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 $\alpha\le1/2$.