Paper
Novel Stein-type Characterizations of Bivariate Count Distributions with Applications
Authors
Shaochen Wang, Christian H. Weiß
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.23775v1</id>\n <title>Novel Stein-type Characterizations of Bivariate Count Distributions with Applications</title>\n <updated>2026-02-27T08:09:35Z</updated>\n <link href='https://arxiv.org/abs/2602.23775v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.23775v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='stat.ME'/>\n <published>2026-02-27T08:09:35Z</published>\n <arxiv:primary_category term='stat.ME'/>\n <author>\n <name>Shaochen Wang</name>\n </author>\n <author>\n <name>Christian H. Weiß</name>\n </author>\n </entry>"
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