Abstract
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 distribution can be proved in the
strong sense of relative entropy.
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 distribution can be proved in the
strong sense of relative entropy.
| Original language | English |
|---|---|
| Pages (from-to) | 244-254 |
| Number of pages | 11 |
| Journal | Journal of Applied Probability |
| Volume | 61 |
| Issue number | 1 |
| Early online date | 21 Jun 2023 |
| DOIs | |
| Publication status | Published - 1 Mar 2024 |
Bibliographical note
Publisher Copyright:© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust.