Statistics of Extremes Theory and Applications [Hardcover]

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: ? 0.

2.5 The Gumbel Case: ? = 0.

2.6 Alternative Conditions for (C? ).

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.&l³Ë