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Pré-Publication, Document De Travail Année : 2024

Simple sufficient criteria for second-order extended regular variation in the Gumbel domain of attraction

Résumé

Statistical theory for the estimators of the location, scale and shape parameters of the approximating Generalized Pareto distribution in the Peaks-Over-Threshold approach to extreme value statistics typically requires a second-order extended regular variation condition on the tail quantile function of the distribution underlying the random variable of interest. Somewhat surprisingly, the existing sufficient criteria ensuring that this condition holds appear not to easily apply to many common light-tailed distributions, from the well-known Gaussian, log-normal and Gamma distributions to more specific examples arising in finance and reliability theory. We provide several sufficient criteria based on the computation of appropriate asymptotic expansions of a distribution function or of its quantile function. A list of examples to which our theory applies is given.
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Dates et versions

hal-04667111 , version 1 (02-08-2024)

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  • HAL Id : hal-04667111 , version 1

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Gilles Stupfler, Antoine Usseglio-Carleve. Simple sufficient criteria for second-order extended regular variation in the Gumbel domain of attraction. 2024. ⟨hal-04667111⟩
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