Information-theoretic convergence of extreme values to the Gumbel distribution
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866913435709603840 |
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| author | Johnson, Oliver |
| author_facet | Johnson, Oliver |
| contents | We show how convergence to the Gumbel distribution in an extreme value setting can be understood in an information-theoretic sense. We introduce a new type of score function which behaves well under the maximum operation, and which implies simple expressions for entropy and relative entropy. We show that, assuming certain properties of the von Mises representation, convergence to the Gumbel can be proved in the strong sense of relative entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_03569 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Information-theoretic convergence of extreme values to the Gumbel distribution Johnson, Oliver Statistics Theory Information Theory We show how convergence to the Gumbel distribution in an extreme value setting can be understood in an information-theoretic sense. We introduce a new type of score function which behaves well under the maximum operation, and which implies simple expressions for entropy and relative entropy. We show that, assuming certain properties of the von Mises representation, convergence to the Gumbel can be proved in the strong sense of relative entropy. |
| title | Information-theoretic convergence of extreme values to the Gumbel distribution |
| topic | Statistics Theory Information Theory |
| url | https://arxiv.org/abs/2007.03569 |