Further examples of GGC and HCM densities

Abstract

We display several examples of generalized gamma convoluted and hyperbolically completely monotone random variables related to positive $\alpha$-stable laws. We also obtain new factorizations for the latter, refining Kanter's and Pestana-Shanbhag-Sreehari's. These results give stronger credit to Bondesson's hypothesis that positive $\alpha$-stable densities are hyperbolically completely monotone whenever $\alpha \le 1/2.$

Published in at http://dx.doi.org/10.3150/12-BEJ431 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples

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