Statistics of Extremes
Theory and Applications
Published on 6. January 2006
522 pages
978-0-470-01237-6 (ISBN)
Description
Research in the statistical analysis of extreme values hasflourished over the past decade: new probability models, inferenceand data analysis techniques have been introduced; and newapplication areas have been explored. Statistics of Extremescomprehensively covers a wide range of models and applicationareas, including risk and insurance: a major area of interest andrelevance to extreme value theory. Case studies are introducedproviding a good balance of theory and application of eachmodel discussed, incorporating many illustrated examples and plotsof data. The last part of the book covers some interestingadvanced topics, including time series, regression,multivariate and Bayesian modelling of extremes, the use of whichhas huge potential.
Reviews / Votes
"This excellent book provides an overall survey of the mostimportant achievements in the field of extreme value theory."(Mathematical Reviews, 2005j) "...a useful reference for researchers wishing to learn moreabout the analysis of extreme data, including as it does a wealthof information about the topic..." (Technometrics, August2005) "The book is well written and the authors make good use ofgraphical procedures to illustrate and illuminate theirexposition." (International Statistical Institute, Vol 25(2), August 2005) "...a very useful and readable text..." (Journal of the RoyalStatistical Society, Vol 169 (1), January 2006) "...its strengths lie in the combination of the theory andapplications." (Meteorologishe Zeitschrift, April 2007)More details
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Jan Beirlant | Yuri Goegebeur | Johan Segers
Statistics of Extremes - Theory and Applications
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08/2005
Wiley
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08/2004
Wiley
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Persons
Jan Beirlant is the author of Statistics of Extremes: Theory and Applications, published by Wiley.
Yuri Goegebeur is the author of Statistics of Extremes: Theory and Applications, published by Wiley.
Johan Segers is the author of Statistics of Extremes: Theory and Applications, published by Wiley.
Jozef L. Teugels is the author of Statistics of Extremes: Theory and Applications, published by Wiley.
Content
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: gamma > 0.
2.4 The (Extremal) Weibull Case: gamma < 0.
2.5 The Gumbel Case: gamma = 0.
2.6 Alternative Conditions for (Cgamma).
2.7 Further on the Historical Approach.
2.8 Summary.
2.9 Background Information.
3 AWAY FROM THE MAXIMUM.
3.1 Introduction.
3.2 Order Statistics Close to the Maximum.
3.3 Second-order Theory.
3.4 Mathematical Derivations.
4 TAIL ESTIMATION UNDER PARETO-TYPE MODELS.
4.1 A Naive Approach.
4.2 The Hill Estimator.
4.3 Other Regression Estimators.
4.4 A Representation for Log-spacings and AsymptoticResults.
4.5 Reducing the Bias.
4.6 Extreme Quantiles and Small Exceedance Probabilities.
4.7 Adaptive Selection of the Tail Sample Fraction.
5 TAIL ESTIMATION FOR ALL DOMAINS OF ATTRACTION.
5.1 The Method of Block Maxima.
5.2 Quantile View--Methods Based on(Cgamma).
5.3 Tail Probability View--Peaks-Over-Threshold Method.
5.4 Estimators Based on an Exponential Regression Model.
5.5 Extreme Tail Probability, Large Quantile and EndpointEstimation Using Threshold Methods.
5.6 Asymptotic Results Under (Cgamma)-(C*gamma ).
5.7 Reducing the Bias.
5.8 Adaptive Selection of the Tail Sample Fraction.
5.9 Appendices.
6 CASE STUDIES.
6.1 The Condroz Data.
6.2 The Secura Belgian Re Data.
6.3 Earthquake Data.
7 REGRESSION ANALYSIS.
7.1 Introduction.
7.2 The Method of Block Maxima.
7.3 The Quantile View--Methods Based on ExponentialRegression Models.
7.4 The Tail Probability View--Peaks Over Threshold (POT)Method.
7.5 Non-parametric Estimation.
7.6 Case Study.
8 MULTIVARIATE EXTREME VALUE THEORY.
8.1 Introduction.
8.2 Multivariate Extreme Value Distributions.
8.3 The Domain of Attraction.
8.4 Additional Topics.
8.5 Summary.
8.6 Appendix.
9 STATISTICS OF MULTIVARIATE EXTREMES.
9.1 Introduction.
9.2 Parametric Models.
9.3 Component-wise Maxima.
9.4 Excesses over a Threshold.
9.5 Asymptotic Independence.
9.6 Additional Topics.
9.7 Summary.
10 EXTREMES OF STATIONARY TIME SERIES.
10.1 Introduction.
10.2 The Sample Maximum.
10.3 Point-Process Models.
10.4 Markov-Chain Models.
10.5 Multivariate Stationary Processes.
10.6 Additional Topics.
11 BAYESIAN METHODOLOGY IN EXTREME VALUE STATISTICS.
11.1 Introduction.
11.2 The Bayes Approach.
11.3 Prior Elicitation.
11.4 Bayesian Computation.
11.5 Univariate Inference.
11.6 An Environmental Application.
Bibliography.
Author Index.
Subject Index.
