Extreme Value Distributions

Author : Samuel Kotz,Saralees Nadarajah
Publisher : World Scientific
Page : 195 pages
File Size : 54,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9781860944024

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Extreme Value Distributions by Samuel Kotz,Saralees Nadarajah Pdf

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."

Author : Samuel Kotz,Saralees Nadarajah
Publisher : World Scientific
Page : 195 pages
File Size : 50,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9781860942242

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Extreme Value Distributions by Samuel Kotz,Saralees Nadarajah Pdf

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.

Author : V.P. Singh
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 41,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401714310

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Entropy-Based Parameter Estimation in Hydrology by V.P. Singh Pdf

Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution.

Author : Laurens de Haan,Ana Ferreira
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 46,8 Mb
Release : 2007-12-09
Category : Mathematics
ISBN : 9780387344713

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Extreme Value Theory by Laurens de Haan,Ana Ferreira Pdf

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

Author : Jürg Hüsler,Rolf-Dieter Reiss
Publisher : Unknown
Page : 296 pages
File Size : 53,9 Mb
Release : 1989
Category : Mathematics
ISBN : STANFORD:36105030875202

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Extreme Value Theory by Jürg Hüsler,Rolf-Dieter Reiss Pdf

Author : Sidney I. Resnick
Publisher : Springer
Page : 334 pages
File Size : 54,5 Mb
Release : 2013-12-20
Category : Mathematics
ISBN : 9780387759531

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Extreme Values, Regular Variation and Point Processes by Sidney I. Resnick Pdf

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.

Author : Mohammad Ahsanullah
Publisher : Springer
Page : 137 pages
File Size : 51,5 Mb
Release : 2016-09-15
Category : Mathematics
ISBN : 9789462392229

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Extreme Value Distributions by Mohammad Ahsanullah Pdf

The aim of the book is to give a through account of the basic theory of extreme value distributions. The book cover a wide range of materials available to date. The central ideas and results of extreme value distributions are presented. The book rwill be useful o applied statisticians as well statisticians interrested to work in the area of extremen value distributions.vmonograph presents the central ideas and results of extreme value distributions.The monograph gives self-contained of theory and applications of extreme value distributions.

Author : Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels
Publisher : John Wiley & Sons
Page : 522 pages
File Size : 46,6 Mb
Release : 2006-03-17
Category : Mathematics
ISBN : 9780470012376

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Statistics of Extremes by Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels Pdf

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.

Author : J. Galambos,James Lechner,Emil Simiu
Publisher : Springer Science & Business Media
Page : 526 pages
File Size : 45,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461336389

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Extreme Value Theory and Applications by J. Galambos,James Lechner,Emil Simiu Pdf

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.

Author : Stuart Coles
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 54,8 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781447136750

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An Introduction to Statistical Modeling of Extreme Values by Stuart Coles Pdf

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.

Author : Serguei Y. Novak
Publisher : CRC Press
Page : 402 pages
File Size : 53,8 Mb
Release : 2011-12-20
Category : Mathematics
ISBN : 9781439835746

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Extreme Value Methods with Applications to Finance by Serguei Y. Novak Pdf

Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible. Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers: Extremes in samples of random size Methods of estimating extreme quantiles and tail probabilities Self-normalized sums of random variables Measures of market risk Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text. A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.

Author : Barbel Finkenstadt,Holger Rootzen
Publisher : CRC Press
Page : 422 pages
File Size : 48,5 Mb
Release : 2003-07-28
Category : Mathematics
ISBN : 9780203483350

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Extreme Values in Finance, Telecommunications, and the Environment by Barbel Finkenstadt,Holger Rootzen Pdf

Because of its potential to ...predict the unpredictable,... extreme value theory (EVT) and methodology is currently receiving a great deal of attention from statistical and mathematical researchers. This book brings together world-recognized authorities in their respective fields to provide expository chapters on the applications, use, and theory

Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 42,8 Mb
Release : 2008
Category : Mathematics
ISBN : 0387759522

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Extreme Values, Regular Variation, and Point Processes by Sidney I. Resnick Pdf

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.

Author : M. R. Leadbetter,G. Lindgren,H. Rootzen
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461254492

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Extremes and Related Properties of Random Sequences and Processes by M. R. Leadbetter,G. Lindgren,H. Rootzen Pdf

Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.

Author : Nobuaki Hoshino,Shuhei Mano,Takaaki Shimura
Publisher : Springer Nature
Page : 141 pages
File Size : 41,8 Mb
Release : 2021-06-04
Category : Mathematics
ISBN : 9789811607684

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Pioneering Works on Extreme Value Theory by Nobuaki Hoshino,Shuhei Mano,Takaaki Shimura Pdf

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.