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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
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    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.
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