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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2308.11168 |
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| _version_ | 1866913583668920320 |
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| author | Su, Zhonggen Wang, Xiaolin |
| author_facet | Su, Zhonggen Wang, Xiaolin |
| contents | Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectations and variances. We consider the sum $W=\sum_{i\in J}X_i$ and use Stein's method to establish general upper error bounds for the total variation distance $d_{TV}(W, M)$, where $M$ represents a three-parameter random variable. As a direct consequence, we obtain a discretized normal approximation for $W$. As applications, we study in detail four well-known examples, which are counting vertices of all edges point inward, birthday problem, counting monochromatic edges in uniformly colored graphs, and triangles in the Erdős-Rényi random graph. Through delicate analysis and computations, we obtain sharper upper error bounds than existing results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11168 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Three-Parameter Approximations of Sums of Locally Dependent Random Variables via Stein's Method Su, Zhonggen Wang, Xiaolin Probability Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectations and variances. We consider the sum $W=\sum_{i\in J}X_i$ and use Stein's method to establish general upper error bounds for the total variation distance $d_{TV}(W, M)$, where $M$ represents a three-parameter random variable. As a direct consequence, we obtain a discretized normal approximation for $W$. As applications, we study in detail four well-known examples, which are counting vertices of all edges point inward, birthday problem, counting monochromatic edges in uniformly colored graphs, and triangles in the Erdős-Rényi random graph. Through delicate analysis and computations, we obtain sharper upper error bounds than existing results. |
| title | Three-Parameter Approximations of Sums of Locally Dependent Random Variables via Stein's Method |
| topic | Probability |
| url | https://arxiv.org/abs/2308.11168 |