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On Cauchy–Stieltjes kernel families

Author

Listed:
  • Bryc, Włodek
  • Fakhfakh, Raouf
  • Hassairi, Abdelhamid

Abstract

We explore properties of Cauchy–Stieltjes families that have no counterpart in exponential families. We relate the variance function of the iterated Cauchy–Stieltjes family to the pseudo-variance function of the initial Cauchy–Stieltjes family. We also investigate when the domain of means can be extended beyond the “natural domain”.

Suggested Citation

  • Bryc, Włodek & Fakhfakh, Raouf & Hassairi, Abdelhamid, 2014. "On Cauchy–Stieltjes kernel families," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 295-312.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:295-312
    DOI: 10.1016/j.jmva.2013.10.021
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    References listed on IDEAS

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    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, Wlodek, 2010. "Markov processes with free-Meixner laws," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1393-1403, August.
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    Cited by:

    1. 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.
    2. Fakhfakh, Raouf, 2020. "Variance function of boolean additive convolution," Statistics & Probability Letters, Elsevier, vol. 163(C).
    3. Fakhfakh, Raouf, 2017. "The mean of the reciprocal in a Cauchy–Stieltjes family," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 1-11.
    4. Fakhfakh, Raouf, 2022. "A characterization of the Marchenko–Pastur probability measure," Statistics & Probability Letters, Elsevier, vol. 191(C).

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