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On some properties of Cauchy-Stieltjes Kernel families

Author

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  • Raouf Fakhfakh

    (Jouf University
    Sfax University)

Abstract

We explore properties of Cauchy-Stieltjes Kernel (CSK) families that have the same counterpart in natural exponential families (NEFs). We determine the variance function of the finite mixtures of a CSK family with its length-biased family. We also prove that, for a more natural definition for the domain of means, the new domain of means scale nicely under affine transformation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:4:d:10.1007_s13226-021-00020-z
    DOI: 10.1007/s13226-021-00020-z
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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, Włodek & Fakhfakh, Raouf & Hassairi, Abdelhamid, 2014. "On Cauchy–Stieltjes kernel families," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 295-312.
    3. Fakhfakh, Raouf, 2017. "The mean of the reciprocal in a Cauchy–Stieltjes family," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 1-11.
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    Cited by:

    1. Fakhfakh, Raouf, 2022. "A characterization of the Marchenko–Pastur probability measure," Statistics & Probability Letters, Elsevier, vol. 191(C).

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