Description
This book is about the theoretical and practical aspects of the statistics of Extreme Events in Nature. Most importantly, this is the first text in which Copulas are introduced and used in Geophysics. Several topics are fully original, and show how standard models and calculations can be improved by exploiting the opportunities offered by Copulas. In addition, new quantities useful for design and risk assessment are introduced. 1 UNIVARIATE EXTREME VALUE THEORY 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 Hsler-Reiss family C.11 The Elliptical family C.12 The Frchet family C.13 The Marshall-Olkin family C.14 The Archimax family C.15 Construction methods for copulas REFERENCES INDEX GLOSSARY
