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The mean of the reciprocal in a Cauchy–Stieltjes family

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  • Fakhfakh, Raouf

Abstract

If the distribution of X belongs to a Cauchy–Stieltjes Kernel (CSK) family concentrated on the positive real line, we determine the expectation of the reciprocal of X as a function of the expectation m of X. This function characterizes the CSK family. Some examples and characterizations of quadratic and cubic CSK families are given.

Suggested Citation

  • Fakhfakh, Raouf, 2017. "The mean of the reciprocal in a Cauchy–Stieltjes family," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 1-11.
    • Handle: RePEc:eee:stapro:v:129:y:2017:i:c:p:1-11
    DOI: 10.1016/j.spl.2017.04.021
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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, 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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    Cited by:

    1. Fakhfakh, Raouf, 2020. "Variance function of boolean additive convolution," Statistics & Probability Letters, Elsevier, vol. 163(C).
    2. Fakhfakh, Raouf, 2022. "A characterization of the Marchenko–Pastur probability measure," Statistics & Probability Letters, Elsevier, vol. 191(C).
    3. 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.

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    1. Fakhfakh, Raouf, 2022. "A characterization of the Marchenko–Pastur probability measure," Statistics & Probability Letters, Elsevier, vol. 191(C).
    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, 2020. "Variance function of boolean additive convolution," Statistics & Probability Letters, Elsevier, vol. 163(C).
    4. 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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