Distance between exact and approximate distributions of partial maxima under power normalization

TL;DR

This paper investigates the similarity between exact and approximate distributions of partial maxima under power normalization, revealing that certain distance measures are invariant to the type of normalization used.

Contribution

It demonstrates that the Hellinger and variational distances between these distributions are identical under both power and linear normalization, providing new insights into distribution approximation.

Findings

Hellinger and variational distances are equal under power and linear normalization.

Distances between distributions of partial maxima are invariant to normalization type.

Results facilitate better understanding of distribution approximation in extreme value theory.

Abstract

We obtain the distance between the exact and approximate distributions of partial maxima of a random sample under power normalization. It is observed that the Hellinger distance and variational distance between the exact and approximate distributions of partial maxima under power normalization is the same as the corresponding distances under linear normalization.