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arXiv · 2602.23775

Novel Stein-type Characterizations of Bivariate Count Distributions with Applications

Shaochen Wang·Christian H. Weiß
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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.

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Shaochen Wang, Christian H. Weiß. 2026-02-27. Novel Stein-type Characterizations of Bivariate Count Distributions with Applications. https://arxiv.org/abs/2602.23775

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