Positive stable densities and the bell-shape
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Abstract:
We show that positive stable densities are bell-shaped; that is, their $n$-th derivatives vanish exactly $n$ times on $(0,+\infty )$ and have an alternating sign sequence. This confirms the graphic predictions of Holt and Crow (1973) in the positive case.References
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Additional Information
- Thomas Simon
- Affiliation: Laboratoire Paul Painlevé, Université Lille 1, Cité Scientifique, 59655 Villeneuve d’Ascq Cedex, France
- MR Author ID: 640288
- Email: simon@math.univ-lille1.fr
- Received by editor(s): February 4, 2013
- Received by editor(s) in revised form: May 10, 2013
- Published electronically: October 8, 2014
- Additional Notes: Ce travail a bénéficié d’une aide de l’Agence Nationale de la Recherche portant la référence ANR-09-BLAN-0084-01.
- Communicated by: Mark M. Meerschaert
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 885-895
- MSC (2010): Primary 60E07, 62E15
- DOI: https://doi.org/10.1090/S0002-9939-2014-12256-8
- MathSciNet review: 3283675