Title :

Fractional extreme distributions

Author(s) :

Boudabsa, Lotfi [Auteur]
Ecole Polytechnique Fédérale de Lausanne [EPFL]
Simon, Thomas [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Vallois, Pierre [Auteur]
Institut Élie Cartan de Lorraine [IECL]

Journal title :

Electronic Journal of Probability

Pages :

1-20

Publisher :

Institute of Mathematical Statistics (IMS)

Publication date :

2020-09-05

ISSN :

1083-6489

English keyword(s) :

Double Gamma function
extreme distribution
fractional differential equation
Kilbas-Saigo function
Le Roy function
stable subordinator

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We consider three classes of linear differential equations on distribution functions, with a fractional order α ∈ [0,1]. The integer case α = 1 corresponds to the three classical extreme families. In general, we show that ...
Show more >We consider three classes of linear differential equations on distribution functions, with a fractional order α ∈ [0,1]. The integer case α = 1 corresponds to the three classical extreme families. In general, we show that there is a unique distribution function solving these equations, whose underlying random variable is expressed in terms of an exponential random variable and an integral transform of an independent α-stable subordinator. From the analytical viewpoint, this distribution is in one-to-one correspondence with a Kilbas-Saigo function for the Weibull and Fréchet cases, and with a Le Roy function for the Gumbel caseShow less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL