Extremes and Related Properties of Random Sequences and Processes
Extremes and Related Properties of Random Sequences and Processes

Author: M. R. Leadbetter

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 344

ISBN-13: 1461254493

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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.

Statistics of Extremes and Records in Random Sequences
Statistics of Extremes and Records in Random Sequences

Author: Satya N. Majumdar

Publisher: Oxford University Press

Published: 2024-05-16

Total Pages: 257

ISBN-13: 0192517880

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Rare events such as earthquakes, tsunamis, floods etc do not fortunately occur every day, but when they do, their effects are devastating. These days, such rare events are particularly important to understand to characterize the global warming and climate changes. In addition to natural catastrophes, rare events such as big financial crashes also play a significant role in economy. In the absence of predictive models, the best way forward is to analyse the statistics of these extreme events and draw conclusions from it about the probability of their occurrences. Extreme value statistics (EVS) and the statistics of records in a random sequence are examples of a truly interdisciplinary topic, spanning from statistics and mathematics on one side to physics of disordered systems on the other. They have tremendous importance and practical applications in a wide variety of fields, such as climate science, finance, spin-glasses, and random matrices. Statistics and mathematical literature have explored the subject of the classical theory of EVS. However, more recently, EVS started to play a very important role in statistical physics, in particular in disordered systems. This has led to a plethora of activities, both in the statistical physics and in the mathematics communities over the last few decades. This book develops the theory of rare events, both for the classical uncorrelated as well as for correlated sequences, in terms of simple models and examples. Statistics of Extremes and Records in Random Sequences is a pedagogical book with examples illustrating the basic tools and techniques that are essential to a student starting to work in this interesting and rapidly developing field.

Laws of Small Numbers: Extremes and Rare Events
Laws of Small Numbers: Extremes and Rare Events

Author: Michael Falk

Publisher: Birkhäuser

Published: 2013-11-11

Total Pages: 381

ISBN-13: 3034877919

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Since the publication of the first edition of this seminar book, the theory and applications of extremes and rare events have seen increasing interest. Laws of Small Numbers gives a mathematically oriented development of the theory of rare events underlying various applications. The new edition incorporates numerous new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.

Extreme Values in Finance, Telecommunications, and the Environment
Extreme Values in Finance, Telecommunications, and the Environment

Author: Barbel Finkenstadt

Publisher: CRC Press

Published: 2003-07-28

Total Pages: 422

ISBN-13: 0203483359

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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

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.

Extreme Value Methods with Applications to Finance
Extreme Value Methods with Applications to Finance

Author: Serguei Y. Novak

Publisher: CRC Press

Published: 2011-12-20

Total Pages: 402

ISBN-13: 1439835748

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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.

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.

Limit Distributions for Sums of Independent Random Variables
Limit Distributions for Sums of Independent Random Variables

Author: B V (Boris Vladimirovich) Gnedenko

Publisher: Hassell Street Press

Published: 2021-09-09

Total Pages: 284

ISBN-13: 9781014649485

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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Statistics of Extremes
Statistics of Extremes

Author: Jan Beirlant

Publisher: John Wiley & Sons

Published: 2004-10-15

Total Pages: 516

ISBN-13: 9780471976479

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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.