Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Multiplicative strong unimodality for positive stable laws

Author: Thomas Simon
Journal: Proc. Amer. Math. Soc. 139 (2011), 2587-2595
MSC (2010): Primary 60E07, 60E15
Published electronically: December 20, 2010
MathSciNet review: 2784828
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Abstract: It is known that real non-Gaussian stable laws are unimodal, not additive strongly unimodal, multiplicative strongly unimodal in the symmetric case, and that the only remaining relevant situation for the multiplicative strong unimodality is the one-sided case. It is shown here that positive $ \alpha$-stable distributions are multiplicative strongly unimodal if and only if $ \alpha\le 1/2.$

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Thomas Simon
Affiliation: Laboratoire Paul Painlevé, U. F. R. de Mathématiques, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France

Keywords: Beta and Gamma variables, log-concavity, positive stable law, strong unimodality
Received by editor(s): March 6, 2010
Received by editor(s) in revised form: July 5, 2010
Published electronically: December 20, 2010
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.