Fractional extreme distributions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Electronic Journal of Probability Année : 2020

Fractional extreme distributions

Résumé

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 case
Fichier principal
Vignette du fichier
20-EJP520.pdf (282.67 Ko) Télécharger le fichier
Origine : Publication financée par une institution

Dates et versions

hal-04383263 , version 1 (09-04-2024)

Identifiants

Citer

Lotfi Boudabsa, Thomas Simon, Pierre Vallois. Fractional extreme distributions. Electronic Journal of Probability, 2020, 25, pp.1-20. ⟨10.1214/20-EJP520⟩. ⟨hal-04383263⟩
8 Consultations
1 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More