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

Zbigniew J. Jurek

Statistics & Probability Letters, 2023, vol. 197, issue C

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.

Keywords: Selfdecomposability; Lévy process; Urbanik classes; Random integral; Hyperbolic characteristic functions; Generalized logistic distribution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109814

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