Extremes in Nature: An Approach Using Copulas by Gianfausto SalvadoriExtremes in Nature: An Approach Using Copulas by Gianfausto Salvadori

Extremes in Nature: An Approach Using Copulas

byGianfausto Salvadori, Carlo De Michele, Nathabandu T. Kottegoda

Paperback | November 23, 2014

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The most powerful earthquake in 40 years occurred on 26th December 2004 off the west coast of Sumatra, Indonesia. The tsunami it generated turned into one of the worst known natural disasters when walls of water crashed across the Indian Ocean, causing waves to reach Somalia in Africa. The death toll, mainly in Indonesia and Sri Lanka, exceeded 200,000. Nine months later, hurricane Katrina devastated the southern coast of USA along the Gulf coast. Winds reached 281 kilometers per hour and the storm surge of over nine meters was the highest recorded in the United States. It brought destruction to New Orleans when portions of the 563 kilometers of levees surrounding the city were suddenly breached. Nearly 1700 people died and damages are currently estimated at $100 billion, the costliest natural disaster in the United States. Within days hurricane Rita, another maximum category hurricane, struck the same coastal region damaging Texas and other states, followed soon aft- wards by hurricane Wilma. Then on October 8th 2005 an earthquake in Kashmir, part of northern Pakistan and India, killed 75,000 inhabitants when innumerable buildings collapsed. Simultaneously, hurricane Stan led to costly landslides and more than 2000 deaths in Central America. To highlight the major catastrophes of nature during the previous decade, Cyclone Gorky and its storm surge caused 139,000 deaths in coastal Bangladesh during 1991.
Title:Extremes in Nature: An Approach Using CopulasFormat:PaperbackPublished:November 23, 2014Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:940178275X

ISBN - 13:9789401782753

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Table of Contents

1 UNIVARIATE EXTREME VALUE THEORY1.1 Order Statistics1.2 Extreme value theory1.3 Hazard, return period, and risk1.4 Natural Hazards 2 MULTIVARIATE EXTREME VALUE THEORY2.1 Multivariate Extreme Value Distributions2.2 Characterizations of the domain of attraction 2.3 Multivariate dependence 2.4 Multivariate return periods 3 BIVARIATE ANALYSIS VIA COPULAS3.1 2-Copulas3.2 Archimedean copulas3.3 Return periods via copulas3.4 Tail dependence 4 MULTIVARIATE ANALYSIS VIA COPULAS4.1 Multivariate copulas4.2 Archimedean copulas4.3 Conditional mixtures 5 EXTREME VALUE ANALYSIS VIA COPULAS5.1 Extreme Value copulas5.2 Dependence function5.3 Tail dependence A SIMULATION OF COPULASA.1 The 2-dimensional caseA.2 The general case B DEPENDENCEB.1 Bivariate concepts of dependenceB.2 Measures of association C FAMILIES OF COPULASC.1 The Frank familyC.2 The Gumbel-Hougaard familyC.3 The Clayton familyC.4 The Ali-Mikhail-Haq (AMH) familyC.5 The Joe familyC.6 The Farlie-Gumbel-Morgenstern (FGM) familyC.7 The Plackett familyC.8 The Raftery familyC.9 The Galambos familyC.10 The Hüsler-Reiss familyC.11 The Elliptical familyC.12 The Fréchet familyC.13 The Marshall-Olkin familyC.14 The Archimax familyC.15 Construction methods for copulas REFERENCES INDEX GLOSSARY

Editorial Reviews

From the reviews:"This monograph deals with both theoretical and practical aspects of the mathematical theory of extremes. ... The book surely will be interesting and useful to researchers and practitioners in the areas of geophysics and environmental sciences and engineering. It can be also useful to any one interested in having a rigorous summary of the main results and modern developments of the theory of extreme events in the context of physical applications." (Jaume Masoliver, Journal of Statistical Physics, Vol. 134, 2009)