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Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire
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This article is published in Annals of Mathematics.The article was published on 1943-07-01. It has received 2037 citations till now.read more
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The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution
TL;DR: In this paper, it was shown that the limit distribution of the maximum increment of a random walk is one of the classical extreme value distributions, the Fr\'{e}chet distribution.
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Extreme value analysis of the Haezendonck–Goovaerts risk measure with a general Young function
Qihe Tang,Fan Yang,Fan Yang +2 more
TL;DR: In this paper, the authors extended the asymptotic analysis for H q [X ] to the case with a general Young function and established a unified approach for the three extreme value cases for the Frechet, Weibull and Gumbel cases separately.
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Spacings around an order statistic
TL;DR: In this paper, the authors determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic of a random sample of size (i.i.d. exponential random variables) from a continuous distribution.
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A large deviation theory-based analysis of heat waves and cold spells in a simplified model of the general circulation of the atmosphere
Vera Melinda Galfi,Vera Melinda Galfi,Valerio Lucarini,Valerio Lucarini,Jeroen Wouters,Jeroen Wouters +5 more
TL;DR: In this paper, the authors study temporally persistent and spatially extended extreme events of temperature anomalies, i.e. heat waves and cold spells, using large deviation theory and find that large deviations are relatively more likely to occur when looking at these spatial averages performed over intermediate scales, thus pointing to the existence of weather patterns associated to the low-frequency variability of the atmosphere.
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A new three parameter Fréchet model with mathematical properties and applications
TL;DR: In this article, a three-parameter extension of the Frechet model is proposed and some statistical properties of its statistical properties are derived, and a simple type Copula-based construction via Morgenstern family and via...