Location- and scale-free procedures for distinguishing between distribution tail models

TL;DR

This paper introduces two new procedures for distinguishing between distribution tail models, emphasizing their scale-free properties, and demonstrates their effectiveness through theoretical analysis, simulations, and real-world precipitation data applications.

Contribution

The paper proposes novel scale-free and location- and scale-free procedures for tail model discrimination, with proven asymptotic properties and improved performance over existing tests.

Findings

Procedures are asymptotically consistent.

Simulation shows superior performance over existing methods.

Applied successfully to precipitation data from Green Bay and Saentis.

Abstract

We consider distinguishing between two distribution tail models when tails of one model are lighter (or heavier) than those of the other. Two procedures are proposed: one scale-free and one location- and scale-free, and their asymptotic properties are established. We show the advantage of using these procedures for distinguishing between certain tail models in comparison with the tests proposed in the literature by simulation and apply them to data on daily precipitation in Green Bay, US and Saentis, Switzerland.