A note on power generalized extreme value distribution and its properties

TL;DR

This paper investigates the properties of power normalized generalized extreme value distributions, focusing on their asymptotic behavior, moments, entropy, and applications to real data, revealing entropy and variance ordering under certain conditions.

Contribution

It provides new insights into the asymptotic properties, moments, and entropy of power normalized GEV distributions, extending understanding beyond classical GEV models.

Findings

Derived expressions for moments and entropy of power normalized GEV distributions

Showed conditions under which Shannon entropy and variance are ordered

Applied findings to real data set analysis

Abstract

Similar to the generalized extreme value (GEV) family, the generalized extreme value distributions under power normalization are introduced by Roudsari (1999) and Barakat et al. (2013). In this article, we study the asymptotic behavior of GEV laws under power normalization and derive expressions for the kth moments, entropy, ordering in dispersion, rare event estimation and application of real data set. We also show that, under some conditions, the Shannon entropy and variance of GEV families are ordered.