Statistics of ExtremesTheory and Applications
Wiley Series in Probability and Statistics 1. Aufl.
Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.
Preface. 1 WHY EXTREME VALUE THEORY? 1.1 A Simple Extreme Value Problem. 1.2 Graphical Tools for Data Analysis. 1.3 Domains of Applications. 1.4 Conclusion. 2 THE PROBABILISTIC SIDE OF EXTREME VALUE THEORY. 2.1 The Possible Limits. 2.2 An Example. 2.3 The Fr´echet-Pareto Case: ? > 0. 2.4 The (Extremal) Weibull Case: ?
"This excellent book provides an overall survey of the most important achievements in the field of extreme value theory." (Mathematical Reviews, 2005j) "...a useful reference for researchers wishing to learn more about the analysis of extreme data, including as it does a wealth of information about the topic..." (Technometrics, August 2005) "The book is well written and the authors make good use of graphical procedures to illustrate and illuminate their exposition." (International Statistical Institute, Vol 25 (2), August 2005) "...a very useful and readable text..." (Journal of the Royal Statistical Society, Vol 169 (1), January 2006) "…its strengths lie in the combination of the theory and applications." (Meteorologishe Zeitschrift, April 2007)
Research in the statistical analysis of extreme values has flourished over the past decades: new probability models, inference and data analysis techniques have been introduced, while new application areas have been explored. Statistics of Extremes: Theory and Applications covers a wide range of models and applications, in particular in financial and actuarial risk management, a major area of interest and relevance to extreme value theory. Case studies are introduced in the first part of the book and are used throughout to show the application of each model discussed. The second part of the book covers advanced topics, such as multivariate and Bayesian modelling of extremes. Provides comprehensive coverage of a growing area of research. Provides a good balance of theory and real-world applications. Includes coverage of time series, regression, multivariate and Bayesian modelling. Introduces a number of case studies early in the book and develops the theory around them. Illustrated with many data examples and plots. Statistics of Extremes: Theory and Applications will appeal to researchers and graduate students of applied probability and statistics, particularly those studying extreme values. It is also suitable for applied statisticians working in finance and insurance, pollution and climatology, geology, metallurgy, and engineering.
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