Statistics Of Extremes

Author : Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels
Publisher : John Wiley & Sons
Page : 522 pages
File Size : 49,6 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 : E. J. Gumbel
Publisher : Courier Corporation
Page : 400 pages
File Size : 48,9 Mb
Release : 2012-04-27
Category : Mathematics
ISBN : 9780486154480

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Statistics of Extremes by E. J. Gumbel Pdf

This classic text covers order statistics and their exceedances; exact distribution of extremes; the 1st asymptotic distribution; uses of the 1st, 2nd, and 3rd asymptotes; more. 1958 edition. Includes 44 tables and 97 graphs.

Author : Jan Beirlant,Yuri Goegebeur,Johan Segers,Jozef L. Teugels
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 54,8 Mb
Release : 2004-10-15
Category : Mathematics
ISBN : 0471976474

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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 : Stuart Coles
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 54,9 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 : J. Tiago de Oliveira
Publisher : Springer Science & Business Media
Page : 690 pages
File Size : 53,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401730693

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Statistical Extremes and Applications by J. Tiago de Oliveira Pdf

The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.

Author : Barbel Finkenstadt,Holger Rootzen
Publisher : CRC Press
Page : 422 pages
File Size : 49,5 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 : Leonard C. MacLean,Edward O. Thorp,W. T. Ziemba
Publisher : World Scientific
Page : 883 pages
File Size : 41,8 Mb
Release : 2011
Category : Business & Economics
ISBN : 9789814293495

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The Kelly Capital Growth Investment Criterion by Leonard C. MacLean,Edward O. Thorp,W. T. Ziemba Pdf

This volume provides the definitive treatment of fortune's formula or the Kelly capital growth criterion as it is often called. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Mathematical theorems show that only the log utility function maximizes asymptotic long run wealth and minimizes the expected time to arbitrary large goals. In general, the strategy is risky in the short term but as the number of bets increase, the Kelly bettor's wealth tends to be much larger than those with essentially different strategies. So most of the time, the Kelly bettor will have much more wealth than these other bettors but the Kelly strategy can lead to considerable losses a small percent of the time. There are ways to reduce this risk at the cost of lower expected final wealth using fractional Kelly strategies that blend the Kelly suggested wager with cash. The various classic reprinted papers and the new ones written specifically for this volume cover various aspects of the theory and practice of dynamic investing. Good and bad properties are discussed, as are fixed-mix and volatility induced growth strategies. The relationships with utility theory and the use of these ideas by great investors are featured.

Author : Manfred Mudelsee
Publisher : Cambridge University Press
Page : 213 pages
File Size : 50,5 Mb
Release : 2020
Category : Electronic
ISBN : 9781107033184

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Statistical Analysis of Climate Extremes by Manfred Mudelsee Pdf

The risks posed by climate change and its effect on climate extremes are an increasingly pressing societal problem. This book provides an accessible overview of the statistical analysis methods which can be used to investigate climate extremes and analyse potential risk. The statistical analysis methods are illustrated with case studies on extremes in the three major climate variables: temperature, precipitation, and wind speed. The book also provides datasets and access to appropriate analysis software, allowing the reader to replicate the case study calculations. Providing the necessary tools to analyse climate risk, this book is invaluable for students and researchers working in the climate sciences, as well as risk analysts interested in climate extremes.

Author : M. R. Leadbetter,G. Lindgren,H. Rootzen
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 41,5 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 : Rolf-Dieter Reiss
Publisher : Unknown
Page : 0 pages
File Size : 48,6 Mb
Release : 1997
Category : Electronic
ISBN : OCLC:879921776

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Statistical Analysis of Extreme Values by Rolf-Dieter Reiss Pdf

Author : Laurens de Haan,Ana Ferreira
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 51,8 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 : Sidney I. Resnick
Publisher : Springer
Page : 334 pages
File Size : 51,5 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 : Serguei Y. Novak
Publisher : CRC Press
Page : 402 pages
File Size : 41,7 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 : Samuel Kotz,Saralees Nadarajah
Publisher : World Scientific
Page : 195 pages
File Size : 46,5 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 : Enrique Castillo
Publisher : Elsevier
Page : 389 pages
File Size : 50,7 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780080917252

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Extreme Value Theory in Engineering by Enrique Castillo Pdf

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.