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Informationen zum Autor 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. Klappentext 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. Zusammenfassung States that research in the statistical analysis of extreme values has flourished over the years: probability models, inference and data analysis techniques have been introduced; and fresh application areas have been explored. Inhaltsverzeichnis 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. > 0. 2.4 The (Extremal) Weibull Case: ³ 0. 2.5 The Gumbel Case: ³ = 0. 2.6 Alternative Conditions for (C³ ). 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 Asymptotic Results. 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 (C³). 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 Endpoint Estimation Using Threshold Methods. 5.6 Asymptotic Results Under (C³ )-(C*³ ). 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. ...
