Laws Of Small Numbers Extremes And Rare Events
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Laws Of Small Numbers Extremes And Rare Events
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Author : Michael Falk
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-07
Laws Of Small Numbers Extremes And Rare Events written by Michael Falk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-07 with Mathematics categories.
Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika
Laws Of Small Numbers
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Author : Michael Falk
language : en
Publisher: Springer Science & Business Media
Release Date : 2004
Laws Of Small Numbers written by Michael Falk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages. Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework.
The Novikov Conjecture
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Author : Matthias Kreck
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-11-22
The Novikov Conjecture written by Matthias Kreck and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-22 with Mathematics categories.
These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.
Multivariate Extreme Value Theory And D Norms
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Author : Michael Falk
language : en
Publisher: Springer
Release Date : 2019-02-07
Multivariate Extreme Value Theory And D Norms written by Michael Falk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-07 with Mathematics categories.
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.
Statistical Analysis Of Extreme Values
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Author : Rolf-Dieter Reiss
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-08
Statistical Analysis Of Extreme Values written by Rolf-Dieter Reiss and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-08 with Mathematics categories.
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.
Mathematica As A Tool
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Author : Stephan Kaufmann
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-09-01
Mathematica As A Tool written by Stephan Kaufmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-01 with Computers categories.
Mathematica combines symbolic and numerical calculations, plots, graphics programming, list calculations and structured documentation into an interactive environment. This book covers the program and shows with practical examples how even more complex problems can be solved with just a few commands. From the reviews: "A valuable introductory textbook on Mathematica and is very useful to scientists and engineers who use Mathematica in their work." -- ZENTRALBLATT MATH
Extreme Events In Nature And Society
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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-18
Extreme Events In Nature And Society written by Sergio Albeverio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-18 with Science categories.
Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of Extreme Events in Nature and Society. The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme events, including problems of understanding and modelling their origin, spatial and temporal extension, and potential impact. The chapters converge towards the difficult problem of anticipation: forecasting the event and proposing measures to moderate or prevent it. Extreme Events in Nature and Society will interest not only specialists, but also the general reader eager to learn how the multifaceted field of extreme events can be viewed as a coherent whole.
Extreme Values In Random Sequences
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Author : Pavle Mladenović
language : en
Publisher: Springer Nature
Release Date : 2024-05-17
Extreme Values In Random Sequences written by Pavle Mladenović and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-17 with Mathematics categories.
The main subject is the probabilistic extreme value theory. The purpose is to present recent results related to limiting distributions of maxima in incomplete samples from stationary sequences, and results related to extremal properties of different combinatorial configurations. The necessary contents related to regularly varying functions and basic results of extreme value theory are included in the first two chapters with examples, exercises and supplements. The motivation for consideration maxima in incomplete samples arises from the fact that real data are often incomplete. A sequence of observed random variables from a stationary sequence is also stationary only in very special cases. Hence, the results provided in the third chapter are also related to non-stationary sequences. The proof of theorems related to joint limiting distribution of maxima in complete and incomplete samples requires a non-trivial combination of combinatorics and point process theory. Chapter four provides results on the asymptotic behavior of the extremal characteristics of random permutations, the coupon collector's problem, the polynomial scheme, random trees and random forests, random partitions of finite sets, and the geometric properties of samples of random vectors. The topics presented here provide insight into the natural connections between probability theory and algebra, combinatorics, graph theory and combinatorial geometry. The contents of the book may be useful for graduate students and researchers who are interested in probabilistic extreme value theory and its applications.
Extreme Value Theory
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Author : Laurens de Haan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-09
Extreme Value Theory written by Laurens de Haan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-09 with Mathematics categories.
Extreme Value Theory offers a careful, coherent exposition of the subject starting from the probabilistic and mathematical foundations and proceeding to the statistical theory. The book covers both the classical one-dimensional case as well as finite- and infinite-dimensional settings. All the main topics at the heart of the subject are introduced in a systematic fashion so that in the final chapter even the most recent developments in the theory can be understood. The treatment is geared toward applications. The presentation concentrates on the probabilistic and statistical aspects of extreme values such as limiting results, domains of attraction and development of estimators without emphasizing related topics such as point processes, empirical distribution functions and Brownian motion. An appendix on regular variation has been added since some required results in that area are not available in book form. The usefulness of the statistical theory is shown by treating several case studies in detail. The book is a thorough, accessible, self-contained, graduate level treatment of modern extreme value theory and some of its applications. It is aimed at graduate students and researchers and requires only maturity in mathematics and statistics.
Extreme Value Theory And Applications
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Author : J. Galambos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Extreme Value Theory And Applications written by J. Galambos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
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.