On A New Class of Tempered Stable Distributions: Moments and Regular Variation

TL;DR

This paper extends tempered stable distributions to include more tail behaviors, providing detailed moment conditions and tail regular variation criteria, which help identify their domains of attraction.

Contribution

It introduces a new class of tempered stable distributions with enhanced structure and tail diversity, along with moment and tail behavior characterizations.

Findings

Detailed conditions for finiteness of moments

Necessary and sufficient conditions for regular variation

Characterization of domains of attraction

Abstract

We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss various subclasses and the relation between them. To characterize the possible tails we give detailed results about finiteness of various moments. We also give necessary and sufficient conditions for the tails to be regularly varying. This last part allows us to characterize the domain of attraction to which a particular tempered stable distribution belongs.