Novel Stein-type Characterizations of Bivariate Count Distributions with Applications
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917299283296256 |
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| author | Wang, Shaochen Weiß, Christian H. |
| author_facet | Wang, Shaochen Weiß, Christian H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23775 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Novel Stein-type Characterizations of Bivariate Count Distributions with Applications Wang, Shaochen Weiß, Christian H. Methodology 60E05, 62F03 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. |
| title | Novel Stein-type Characterizations of Bivariate Count Distributions with Applications |
| topic | Methodology 60E05, 62F03 |
| url | https://arxiv.org/abs/2602.23775 |