Statistical Analysis of Extreme Values - Softcover

Reiss, R.D.; Thomas, M.

Softcover

ISBN 10: 3764357681 ISBN 13: 9783764357689

Publisher: Birkhauser Boston, 1997

Synopsis

57681

"The book is well written. It assumes a knowledge of statistics, but many of the ideas and techniques can be used by a nonstatistician. As a handbook for XTREMES, it is excellent , and I recommend it highly." --Computing Reviews

"The present book is a valuable contribution to the various theoretical and applied problems in the area of extreme value theory...a pleasure to read." --Statistics & Decisions

"This book is complemented by an excellent statistical package on CD ROM... The book is however much more than a manual for the program and it would provide an excellent introduction to the subject for any statistician looking for a practical introduction to the subject of extreme values." -- J. Time Series Analysis

"With general statistics software, appropriate tools for the analysis of real extreme value problems are rarely provided. XTREMES excellently fills this gap in the statistics software market." --Computational Statistics

"For a practitioner from industry, insurance, or finance who is less concerned with understanding the underlying probability and more interested in applications, this new book will be a good buy." --JASA The statistical analysis of extreme data is important for various disciplines, including insurance, finance, hydrology, engineering and environmental sciences. This book provides a self-contained introduction to the parametric modeling, exploratory analysis and statistical inference for extreme events. Besides numerous data-based examples, the book contains special chapters about insurance (coauthored by M. Radtke), returns in asset prices (coauthored by C.G. de Vries), and flood frequency analysis. In addition, five longer case studies are included.The applicability of the system is enhanced by the Pascal-like integrated programming language XPL.

Contents:

Preface XTREMES: An Overview and the Hierarchy List of Special Symbols I. Modeling and Data Analysis

1. Parametric Modeling 1.1 Applications of Extreme Value Analysis 1.2 Observing Exceedances and Maxima 1.3 Modeling by Extreme Value Distributions 1.4 Modeling by Generalized Pareto Distributions 1.5 Quantiles, Transformations and Simulations 1.6 Robust Statistics: A Converse View 1.7 Implementation in XTREMES

2. Diagnostic Tools 2.1 Visualization of Data 2.2 Excess and Hazard Functions 2.3 Fitting Parametric Distributions 2.4 Q-Q and P-P Plots 2.5 Trends, Seasonality and Autocorrelation 2.6 Clustering of Exceedances 2.7 Implementation in XTREMES

II. Statistical Inference in Parametric Models

3. An Introduction to Parametric Inference 3.1 Estimation 3.2 Confidence Intervals 3.3 Test Procedures and p- Values 3.4 Inference in Poisson and Mixed Poisson Models 3.5 Implementation in XTREMES

4. Extreme Value Models 4.1 Estimation in Extremes Value Model 4.2 Testing Extreme Value Models 4.3 Extended Extreme Value Models and Related Models 4.4 Implementation in XTREMES

5. Generalized Pareto Models 5.1 Estimation in Generalized Pareto Models 5.2 Testing Generalized Pareto Models 5.3 Statistics in Poisson-GP Models 5.4 Extending Generalized Pareto Models 5.5 Implementation in XTREMES

6. Advanced Statistical Analysis 6.1 Non-Random and Random Censoring 6.2 Modeling Exceedances by Poisson and Mixed Poisson Processes 6.3 Mean and Median T- Year Thresholds 6.4 Models of Time Series, the Extremal Index 6.5 Rates of Convergence and Penultimate Distributions 6.6 Implementation in XTREMES

III. Elements of Multivariate Statistical Analysis

7. Basic Multivariate Concepts and Visualization 7.1 An Introduction to Basic Multivariate Concepts 7.2 Visualizing Multivariate Data 7.3 Multivariate Parametric Models 7.4 Implementation in XTREMES

8. Multivariate Maxima 8.1 Nonparametric and Parametric Extreme Value Models 8.2 Estimation in Extreme Value Models 8.3 Implemetation in XTREMES

IV. Topics in Insurance, Finance and Hydrology

9. The Impact of Large Claims on Acturial Decisions /co-authored by M. Radtke 9.1 Numbers of Claims and the Total Claim Amount 9.2 Estimation of the Net Premium 9.3 Segmentation According to the Probable Maximum Loss 9.4 The Reserve Process and the T- Year Initial Review 9.5 Elements of Ruin Theory 9.6 Implemenatation

10. Extreme Returns in Asset Prices /co-authored by C.G. de Vries 10.1 Empirical Evidence in Returns Series and Exploratory Analysis 10.2 ARCH and Stochastic Volatility Structures 10.3 Implementation in XTREMES

11. Site - Specific Flood Frequency Analysis 11.1 Analyzing Annual Flood Series 11.2 Analyzing Partial Duration Series 11.3 Implementation in XTREMES

V. Case Studies in Extreme Value Analysis

Study 1 Extreme Sea Levels in Venice/ A.M. Ferreira

Study 2 Extreme Life Spans/ R.-D. Reiss

Study 3 Extrapolating Life Tables to Extreme Life Spans: A Regression Approach Using XPL/ E. Kaufmann & C. Hillgärtner

Study 4 A Case Study of Ozone Pollution with XTREMES/ T. Hsing

Study 5 Global Warming in Relation with the Clustering of Extremes/ J. Hüsler

Appendix: An Introduction to XTREMES

A. The Menu System A.1 Installation A.2 Becoming Acquainted with the Menu System A.3 Technical Aspects of XTREMES A.4 List of Windows and XTREMES Commands

B. UserFormula Facilities

C. The XPL Programming Language C.1 Programming with XPL: First Steps C.2 Generating and Accessing Data C.3 Plotting Curves C.4 Implementing Estimators C.5 Advanced XPL Techniques

Author Index Subject Index Bibliography

About this title

From the Back Cover

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 has been thoroughly updated and rearranged to meet the new requirements. Additional sections and chapters, elaborated on more than 100 pages, are particularly concerned with topics like dependencies, the conditional analysis and the multivariate modeling of extreme data. 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). Other new topics, e.g., a chapter about "Environmental Sciences", (co--authored by R.W. Katz), are collected within Parts IV–VI.

Review

"The book is well written. It assumes a knowledge of statistics, but many of the ideas and techniques can be used by a nonstatistician. As a handbook for XTREMES, it is excellent, and I recommend it highly."

-Computing Reviews

"The present book is a valuable contribution to the various theoretical and applied problems in the area of extreme value theory...a pleasure to read."

-Statistics & Decisions

"The book is however much more than a manual for the program and it would provide an excellent introduction to the subject for any statistician looking for a practical introduction to the subject of extreme values."

- J. Time Series Analysis

"With general statistics software, appropriate tools for the analysis of real extreme value problems are rarely provided. XTREMES excellently fills this gap in the statistics software market."

-Computational Statistics

"For a practitioner from industry, insurance, or finance who is less concerned with understanding the underlying probability and more interested in applications, this new book will be a good buy."

-JASA

"The book can be highly recommended to all who deal with statistics of extremes." - Zeitschrift fur Mathematik

Edition details

• Publisher: Birkhauser Boston
• Publication date: 1997
• Language: English
• ISBN 10: 3764357681
• ISBN 13: 9783764357689
• Binding: Paperback
• Number of pages: 336