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book
Statistical Analysis of Extreme Values,
with Applications to Insurance, Finance, Hydrology and Other Fields

3rd, revised and extended edition of the Birkhäuser bestseller for many years,

by R.-D. Reiss and M. Thomas, University of Siegen,

published in Birkhäuser, June 2007.

Xtremes 4.1, Academic Version



Overview

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 inference for extreme values.

The entire 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
  • "The Log-Pareto Model and other Pareto-Extensions" with a view towards super-heavy tailed distributions (a term coined in the 1st ed., 1997),
  • "An Overview of Reduced-Bias Estimation" (co-authored by M.I. Gomes),
  • "The Spectral Decomposition Methodology",
  • "About Tail Independence" (co-authored by M. Frick),
and a new chapter about "Extreme Value Statistics of Dependent Random Variables" (co-authored by H. Drees).

Applications of extreme value analysis are collected in

  • Part IV: Topics in Hydrology and Environmental Sciences which includes a new chapter about "Environmental Sciences" (co-authored by R.W. Katz),
  • Part V: Topics in Finance and Insurance with a new section about "Predicting the Serial Conditional VaR" (co-authored by A. Kozek and C.S. Wehn),
  • Part VI: Topics in Material and Life Sciences with, e.g., a new section about "The Stereology of Extremes" (co-authored by E. Kaufmann).
Extreme Mountains