Which Urbanik class Lk, do the hyperbolic and the generalized logistic characteristic functions belong to?
Abstract
Selfdecomposable variables obtained from series of Laplace (double exponential) variables are objects of this study. We proved 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.
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