极值统计建模导论

1 Introduction

1.1 Basic Concepts

1.2 Examples

1.3 Structure of the Book

1.4 Further Reading

2 Basics of Statistical Modeling

2.1 Introduction

2.2 Basic Statistical Concepts

2.3 Multivariate Distributions

2.4 Random Processes

2.5 Limit Laws

2.6 Parametric Modeling

2.7 Example

2.8 Further Reading

3 Classical Extreme Value Theory and Models

3.1 Asymptotic Models

3.2 Asymptotic Models for Minima

3.3 Inference for the GEV Distribution

3.4 Examples

3.5 Model Generalization: the r Largest Order Statistic Model

3.6 Further Reading

4 Threshold Models

4.1 Introduction

4.2 Asymptotic Model Characterization

4.3 Modeling Threshold Excesses

4.4 Examples

4.5 Further Reading

5 Extremes of Dependent Swquences

6 Extremes of Non-stationary Sequences

7 A Point Process Characterization of Extremes

8 Multivariate Extremes

9 Further Topics

A Computational Aspencts

References

Index

This book is intended for both statisticians and non-statisticians alike. It is hoped, in particular, that it will appeal to practitioners of extreme value modeling with limited statistical expertise. The mathematical level is elementary, and detailed mathematical proof is usually sacrificed in favor of heuristic argument. Rather more attention is paid to statistical detail, and many examples are provided by way of illustration. All the computations were carried out using the S-PLUS statistical software program, and corre-sponding datasets and functions are available via the internet as explained in the Appendix.