Multiplicative strong unimodality for positive stable laws
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- Proc. Amer. Math. Soc. 139 (2011), 2587-2595 Request permission
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 $\alpha \le 1/2.$References
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Additional Information
- Thomas Simon
- Affiliation: Laboratoire Paul Painlevé, U. F. R. de Mathématiques, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France
- MR Author ID: 640288
- Email: simon@math.univ-lille1.fr
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2587-2595
- MSC (2010): Primary 60E07, 60E15
- DOI: https://doi.org/10.1090/S0002-9939-2010-10697-4
- MathSciNet review: 2784828