A new notion of majorization with applications to the comparison of extreme order statistics

TL;DR

This paper introduces the f-majorization order, a new partial order that generalizes existing majorization concepts, and applies it to compare extreme order statistics in various stochastic models.

Contribution

The paper defines the f-majorization order, explores its properties, and demonstrates its applications in stochastic comparison of extreme order statistics across different distributional and dependence structures.

Findings

f-majorization includes majorization, reciprocal majorization, and p-larger orders

New stochastic comparison results for extreme order statistics

Applications to series systems with heterogeneous components

Abstract

In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the mathematical properties of the f-majorization order and give applications of this order in the context of stochastic comparison for extreme order statistics of independent samples following the Frechet distribution and scale model. We discuss stochastic comparisons of series systems with independent heterogeneous exponentiated scale components in terms of the usual stochastic order and the hazard rate order. We also derive new result on the usual stochastic order for the largest order statistics of samples having exponentiated scale marginals and Archimedean copula structure.