Journal ArticleDOI
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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Book ChapterDOI
Extrema of Log-correlated Random Variables: Principles and Examples
TL;DR: In this paper, a branching random walk is used as a guiding example to prove the correct leading and sub-leading order of the maximum following the multiscale renement of the second moment method of Kistler.
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Which Extreme Values Are Really Extreme
Jesus Gonzalo,Jose Olmo +1 more
TL;DR: In this article, the extreme values of any random sample of size n from a distribution function F are defined as the observations exceeding a threshold and following a type of generalized Pareto distribution involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD.
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The convex hull of a random sample in
TL;DR: In this article, it was shown that the sample convex hull of the points of a two-dimensional Poisson process converges in the metric space of compact convex sets of with metric given by the Hausdorff distance.
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The Modelling of Extreme Events
TL;DR: A review of non-standard extreme events is given, and issues of public policy are outlined in this paper, which outlines the consistent theory underlying many of the differing approaches and gives examples of the analysis of models.
Journal ArticleDOI
Extreme value theory of generalized order statistics
TL;DR: In this paper, the extreme value theory of generalized order statistics has been applied to generalized order distributions, and a new representation of the (marginal) distribution function of the rth generalized order statistic is derived.