Titre :

A note on the α-Sun distribution

Auteur(s) :

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

Titre de la revue :

Electronic Communications in Probability

Pagination :

1-13

Éditeur :

Institute of Mathematical Statistics (IMS)

Date de publication :

2023-04-08

ISSN :

1083-589X

Mot(s)-clé(s) en anglais :

Generalized gamma convolution
integro-differential equation
multiplicative martingale
perpetuity
subordinator
α−sun random variable

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

We investigate the analytical properties of the α-Sun random variable, which arises from the domain of attraction of certain storage models involving a maximum and a sum. In the Fréchet case we show that this random variable ...
Lire la suite >We investigate the analytical properties of the α-Sun random variable, which arises from the domain of attraction of certain storage models involving a maximum and a sum. In the Fréchet case we show that this random variable is infinitely divisible, and we give the exact behaviour of the density at zero. In the Weibull case we give the exact behaviour of the density at infinity, and we show that the behaviour at zero is neither polynomial nor exponential. This answers the open questions in a recent paper by Greenwood and Witte.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T12:21:36Z