Positive stable densities and the bell-shape

Simon, Thomas

doi:10.1090/S0002-9939-2014-12256-8

Positive stable densities and the bell-shape
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Proc. Amer. Math. Soc. 143 (2015), 885-895 Request permission

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.

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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