Which Urbanik class $L_k$, do the hyperbolic and the generalized logistic characteristic functions belong to?
Probability
2022-12-01 v1 Classical Analysis and ODEs
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 and while generalized logistic variable is at least in the Urbanik class . Hence some ratios of those corresponding selfdecomposable characteristic functions are again selfdecomposable.
Keywords
Cite
@article{arxiv.2211.17064,
title = {Which Urbanik class $L_k$, do the hyperbolic and the generalized logistic characteristic functions belong to?},
author = {Zbigniew J. Jurek},
journal= {arXiv preprint arXiv:2211.17064},
year = {2022}
}