An easily verifiable dispersion order for discrete distributions

TL;DR

This paper introduces a new weak dispersive order for discrete distributions that overcomes limitations of classical orders, along with variability measures based on probability concentration, supported by empirical examples.

Contribution

It proposes a novel weak dispersive order for discrete distributions and introduces variability measures based on probability concentration, expanding applicability.

Findings

The new order relaxes structural constraints of classical dispersive order.

Variability measures based on probability concentration are robust and interpretable.

Empirical illustrations demonstrate practical relevance.

Abstract

Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous distributions, becomes overly restrictive for discrete random variables due to support inclusion requirements. To address this, we propose a novel weak dispersive order for discrete distributions. This order retains desirable properties while relaxing structural constraints, thereby broadening applicability. We further introduce a class of variability measures based on probability concentration, offering robust and interpretable alternatives that conform to classical axioms. Empirical illustrations highlight the practical relevance of this framework.