On some analytical properties of stable densities
Probability
2016-04-27 v1
Abstract
L.Bondesson [1] conjectured that the density of a positive -stable distribution is hyperbolically completely monotone (HCM in short) if and only if 1/2. This was proved recently by P. Bosch and Th. Simon, who also conjectured a strengthened version of this result. We disprove this conjecture as well as a correlated conjecture of Bondesson, while giving a short new proof of the initial conjecture, as a direct consequence of a new algebraic property of HCM and Generalized Gamma convolution densities (GGC in short) which we establish.
Keywords
Cite
@article{arxiv.1604.07705,
title = {On some analytical properties of stable densities},
author = {Sonia Fourati},
journal= {arXiv preprint arXiv:1604.07705},
year = {2016}
}