Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/hal-02545121
Contributor : Mariia Vladimirova <>
Submitted on : Monday, November 30, 2020 - 5:43:16 PM
Last modification on : Thursday, December 3, 2020 - 5:36:18 PM

File

paper_2020_Sub_Weibull__arXiv_...
Files produced by the author(s)

Identifiers

Collections

Citation

Mariia Vladimirova, Stéphane Girard, Hien Nguyen, Julyan Arbel. Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions. Stat, John Wiley & Sons, 2020, ⟨10.1002/sta4.318⟩. ⟨hal-02545121v2⟩

Share

Metrics

Record views

23

Files downloads

146