Further examples of GGC and HCM densities

Wissem Jedidi; Thomas Simon

doi:10.3150/12-BEJ431

Further examples of GGC and HCM densities

Statistics Theory 2013-12-11 v1 Statistics Theory

Authors: Wissem Jedidi , Thomas Simon

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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 $\alpha\le1/2.$

Keywords

generalized gamma convoluted hyperbolically completely monotone positive alpha-stable laws random variables factorizations Bondesson's hypothesis densities

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@article{arxiv.1312.2809,
  title  = {Further examples of GGC and HCM densities},
  author = {Wissem Jedidi and Thomas Simon},
  journal= {arXiv preprint arXiv:1312.2809},
  year   = {2013}
}

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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)

Further examples of GGC and HCM densities

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