Applied Extreme Value Statistics

This book does not focus solely on asymptotic extreme value distributions. In addition to the traditional asymptotic methods, it introduces a data-driven, computer-based method, which provides insights into the exact extreme value distribution inherent in the data, and which avoids asymptotics. It therefore differs from currently available texts on extreme value statistics in one very important aspect. The method described provides a unique tool for diagnostics, and for efficient and accurate extreme value prediction based on measured or simulated data. It also has straightforward extensions to multivariate extreme value distributions.

The first half provides an introduction to extreme value statistics with an emphasis on applications. It includes chapters on classical asymptotic theories and threshold exceedance models, with many illustrative examples. The mathematical level is elementary and, to increase readability, detailed mathematical proofs have been avoided in favour of heuristic arguments. The second half presents in some detail specialized topics that illustrate the power and the limitations of the concepts discussed. With diverse applications to science, engineering and finance, the techniques described in this book will be useful to readers from many different backgrounds.

Enables the reader to carry out accurate extreme value estimation without having to assume asymptotic distributions Since real life data are never asymptotic, methods are presented that avoid making this kind of assumption The methods developed enable user to see real extreme value distribution inherent in the data, which allows diagnostics

Autorentext

Arvid Naess is Professor of Statistics at the Norwegian University of Science and Technology in Trondheim, Norway. Over many years he has worked on a wide range of problems related to the application of probability and statistics in science and engineering. He is a recipient of the Alfred M. Freudenthal Medal from ASCE, and a Fellow of ASCE, ASME, EMI. He is an elected member of The Royal Norwegian Society (DKNVS) and The Norwegian Academy of Technological Sciences (NTVA).

Inhalt

• Challenges of Applied Extreme Value Statistics.- Classical Extreme Value Theory.- The Peaks-Over-Threshold Method.- A Point Process Approach to Extreme Value Statistics.- The ACER Method.- Some Practical Aspects of Extreme Value Analyses.- Estimation of Extreme Values for Financial Risk Assessment.- The Upcrossing Rate via the Characteristic Function.- Monte Carlo Methods and Extreme Value Estimation.- Bivariate Extreme Value Distributions.- Space-Time Extremes of Random Fields.- A Case Study - Extreme Water Levels.