Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Stat Year : 2020

Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions

Abstract

We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to potentially heavier-tailed distributions. Sub-Weibull distributions are parameterized by a positive tail index θ and reduce to sub-Gaussian distributions for θ = 1/2 and to sub-Exponential distributions for θ = 1. A characterisation of the sub-Weibull property based on moments and on the moment generating function is provided and properties of the class are studied. An estimation procedure for the tail parameter is proposed and is applied to an example stemming from Bayesian deep learning.
Fichier principal
Vignette du fichier
paper_2020_Sub_Weibull__arXiv_.pdf (525.68 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02545121 , version 1 (16-04-2020)
hal-02545121 , version 2 (30-11-2020)

Identifiers

Cite

Mariia Vladimirova, Stéphane Girard, Hien Nguyen, Julyan Arbel. Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions. Stat, 2020, 9 (1), pp.e318:1-8. ⟨10.1002/sta4.318⟩. ⟨hal-02545121v2⟩
157 View
1296 Download

Altmetric

Share

Gmail Facebook X LinkedIn More