Big Outliers Versus Heavy Tails: what to use?

TL;DR

This paper discusses mathematical definitions of outliers and heavy-tailed distributions, proposing alternatives for tail index measures to better characterize distribution tails.

Contribution

It introduces new definitions and alternative measures for tail index, enhancing the understanding of outliers and heavy tails in statistical distributions.

Findings

Proposes mathematical definitions for outliers and heavy tails.

Suggests alternative tail index measures.

Provides insights into distribution tail characterization.

Abstract

A possibility to give strong mathematical definitions of outliers and heavy tailed distributions or their modification is discussed. Some alternatives for the notion of tail index are proposed. Key words: outliers, heavy tails, tail index.