Statistical Analysis of Extreme Values : With Applications to Insurance, Finance, Hydrology and Other Fields
by Reiss, Rolf-DieterEdition: 3rd
Format: Paperback
Pub. Date: 2007-06-21
Publisher(s): Birkhauser
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Summary
The statistical analysis of extreme data is important for various disciplines, including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to the parametric modeling, exploratory analysis and statistical interference for extreme values. The entire text of this third edition is thoroughly updated and rearranged to meet the new requirements. Additional sections and chapters, elaborated on more than 100 pages, especially concern topics like dependencies, the conditional analysis and the multivariate modeling of extreme data. The Parts I-III about the basic extreme value methodology remain unchanged to some larger extent, yet notable are, e.g., the new sections about An Overview of Reduced-Bias Estimation (co-authored by M.I. Gomes), The Spectral Decomposition Methodology, and About Tail Independence (co-authored by M. Frick), and the new chapter about Extreme Value Statistics of Dependent Random Variables co-authored by H. Drees).
Table of Contents
| 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. Hüsler 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 |
| Table of Contents provided by Publisher. All Rights Reserved. |
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