Preface to the Third Edition p. v
Preface to the Second Edition p. vii
Preface to the First Edition p. ix
List of Special Symbols p. xviii
Modeling and Data Analysis p. 1
Parametric Modeling p. 3
Applications of Extreme Value Analysis p. 3
Observing Exceedances and Maxima p. 7
Modeling by Extreme Value Distributions p. 14
Modeling by Generalized Pareto Distributions p. 23
Heavy and Fat-Tailed Distributions p. 30
Quantiles, Transformations and Simulations p. 35
Diagnostic Tools p. 39
Visualization of Data p. 39
Excess and Hazard Functions p. 49
Fitting Parametric Distributions to Data p. 56
Q-Q and P-P Plots p. 61
Trends, Seasonality and Autocorrelation p. 64
The Tail Dependence Parameter p. 74
Clustering of Exceedances p. 76
Statistical Inference in Parametric Models p. 81
An Introduction to Parametric Inference p. 83
Estimation in Exponential and Gaussian Models p. 84
Confidence Intervals p. 90
Test Procedures and p-Values p. 93
Inference in Poisson and Mixed Poisson Models p. 96
The Bayesian Estimation Principle p. 102
Extreme Value Models p. 107
Estimation in Extremes Value Models p. 107
Testing within Extreme Value Models p. 118
Extended Extreme Value Models and Related Models p. 120
Generalized Pareto Models p. 127
Estimation in Generalized Pareto Models p. 127
Testing Within Generalized Pareto Models p. 143
Testing Extreme Value Conditions with Applications (co-authored by J. H眉sler and D. Li) p. 144
Statistics in Poisson-GP Models p. 152
The Log-Pareto Model and Other Pareto-Extensions p. 154
Advanced Statistical Analysis p. 159
Non-Random and Random Censoring p. 159
Models of Time Series, the Extremal Index p. 164
Statistics for Student Distributions p. 170
Statistics for Sum-Stable Distributions (co-authored by J.P. Nolan) p. 172
Ultimate and Penultimate GP Approximation (co-authored by E. Kaufmann) p. 182
An Overview of Reduced-Bias Estimation (co-authored by M.I. Gomes) p. 190
Statistics of Dependent Variables (coauthored by H. Drees) p. 207
The Impact of Serial Dependence p. 208
Estimating the Extreme Value Index p. 209
Extreme Quantile Estimation p. 215
A Time Series Approach p. 219
Conditional Extremal Analysis p. 227
Interpretations and Technical Preparations p. 227
Conditional Extremes: a Nonparametric Approach p. 238
Maxima Under Covariate Information p. 240
The Bayesian Estimation Principle, Revisited p. 242
Statistical Models for Exceedance Processes p. 247
Modeling Exceedances by Poisson Processes: the Homogeneous Case p. 247
Mean and Median T-Year Return Levels p. 250
ML and Bayesian Estimation in Models of Poisson Processes p. 252
GP Process Approximations (co-authored by E. Kaufmann) p. 256
Inhomogeneous Poisson Processes, Exceedances Under Covariate Information p. 258
Elements of Multivariate Statistical Analysis p. 263
Basic Multivariate Concepts and Visualization p. 265
An Introduction to Basic Multivariate Concepts p. 265
Visualizing Multivariate Data p. 270
Decompositions of Multivariate Distributions p. 275
Elliptical and Related Distributions p. 279
Multivariate Gaussian Models p. 279
Spherical and Elliptical Distributions p. 281
Multivariate Student Distributions p. 283
Multivariate Sum-Stable Distributions (co-authored by J.P. Nolan) p. 285
Multivariate Maxima p. 291
Nonparametric and Parametric Extreme Value Models p. 291
The Gumbel-McFadden Model p. 301
Estimation in Extreme Value Models p. 305
A Spectral Decomposition Methodology p. 309
Multivariate Peaks Over Threshold (co-authored by M. Falk) p. 313
Nonparametric and Parametric Generalized Pareto Models p. 313
Estimation of the Canonical Dependence Function p. 318
About Tail Independence (co-authored by M. Frick) p. 321
The Point Process Approach to the Multivariate POT Method p. 333
Topics in Hydrology and Environmental Sciences p. 335
Flood Frequency Analysis (co-authored by J.R.M. Hosking) p. 337
Analyzing Annual Flood Series p. 337
Analyzing Partial Duration Series p. 338
Regional Flood Frequency Analysis p. 343
The L-Moment Estimation Method p. 345
A Bayesian Approach to Regional Estimation p. 349
Environmental Sciences (co-authored by R.W. Katz) p. 353
Environmental Extremes p. 353
Inclusion of Covariates p. 356
Example of Trend p. 359
Example of Cycle p. 361
Example of Covariate p. 364
Numerical Methods and Software p. 367
Topics in Finance and Insurance p. 369
Extreme Returns in Asset Prices (co-authored by C.G. de Vries and S. Caserta) p. 371
Stylized Facts and Historical Remarks p. 372
Empirical Evidence in Returns Series p. 375
Parametric Estimation of the Tails of Returns p. 378
The Profit/Loss Variable and Risk Parameters p. 382
Evaluating the Value-at-Risk (VaR) p. 386
The VaR for a Single Derivative Contract p. 392
GARCH and Stochastic Volatility Structures p. 395
Predicting the Serial Conditional VaR (co-authored by A. Kozek and C.S. Wehn) p. 401
The Impact of Large Claims on Actuarial Decisions (co-authored by M. Radtke) p. 411
Numbers of Claims and the Total Claim Amount p. 412
Estimation of the Net Premium p. 415
Segmentation According to the Probable Maximum Loss p. 419
The Risk Process and the T-Year Initial Reserve p. 426
Elements of Ruin Theory p. 432
Credibility (Bayesian) Estimation of the Net Premium p. 434
Topics in Material and Life Sciences p. 439
Material Sciences p. 441
Extremal Corrosion Engineering p. 441
Stereology of Extremes (co-authored by E. Kaufmann) p. 445
Life Science (co-authored by E. Kaufmann) p. 453
About the Longevity of Humans p. 453
Extrapolating Life Tables To Extreme Life Spans: A Regression Approach p. 458
Appendix: First Steps towards Xtremes and StatPascal p. 465
The Menu System p. 467
Installation p. 467
Overview and the Hierarchy p. 467
Becoming Acquainted with the Menu System p. 470
Technical Aspects of Xtremes p. 476
The UserFormula (UFO) Facilities p. 481
The StatPascal Programming Language p. 485
Programming with StatPascal: First Steps p. 486
Plotting Curves p. 490
Generating and Accessing Data p. 492
Author Index p. 495
Subject Index p. 501
Bibliography p. 509