Title :

A note on the α-Sun distribution

Author(s) :

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

Journal title :

Electronic Communications in Probability

Pages :

1-13

Publisher :

Institute of Mathematical Statistics (IMS)

Publication date :

2023-04-08

ISSN :

1083-589X

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T12:21:36Z