On discrete approximations of stable distributions

TL;DR

This paper proposes methods to approximate stable distributions with discrete distributions that can better model data with lighter tails, offering an alternative to tempered stable distributions that blend Gaussian and stable characteristics.

Contribution

It introduces novel discrete approximation methods for stable distributions, addressing tail behavior differences and providing alternatives to tempered stable models.

Findings

Discrete approximations can effectively model lighter tails.

Proposed methods offer flexible tail behavior in stable distribution approximation.

Alternative models combine Gaussian and stable features.

Abstract

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several methods of approximation of stable distributions by some discrete distributions, which may have different tail behavior. In a sense the introduced distributions form an alternative to tempered stable distributions that combine Gaussian and stable behavior.