Outliers, the Law of Large Numbers, Index of Stability and Heavy Tails

TL;DR

This paper proposes a mathematically rigorous definition of outliers using order statistics, linking it to the law of large numbers and heavy-tailed distributions, with implications for stability analysis.

Contribution

It introduces a novel, mathematically sound definition of outliers based on order statistics and explores its connection to the law of large numbers and heavy tails.

Findings

New definition of outliers based on order statistics

Connection established between outliers and the law of large numbers

Implications for heavy-tailed distributions and stability index

Abstract

We are trying to give a mathematically correct definition of outliers. Our approach is based on the distance between two last order statistics and appears to be connected to the law of large numbers. Key words: outliers, law of large numbers, heavy tails, stability index.