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 α-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 α-stable densities are hyperbolically completely monotone whenever α ≤ 1/2. © 2013 ISI/BS.