variance function of boolean additive convolution," Statistics & Probability Letters, Elsevier, vol. 163(C).
    6. Fahad Alsharari & Raouf Fakhfakh & Fatimah Alshahrani, 2025. "Analytical Bounds for Mixture Models in Cauchy–Stieltjes Kernel Families," Mathematics, MDPI, vol. 13(3), pages 1-9, January.
    7. Ayed. R. A. Alanzi & Shokrya S. Alshqaq & Raouf Fakhfakh, 2024. "Stability of Cauchy–Stieltjes Kernel Families by Free and Boolean Convolutions Product," Mathematics, MDPI, vol. 12(22), pages 1-9, November.
    8. Bryc, Włodek & Fakhfakh, Raouf & Hassairi, Abdelhamid, 2014. "On Cauchy–Stieltjes kernel families," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 295-312.
    9. Fahad Alsharari & Raouf Fakhfakh & Fatimah Alshahrani, 2025. "Invariance Property of Cauchy–Stieltjes Kernel Families Under Free and Boolean Multiplicative Convolutions," Mathematics, MDPI, vol. 13(7), pages 1-9, March.

    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:13:y:2025:i:5:p:818-:d:1602825. 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.