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Which Urbanik class Lk, do the hyperbolic and the generalized logistic characteristic functions belong to?

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  • Jurek, Zbigniew J.

Abstract

Selfdecomposable variables obtained from series of Laplace (double exponential) variables are objects of this study. We prove that hyperbolic-sine and hyperbolic-cosine variables are in the difference of the Urbanik classes L2 and L3 while generalized logistic variable is at least in the Urbanik class L1. Hence some ratios of those corresponding selfdecomposable characteristic functions are again selfdecomposable.

Suggested Citation

  • Jurek, Zbigniew J., 2023. "Which Urbanik class Lk, do the hyperbolic and the generalized logistic characteristic functions belong to?," Statistics & Probability Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s016771522300038x
    DOI: 10.1016/j.spl.2023.109814
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    References listed on IDEAS

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    1. Jurek, Zbigniew J., 1983. "Limit distributions and one-parameter groups of linear operators on Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 578-604, December.
    2. Jurek, Zbigniew J., 2000. "A note on gamma random variables and Dirichlet series," Statistics & Probability Letters, Elsevier, vol. 49(4), pages 387-392, October.
    3. Sato, Ken-iti, 1980. "Class L of multivariate distributions and its subclasses," Journal of Multivariate Analysis, Elsevier, vol. 10(2), pages 207-232, June.
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