Novel Stein-type Characterizations of Bivariate Count Distributions with Applications

TL;DR

This paper develops new Stein-type characterizations for bivariate count distributions and demonstrates their applications in moment calculations, goodness-of-fit testing, and symmetry testing, with real-world data analysis.

Contribution

It introduces novel Stein identities for bivariate Poisson, binomial, and negative-binomial distributions, expanding the tools for statistical analysis of count data.

Findings

Derived Stein identities for three bivariate count distributions

Enabled new goodness-of-fit and symmetry tests

Applied methods to real-world data examples

Abstract

The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by deriving and investigating Stein-type characterizations for the three most common types of bivariate count distributions, namely the bivariate Poisson, binomial, and negative-binomial distribution. Then, we demonstrate the practical relevance of these novel Stein identities by a couple of applications, namely the deduction of sophisticated moment expressions, of flexible goodness-of-fit tests, and of novel tests for the symmetry of bivariate count distributions. The paper concludes with an analysis of real-world data examples.