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The study of the statistics of extreme events is an essential first step in the mitigation of natural catastrophies. This book reviews the theoretical and practical aspects of the statistics of extreme events in nature. Topics range from high and low flows, to earthquakes and volcanic eruptions, land slides, avalanches, windstorms, extreme sea levels and high waves, forest fires and other disasters that threaten lives and properties and often cause severe economic losses worldwide. In many applications it is important to consider extreme events in a bivariate or multivariate context. Copulas exactly describe and model the dependence structure between random variables independently of the marginal laws involved. This approach simplifies the analysis of phenomena involved and makes it possible to introduce new parameters for the characterization of the extreme behaviour of a system.
1.1 Order Statistics
1.2 Extreme value theory
1.3 Hazard, return period, and risk
1.4 Natural Hazards
2 MULTIVARIATE EXTREME VALUE THEORY
2.1 Multivariate Extreme Value Distributions
2.2 Characterizations of the domain of attraction 2.3 Multivariate dependence 2.4 Multivariate return periods 3 BIVARIATE ANALYSIS VIA COPULAS
3.1 2-Copulas
3.2 Archimedean copulas
3.3 Return periods via copulas
3.4 Tail dependence 4 MULTIVARIATE ANALYSIS VIA COPULAS
4.1 Multivariate copulas
4.2 Archimedean copulas
4.3 Conditional mixtures
5 EXTREME VALUE ANALYSIS VIA COPULAS
5.1 Extreme Value copulas
5.2 Dependence function
5.3 Tail dependence A SIMULATION OF COPULAS
A.1 The 2-dimensional case
A.2 The general case B DEPENDENCE
B.1 Bivariate concepts of dependence
B.2 Measures of association
C FAMILIES OF COPULAS
C.1 The Frank family
C.2 The Gumbel-Hougaard family
C.3 The Clayton family
C.4 The Ali-Mikhail-Haq (AMH) family
C.5 The Joe family
C.6 The Farlie-Gumbel-Morgenstern (FGM) family
C.7 The Plackett family
C.8 The Raftery family
C.9 The Galambos family
C.10 The Hüsler-Reiss family
C.11 The Elliptical family
C.12 The Fréchet family
C.13 The Marshall-Olkin family
C.14 The Archimax family
C.15 Construction methods for copulas
REFERENCES INDEX
GLOSSARY
| Erscheinungsjahr: | 2014 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Geowissenschaften, Importe |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Reihe: | Water Science and Technology Library |
| Inhalt: |
xiv
292 S. |
| ISBN-13: | 9789401782753 |
| ISBN-10: | 940178275X |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Salvadori, Gianfausto
De Michele, Carlo Kottegoda, Nathabandu T. Rosso, Renzo |
| Hersteller: |
Springer
Water Science and Technology Library |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 17 mm |
| Von/Mit: | Gianfausto Salvadori (u. a.) |
| Erscheinungsdatum: | 23.11.2014 |
| Gewicht: | 0,476 kg |
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