Extremes in Nature: An Approach Using Copulas

ISBN-13: 9781402044144 / Angielski / Twarda / 2007 / 292 str.

Gianfausto Salvadori; Carlo De Michele

Opis

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.

Recenzje

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)

Spis treści

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 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

Blurb

The study of the statistics of extreme events is an essential first step in the mitigation of natural catastrophies, that often cause severe economic losses worldwide. 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. Practicioners in all research areas of Geosciences and extreme events (including Finance and Insurance, closely related to natural disasters) will definitely benefit from the new Copula-approach outlined in the book.

 

Audience

This volume will be of interest to researchers and practitioners in the fields of civil and environmental engineering, geophysics, geosciences, geography and environmental science. Also scientists and undergraduate up to post graduate level students in water resources and hydrology will find valuable information in this book.