Rates of convergence towards the Fréchet distribution

Bartholmé, Carine; Swan, Yvik

doi:10.48550/arxiv.1311.3896

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2020

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Cited by 2 publications

(2 citation statements)

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“…The standard Fisher score was used in an extreme value context in [4] in a version of Stein's method. Extreme value distributions were considered in the context of Tsallis entropy in [5].…”

Section: Introduction and Notationmentioning

confidence: 99%

Information-theoretic convergence of extreme values to the Gumbel distribution

Johnson

2023

J. Appl. Probab.

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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.

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“…The standard Fisher score was used in an extreme value context in [4] in a version of Stein's method. Extreme value distributions were considered in the context of Tsallis entropy in [5].…”

Section: Introduction and Notationmentioning

confidence: 99%

Information-theoretic convergence of extreme values to the Gumbel distribution

Johnson

2023

J. Appl. Probab.

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show abstract

“…We briefly remark that entropy was studied in this regime by Saeb [17], though using a direct computation based on the density. The standard Fisher score was used in an extreme value context by Bartholmé and Swan [2] in a version of Stein's method. Extreme value distributions were considered in the context of Tsallis entropy by Bercher and Vignat [3].…”

Section: Introduction and Notationmentioning

confidence: 99%

Information-theoretic convergence of extreme values to the Gumbel distribution

Johnson¹

2020

Preprint

View full text Add to dashboard Cite

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.

show abstract

Rates of convergence towards the Fréchet distribution

Abstract: We develop Stein's method for the Fréchet distribution and apply it to compute rates of convergence in distribution of renormalized sample maxima to the Fréchet distribution.

Cited by 2 publications

References 8 publications

Information-theoretic convergence of extreme values to the Gumbel distribution

Information-theoretic convergence of extreme values to the Gumbel distribution

Information-theoretic convergence of extreme values to the Gumbel distribution

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