Comparisons of Order Statistics from Some Heterogeneous Discrete Distributions

TL;DR

This paper compares the extreme order statistics of heterogeneous Poisson and geometric distributions using vector majorization and stochastic ordering to understand their probabilistic behavior.

Contribution

It introduces a novel comparison framework for order statistics from heterogeneous discrete distributions based on vector majorization and stochastic orderings.

Findings

Order statistics from heterogeneous Poisson and geometric variables can be compared using majorization.

Stochastic dominance relationships are established between different order statistics.

The results provide insights into the probabilistic structure of heterogeneous discrete distributions.

Abstract

In this paper, we compare extreme order statistics through vector majorization arising from heterogeneous Poisson and geometric random variables. These comparisons are carried out with respect to usual stochastic ordering.