Extreme Value and Related Models with Applications in Engineering and Science
Extreme Value and Related Models with Applications in Engineering and Science

Author: Enrique Castillo

Publisher: Wiley-Interscience

Published: 2004-11-04

Total Pages: 0

ISBN-13: 9780471671725

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A straightforward, practical guide to extreme value modeling for today's world 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.

Extreme Value Distributions
Extreme Value Distributions

Author: Samuel Kotz

Publisher: World Scientific

Published: 2000

Total Pages: 195

ISBN-13: 1860944027

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This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions OCo one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field. Sample Chapter(s). Chapter 1.1: Historical Survey (139 KB). Chapter 1.2: The Three Types of Extreme Value Distributions (146 KB). Chapter 1.3: Limiting Distributions and Domain of Attraction (210 KB). Chapter 1.4: Distribution Function and Moments of Type 1 Distribution (160 KB). Chapter 1.5: Order Statistics, Record Values and Characterizations (175 KB). Contents: Univariate Extreme Value Distributions; Generalized Extreme Value Distributions; Multivariate Extreme Value Distributions. Readership: Applied probabilists, applied statisticians, environmental scientists, climatologists, industrial engineers and management experts."

An Introduction to Statistical Modeling of Extreme Values
An Introduction to Statistical Modeling of Extreme Values

Author: Stuart Coles

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 219

ISBN-13: 1447136756

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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 Theory and Applications
Extreme Value Theory and Applications

Author: J. Galambos

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 526

ISBN-13: 1461336384

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It appears that we live in an age of disasters: the mighty Missis sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it might still suddenly fail if the aircraft has been in operation over an extended period of time. Our theory has by now penetrated the so cial sciences, the medical profession, economics and even astronomy. We believe that our field has come of age. In or~er to fully utilize the great progress in the theory of extremes and its ever increasing acceptance in practice, an international conference was organized in which equal weight was given to theory and practice. This book is Volume I of the Proceedings of this conference. In selecting the papers for Volume lour guide was to have authoritative works with a large variety of coverage of both theory and practice.

Extreme Value Theory with Applications to Natural Hazards
Extreme Value Theory with Applications to Natural Hazards

Author: Nicolas Bousquet

Publisher: Springer Nature

Published: 2021-10-09

Total Pages: 491

ISBN-13: 3030749428

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This richly illustrated book describes statistical extreme value theory for the quantification of natural hazards, such as strong winds, floods and rainfall, and discusses an interdisciplinary approach to allow the theoretical methods to be applied. The approach consists of a number of steps: data selection and correction, non-stationary theory (to account for trends due to climate change), and selecting appropriate estimation techniques based on both decision-theoretic features (e.g., Bayesian theory), empirical robustness and a valid treatment of uncertainties. It also examines and critically reviews alternative approaches based on stochastic and dynamic numerical models, as well as recently emerging data analysis issues and presents large-scale, multidisciplinary, state-of-the-art case studies. Intended for all those with a basic knowledge of statistical methods interested in the quantification of natural hazards, the book is also a valuable resource for engineers conducting risk analyses in collaboration with scientists from other fields (such as hydrologists, meteorologists, climatologists).

Extreme Value Theory
Extreme Value Theory

Author: Laurens de Haan

Publisher: Springer Science & Business Media

Published: 2007-12-09

Total Pages: 421

ISBN-13: 0387344713

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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

Loss Models
Loss Models

Author: Stuart A. Klugman

Publisher: John Wiley & Sons

Published: 2013-08-29

Total Pages: 368

ISBN-13: 1118573749

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An essential resource for constructing and analyzing advanced actuarial models Loss Models: Further Topics presents extended coverage of modeling through the use of tools related to risk theory, loss distributions, and survival models. The book uses these methods to construct and evaluate actuarial models in the fields of insurance and business. Providing an advanced study of actuarial methods, the book features extended discussions of risk modeling and risk measures, including Tail-Value-at-Risk. Loss Models: Further Topics contains additional material to accompany the Fourth Edition of Loss Models: From Data to Decisions, such as: Extreme value distributions Coxian and related distributions Mixed Erlang distributions Computational and analytical methods for aggregate claim models Counting processes Compound distributions with time-dependent claim amounts Copula models Continuous time ruin models Interpolation and smoothing The book is an essential reference for practicing actuaries and actuarial researchers who want to go beyond the material required for actuarial qualification. Loss Models: Further Topics is also an excellent resource for graduate students in the actuarial field.

Extreme Values, Regular Variation and Point Processes
Extreme Values, Regular Variation and Point Processes

Author: Sidney I. Resnick

Publisher: Springer

Published: 2013-12-20

Total Pages: 334

ISBN-13: 0387759530

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This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.

Dependence Modeling
Dependence Modeling

Author: Harry Joe

Publisher: World Scientific

Published: 2011

Total Pages: 370

ISBN-13: 981429988X

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1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka