Titre :

HCM PROPERTY AND THE HALF-CAUCHY DISTRIBUTION

Auteur(s) :

Bosch, Pierre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Mot(s)-clé(s) en anglais :

Half-Cauchy distribution
Complete monotonicity
Generalized gamma convolution
Hyperbolically completely monotone
Pick function
Positive stable density.
Positive stable density

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

Let $Z_\al$ be a positive $\alpha$-stable random variable and $T_\al=(Z_\al/\tilde Z_\al)^\al,$ with independents components in the quotient. It is known that $T_\al$ is distributed as the positive branch of a Cauchy random ...
Lire la suite >Let $Z_\al$ be a positive $\alpha$-stable random variable and $T_\al=(Z_\al/\tilde Z_\al)^\al,$ with independents components in the quotient. It is known that $T_\al$ is distributed as the positive branch of a Cauchy random variable with drift. We show that the density of the power transformation $T_\al^\beta$ is hyperbolically completely monotone in the sense of Thorin and Bondesson if and only if $\al\le1/2$ and $|\beta|\ge 1/(1-\al).$ This clarifies a conjecture of Bondesson (1992) on positive stable densities.Lire moins >

Langue :

Anglais

Commentaire :

11 pages

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-22T07:19:26Z