extreme-value-theory

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Extreme Value Theory

Author : Laurens de Haan
ISBN : 9780387239460
Genre : Mathematics
File Size : 41. 38 MB
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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

Extreme Value Theory With Applications To Natural Hazards

Author : Nicolas Bousquet
ISBN : 9783030749422
Genre : Mathematics
File Size : 54. 46 MB
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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 Distributions

Author : Samuel Kotz
ISBN : 9781860942242
Genre : Mathematics
File Size : 74. 51 MB
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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 ? 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.

An Introduction To Statistical Modeling Of Extreme Values

Author : Stuart Coles
ISBN : 9781447136750
Genre : Mathematics
File Size : 47. 15 MB
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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

Author : Jürg Hüsler
ISBN : 9781461236344
Genre : Mathematics
File Size : 32. 20 MB
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The urgent need to describe and to solve certain problems connected to extreme phenomena in various areas of applications has been of decisive influence on the vital development of extreme value theory. After the pioneering work of M. Frechet (1927) and of R.A. Fisher and L.R.C. Tippett (1928), who discovered the limiting distributions of extremes, the importance of mathematical concepts of extreme behavior in applications was impressively demonstrated by statisticians like E.J. Gumbel and W. Weibull. The predominant role of applied aspects in that early period may be highlighted by the fact that two of the "Fisher-Tippett asymptotes" also carry the names of Gumbel and Weibull. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more of interest for mathematically oriented research workers. This was one of the reasons to organize a conference on extreme value theory which was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987.

Extreme Value Theory

Author : Laurens de Haan
ISBN : 9780387344713
Genre : Mathematics
File Size : 67. 65 MB
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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

Extreme Value Theory And Applications

Author : J. Galambos
ISBN : 9781461336389
Genre : Mathematics
File Size : 49. 31 MB
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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 In Engineering

Author : Enrique Castillo
ISBN : 9780080917252
Genre : Mathematics
File Size : 87. 16 MB
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This book is a comprehensive guide to extreme value theory in engineering. Written for the end user with intermediate and advanced statistical knowledge, it covers classical methods as well as recent advances. A collection of 150 examples illustrates the theoretical results and takes the reader from simple applications through complex cases of dependence.

Extreme Value Theory Based Methods For Visual Recognition

Author : Walter J. Scheirer
ISBN : 9783031018176
Genre : Computers
File Size : 27. 11 MB
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A common feature of many approaches to modeling sensory statistics is an emphasis on capturing the "average." From early representations in the brain, to highly abstracted class categories in machine learning for classification tasks, central-tendency models based on the Gaussian distribution are a seemingly natural and obvious choice for modeling sensory data. However, insights from neuroscience, psychology, and computer vision suggest an alternate strategy: preferentially focusing representational resources on the extremes of the distribution of sensory inputs. The notion of treating extrema near a decision boundary as features is not necessarily new, but a comprehensive statistical theory of recognition based on extrema is only now just emerging in the computer vision literature. This book begins by introducing the statistical Extreme Value Theory (EVT) for visual recognition. In contrast to central-tendency modeling, it is hypothesized that distributions near decision boundaries form a more powerful model for recognition tasks by focusing coding resources on data that are arguably the most diagnostic features. EVT has several important properties: strong statistical grounding, better modeling accuracy near decision boundaries than Gaussian modeling, the ability to model asymmetric decision boundaries, and accurate prediction of the probability of an event beyond our experience. The second part of the book uses the theory to describe a new class of machine learning algorithms for decision making that are a measurable advance beyond the state-of-the-art. This includes methods for post-recognition score analysis, information fusion, multi-attribute spaces, and calibration of supervised machine learning algorithms.

Probability Theory And Extreme Value Theory

Author : Madan Lal Puri
ISBN : 9783110917826
Genre : Mathematics
File Size : 86. 84 MB
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Extreme Value Theory And Applications

Author : Janos Galambos
ISBN : 0792328655
Genre : Mathematics
File Size : 66. 97 MB
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The contributions in this volume represent a selection of the papers presented at the Conference on Extreme Value Theory and Applications held in Gaithersburg, Maryland in 1993. Recent rapid advancement in the theory of extremes, in the statistical inference of extreme-related problems and the ever-increasing acceptance of the theory in applications brought together the leading experts in the fields of model building statistics, engineering and business, whose authoritative presentations on these matters are published in this volume. A variety of engineering applications are covered: strength due to fatigue failure, bundle strength of fibre, longest living humans, concomitants of extremes such as characteristics of offspring of the present generation, long-run asset risk, reinsurance, high winds, and other applications. The theoreticians address model building and the newest results of statistical inference, including Bayesian methods. This is the first such mix of the theory and applications of extremes to be published. For statisticians, mathematicians, engineers and business professionals with a basic knowledge of probability and statistics.

Extreme Value Theory In Triangular Arrays With An Application To The Reliability Of Fibrous Materials

Author : Wagner de Souza Borges
ISBN : CORNELL:31924004483099
Genre : Fiber bundles (Mathematics)
File Size : 83. 22 MB
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Statistics Of Extremes

Author : Jan Beirlant
ISBN : 9780470012376
Genre : Mathematics
File Size : 23. 39 MB
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Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.

Statistical Analysis Of Extreme Values

Author : Rolf-Dieter Reiss
ISBN : 9783764373993
Genre : Mathematics
File Size : 77. 45 MB
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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.

Extreme Values Regular Variation And Point Processes

Author : Sidney I. Resnick
ISBN : 0387759522
Genre : Mathematics
File Size : 60. 8 MB
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This book is a readable and efficient account of 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.

Extreme Value Distributions

Author : Samuel Kotz
ISBN : 9781860944024
Genre : Mathematics
File Size : 48. 98 MB
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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."

Multivariate Extreme Value Theory And D Norms

Author : Michael Falk
ISBN : 9783030038199
Genre : Mathematics
File Size : 76. 31 MB
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This monograph compiles the contemporary knowledge about D-norms and provides an introductory tour through the essentials of multivariate extreme value theory. Following a clear introduction of D-norms, this book introduces links with the theory through multivariate generalized Pareto distributions and max stable distributions. Further views on D-norms from a functional analysis perspective and from stochastic geometry underline the aim of this book to reveal mathematical structures. This book is intended for mathematicians with a basic knowledge of analysis and probability theory, including Fubini's theorem.

Extremes In Nature

Author : Gianfausto Salvadori
ISBN : 9781402044151
Genre : Science
File Size : 25. 58 MB
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This book is about the theoretical and practical aspects of the statistics of Extreme Events in Nature. Most importantly, this is the first text in which Copulas are introduced and used in Geophysics. Several topics are fully original, and show how standard models and calculations can be improved by exploiting the opportunities offered by Copulas. In addition, new quantities useful for design and risk assessment are introduced.

Pioneering Works On Extreme Value Theory

Author : Nobuaki Hoshino
ISBN : 9789811607684
Genre : Mathematics
File Size : 55. 48 MB
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This book presents the state of the art in extreme value theory, with a collection of articles related to a seminal paper on the bivariate extreme value distribution written by Professor Masaaki Sibuya in 1960, demonstrating various developments of the original idea over the last half-century. Written by active researchers, the unique combination of articles allows readers to gain a sense of the excellence of the field, ranging from theory to practice, and the tradition of theoretical developments motivated by practically important issues such as tsunamis and financial crises. The contributions discuss a range of topics, including the parameter estimation of the generalized beta distribution, resampling with the empirical beta copula, and regression analysis on imbalanced binary data, as well as the semiparametric estimation of the upper bound of extrema, the long-term analysis of extreme precipitation over Japanese river basins, and various rules of thumb in hydrology.

Topics In Extreme Values

Author : Mohammad Ahsanullah
ISBN : 1600217141
Genre : Mathematics
File Size : 28. 60 MB
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Extreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions. The general theory sets out to assess the type of probability distributions generated by processes. Extreme value theory is important for assessing risk for unusual events. Applications of extreme value theory include predicting the probability distribution of: extreme floods; the amounts of large insurance losses; equity risks; day to day market risk; the size of freak waves; and, mutational events during evolution. This new book presents the latest research breakthroughs in this dynamic field.

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