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Directly oriented towards real practical application, this book develops both the basic theoretical framework of extreme value models and the statistical inferential techniques for using these models in practice. Intended for statisticians and non-statisticians alike, the theoretical treatment is elementary, with heuristics often replacing detailed mathematical proof. Most aspects of extreme modeling techniques are covered, including historical techniques (still widely used) and contemporary techniques based on point process models. A wide range of worked examples, using genuine datasets, illustrate the various modeling procedures and a concluding chapter provides a brief introduction to a number of more advanced topics, including Bayesian inference and spatial extremes. All the computations are carried out using S-PLUS, and the corresponding datasets and functions are available via the Internet for readers to recreate examples for themselves. An essential reference for students and researchers in statistics and disciplines such as engineering, finance and environmental science, this book will also appeal to practitioners looking for practical help in solving real problems. Stuart Coles is Reader in Statistics at the University of Bristol, UK, having previously lectured at the universities of Nottingham and Lancaster. In 1992 he was the first recipient of the Royal Statistical Society's research prize. He has published widely in the statistical literature, principally in the area of extreme value modeling.
Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subject. After reviewing univariate extreme value analysis and multivariate extremes, the book explains univariate extreme value mixture modeling, threshold selection in extreme value analysis, and threshold modeling of non-stationary extremes. It presents new results for block-maxima of vine copulas, develops time series of extremes with applications from climatology, describes max-autoregressive and moving maxima models for extremes, and discusses spatial extremes and max-stable processes. The book then covers simulation and conditional simulation of max-stable processes; inference methodologies, such as composite likelihood, Bayesian inference, and approximate Bayesian computation; and inferences about extreme quantiles and extreme dependence. It also explores novel applications of extreme value modeling, including financial investments, insurance and financial risk management, weather and climate disasters, clinical trials, and sports statistics. Risk analyses related to extreme events require the combined expertise of statisticians and domain experts in climatology, hydrology, finance, insurance, sports, and other fields. This book connects statistical/mathematical research with critical decision and risk assessment/management applications to stimulate more collaboration between these statisticians and specialists.
The monograph covers the fundamentals and the consequences of extreme geophysical phenomena like asteroid impacts, climatic change, earthquakes, tsunamis, hurricanes, landslides, volcanic eruptions, flooding, and space weather. This monograph also addresses their associated, local and worldwide socio-economic impacts. The understanding and modeling of these phenomena is critical to the development of timely worldwide strategies for the prediction of natural and anthropogenic extreme events, in order to mitigate their adverse consequences. This monograph is unique in as much as it is dedicated to recent theoretical, numerical and empirical developments that aim to improve: (i) the understanding, modeling and prediction of extreme events in the geosciences, and, (ii) the quantitative evaluation of their economic consequences. The emphasis is on coupled, integrative assessment of the physical phenomena and their socio-economic impacts. With its overarching theme, Extreme Events: Observations, Modeling and Economics will be relevant to and become an important tool for researchers and practitioners in the fields of hazard and risk analysis in general, as well as to those with a special interest in climate change, atmospheric and oceanic sciences, seismo-tectonics, hydrology, and space weather.
Statistical analysis of extreme data is vital to many disciplines including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values. For this Third Edition, the entire text has been thoroughly updated and rearranged to meet contemporary requirements, with new sections and chapters address such topics as dependencies, the conditional analysis and the multivariate modeling of extreme data. New chapters include An Overview of Reduced-Bias Estimation; The Spectral Decomposition Methodology; About Tail Independence; and Extreme Value Statistics of Dependent Random Variables.
Im vorliegenden Buch werden neue Erkenntnisse der Lebensversicherungsmathematik aus dem Gebiet der Markovmodelle und der stochastischen Zinsen behandelt. Besonderes Gewicht wird auf die Anwendbarkeit der Modelle in der Praxis gelegt, so daß die Aussagen direkt angewendet werden können. Die dargestellten Modelle sind in besonderer Weise geeignet, eine schnelle Tarifierung neuer Lebensversicherungsprodukte zu ermöglichen. Gleichzeitig geben diese Modelle einen tieferen Einblick in das Wesen der Lebensversicherungsmathematik. Der besondere Nutzen dieses Buches liegt einerseits in der parallelen Behandlung der Theorie in stetiger und in diskreter Zeit. Zusätzlich wird das für die Behandlung der Theorie nötige Vorwissen im Buch dargestellt. Durch die vielen Beispiele können die entsprechenden Aussagen direkt in die Praxis umgesetzt werden.
Focuses on theoretical results along with applications All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion Concentration is on the probabilistic and statistical aspects of extreme values Excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity

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