Bernstein-Type Bounds for Beta Distribution
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929548195528704 |
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| author | Skorski, Maciej |
| author_facet | Skorski, Maciej |
| contents | This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context.
The proof leverages a novel handy recursion of order 2 for central moments of the beta distribution, obtained from the hypergeometric representations of moments; this recursion is useful for obtaining explicit expressions for central moments and various tail approximations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_02094 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bernstein-Type Bounds for Beta Distribution Skorski, Maciej Probability Statistics Theory Applications 60E05 G.3 This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a novel handy recursion of order 2 for central moments of the beta distribution, obtained from the hypergeometric representations of moments; this recursion is useful for obtaining explicit expressions for central moments and various tail approximations. |
| title | Bernstein-Type Bounds for Beta Distribution |
| topic | Probability Statistics Theory Applications 60E05 G.3 |
| url | https://arxiv.org/abs/2101.02094 |