Title :

On the unimodality of power transformations of positive stable densities

Author(s) :

Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Mathematical News / Mathematische Nachrichten

Pages :

497-506

Publisher :

Wiley-VCH Verlag

Publication date :

2011-11-24

ISSN :

0025-584X

English keyword(s) :

Bernstein function
Complete monotonicity
Kanter function
Mittag-Leffler function
Positive stable distribution
Unimodality

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

Let $Z_\alpha$ be a positive $\alpha-$stable random variable and $r\in{\bf R}.$ We show the existence of an unbounded open domain $D$ in $[1/2,1]\times{\bf R}$ with a cusp at $(1/2,-1/2)$, characterized by the complete ...
Show more >Let $Z_\alpha$ be a positive $\alpha-$stable random variable and $r\in{\bf R}.$ We show the existence of an unbounded open domain $D$ in $[1/2,1]\times{\bf R}$ with a cusp at $(1/2,-1/2)$, characterized by the complete monotonicity of the function $F_{\alpha, r} (\lambda) = (\alpha \lambda^\alpha -r)e^{-\lambda^\alpha}\!\! ,$ such that $Z_\alpha^r$ is unimodal if and only if $(\alpha, r)\notin D.$Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Etude de certains processus autosimilaires et applications

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T10:10:48Z