Extreme Value and Related Models with Applications in Engineering and Science
Measuring and interpreting data for extreme values presents a unique and important challenge that has far-reaching implications for all aspects of modern engineering and science. Extreme Value and Related Models with Applications in Engineering and Science reflects the latest information in this growing field. The book incorporates illuminating real-world examples from such areas as structural engineering, hydraulics, meteorology, materials science, highway traffic analysis, environmetrics, and climatology, and is designed to help engineers, mathematicians, statisticians, and scientists gain a clearer understanding of extreme value theory and then translate that knowledge into practical applications within their own fields of research.
The book provides:
- A unique focus on modern topics including data analysis and inference
- Specific data in such areas as wind, flood, chain strength, electrical insulation, fatigue, precipitation, and wave heights
- Useful techniques for addressing extreme value problems, including discrete, continuous, univariate, and multivariate models
- Coverage of order statistics, return period, exceedances and shortfalls, along with detailed explanations on how to obtain exact distributions for these statistics
- An in-depth look at asymptotic models and the limit distributions of maxima, minima, and other order statistics
Enhanced with numerous graphs and exercises, plus an extensive bibliography for further study, this text is an important reference source for engineers designing structures that will withstand even the most extreme circumstances.
I: DATA, INTRODUCTION AND MOTIVATION.
1. Introduction and Motivation.
II: PROBABILISTIC MODELS USEFUL IN EXTREMES.
2. Discrete Probabilistic Models.
3. Continuous Probabilistic Models.
III: MODEL ESTIMATION, SELECTION, AND VALIDATION.
4. Model Estimation.
5. Model Selection and Validation.
IV: EXACT MODELS FOR ORDER STATISTICS AND EXTREMES.
6. Order Statistics.
7. Point Processes and Exact Models.
V: ASYMPTOTIC MODELS FOR EXTREMES AND EXCEEDANCES.
8. Limit Distributions of Order Statistics.
9. Limit Distributions of Exceedances.
10. Multivariate Extremes.
Appendix: Statistical Tables.
ALI S. HADI, PhD, is a Professor of Mathematical, Statistical, and Computational Sciences at the American University in Cairo, Egypt. He is a Stephen H. Weiss Presidential Fellow and Professor Emeritus at Cornell University.
N. BALAKRISHNAN, PhD, is a Professor in the Department of Mathematics and Statistics at McMaster University in Ontario, Canada. He is a Fellow of the American Statistical Association and currently the Editor-in-Chief of Communications in Statistics and Wiley's Encyclopedia of Statistical Sciences, Second Edition.
JOSÉ M. SARABIA, PhD, is a Professor of Statistics in the Department of Economics at the University of Cantabria, Spain. He is a member of the American Statistical Association and is Associate Editor of the journal Test.