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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive stable densities and the bell-shape
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by Thomas Simon PDF
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