On discrimination between classes of distribution tails

TL;DR

This paper introduces a new statistical test to differentiate between two classes of distribution tails using only the largest sample values, without assuming specific distribution domain properties, and proves its consistency.

Contribution

The paper presents a novel tail discrimination test that does not require assumptions about the distribution's domain of attraction and establishes its theoretical consistency.

Findings

Test effectively distinguishes distribution tail classes

Proven to be consistent under broad conditions

Operates using only extreme order statistics

Abstract

We propose the test for distinguishing between two classes of distribution tails using only the largest order statistics of the sample and state its consistency. We do not assume belonging the corresponding distribution functions to any maximum domain of attraction.