# Domains of Attraction for Positive and Discrete Tempered Stable Distributions

## TL;DR

This paper introduces a broad class of discrete tempered stable distributions and analyzes their domains of attraction, showing they are suitable models for sums of i.i.d. variables with tempered heavy tails that decay faster at infinity.

## Contribution

It presents a new, flexible class of discrete tempered stable distributions and characterizes their domains of attraction, extending understanding of heavy-tailed distributions with tempered decay.

## Key findings

- Discrete tempered stable distributions are natural models for tempered heavy-tailed sums.
- Domains of attraction for these distributions are characterized.
- Results support their applicability in modeling tempered heavy tails.

## Abstract

We introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempered stable distributions. Our results suggest that these are natural models for sums of independent and identically distributed random variables with tempered heavy tails tails, i.e. tails that appear to be heavy up to a point, but ultimately decay faster.