Titlebook: Laws of Small Numbers: Extremes and Rare Events; Michael Falk,Jürg Hüsler,Rolf-Dieter Reiss Book 2011Latest edition Springer Basel AG 2011

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The Pickands Approach in the Bivariate Caseng function ., see Section 6.1, and prove that the pertaining Pickands dependence function .is absolutely continuous, see Lemma 6.2.1 and the subsequent discussion. This property is unknown in higher dimensions.

教育学

Introduction to the Non-IID Casequences. We introduce different classes of non-iid sequences together with the main ideas. The examples show that suitable restrictions for each class are needed to find limit results which are useful for applications.

Affectation

Extremes of Random Sequencesnvergence of the point processes of exceedances or of clusters of exceedances. These results are then applied for special cases, as stationary, independent and particular nonstationary random sequences.

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Statistics of Extremes estimation of the cluster distribution and of the extremal index in a stationary situation. In the last section we treat a frost data problem which is related to an extreme value problem of a nonstationary sequence.

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anesthesia

Campaign

Extensions for Rare Events particular case, triangular arrays of rare events in relation with exceedances of Gaussian sequences are considered since they are basic for maxima of a continuous Gaussian process. This analysis reveals also a new definition of Pickands constants.

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