Exponential tilting of subweibull distributions

TL;DR

This paper explores the properties of subweibull distributions, focusing on their characterization and how exponential tilting affects their tail behavior, which is important for understanding their probabilistic properties.

Contribution

It provides new characterizations of subweibull distributions and identifies conditions under which their tail behavior remains intact after exponential tilting.

Findings

Subweibull distributions generalize subexponential and subgaussian variables.

Exponential tilting preserves tail behavior under specific conditions.

New characterizations of subweibull distributions are proposed.

Abstract

The class of subweibull distributions has recently been shown to generalize the important properties of subexponential and subgaussian random variables. We describe alternative characterizations of subweibull distributions and detail the conditions under which their tail behavior is preserved after exponential tilting.