A factorial moment distance and an application to the matching problem

TL;DR

This paper introduces factorial moment distance for non-negative integer-valued variables, compares it with total variation distance, and analyzes convergence rates in classical and generalized matching problems.

Contribution

It proposes a new distance measure for discrete variables and applies it to study convergence in matching problems.

Findings

Factorial moment distance is distinct from total variation distance.

Convergence rates are established for classical matching problem.

Application to generalized matching distribution demonstrates versatility.

Abstract

In this note we introduce the notion of factorial moment distance for non-negative integer-valued random variables and we compare it with the total variation distance. Furthermore, we study the rate of convergence in the classical matching problem and in a generalized matching distribution.