Modification of Pickands' Dependence Function for the Simulate Ordered Bivariate Extreme Data

TL;DR

This paper modifies Pickands' dependence function to better model the dependence structure in bivariate extreme data, especially for minima, and demonstrates its application through simulation.

Contribution

It introduces modified dependence functions tailored for extreme cases, enhancing the modeling of bivariate minima in extreme value theory.

Findings

Modified Pickands' functions fit simulated extreme data effectively

The approach improves understanding of dependence in bivariate minima

Application to simulated data validates the theoretical modifications

Abstract

We study the characteristics of the Pickands' dependence function for bivariate extreme distribution for minima, BEVM, when considering the stochastics ordering of the two variables. The existing Pickand's dependence function terminologies and theories are modified to suit the dependence functions of extreme cases. We successful implement and apply these functions to our simulate extreme data