Stochastic ordering of extreme order statistics in Archimax copula

TL;DR

This paper extends the theory of Archimax copulas to multivariate cases, analyzing the stochastic ordering of extreme order statistics and providing generalized results with graphical examples.

Contribution

It generalizes existing stochastic ordering results for extreme order statistics to the multivariate Archimax copula framework.

Findings

Generalized stochastic ordering results for extreme order statistics in Archimax copulas.

Proved stochastic ordering of sample extremes for PHR models within Archimax copulas.

Provided graphical illustrations of the theoretical results.

Abstract

An extension of Archimax copula class in more than two random variables ( Multivariate ) was introduced in (J\'agr 2011) for describing dependency structures among random variables in higher dimension, and some properties of Archimax copula were explored in (Charpentier et al. 2014). In this article, some results for stochastic ordering of extreme order statistics in (Li and Fang 2015) are generalized and proved in Archimax copula. Stochastic ordering of sample extremes for PHR models is generalized and proved in Archimax copula. Examples with graphical illustrations are also presented.