Regular Variation

Regular Variation

Author: N. H. Bingham

Publisher: Cambridge University Press

Published: 1989-06-15

Total Pages: 518

ISBN-13: 9780521379434

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A comprehensive account of the theory and applications of regular variation.


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.


Empirical Processes with Applications to Statistics

Empirical Processes with Applications to Statistics

Author: Galen R. Shorack

Publisher: SIAM

Published: 2009-01-01

Total Pages: 992

ISBN-13: 0898719011

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Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables; applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods; and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition. Audience: researchers in statistical theory, probability theory, biostatistics, econometrics, and computer science.


Encyclopaedia of Mathematics

Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 595

ISBN-13: 9401512884

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This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.


Chaos Theory

Chaos Theory

Author: Christos H. Skiadas

Publisher: World Scientific

Published: 2011

Total Pages: 467

ISBN-13: 9814350338

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The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena. This volume includes the best papers presented in the 3rd International Conference on CHAOS. This interdisciplinary conference attracted people from many scientific fields dealing with chaos, nonlinear dynamics, fractals and the works presented and the papers included here are of particular interest that could provide a broad understanding of chaos in its various forms. The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals. Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications, are presented.


Reliability of Large Systems

Reliability of Large Systems

Author: Krzysztof Kolowrocki

Publisher: Elsevier

Published: 2004-04-15

Total Pages: 359

ISBN-13: 008054049X

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As mechanisms grow in size and complexity, safety and reliability become of paramount importance. Such complexity makes the assessment of reliability and safety to particularly difficult. Kolowrocki delivers the complete elaboration of the asymptotic approach to reliability evaluation. The text is mathematical, but applications of these methods cover wide range of engineering fields: from communication networks and microelectronic devices to transportation systems, piping transportation of water, gas, oil and various chemical substances.* Only reference with on asymptotic approach to reliability currently on the market* Suitable for use as a postgraduate course book* Contains many new theoretical results


Statistical Extremes and Applications

Statistical Extremes and Applications

Author: J. Tiago de Oliveira

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 690

ISBN-13: 9401730695

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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.


Statistical Modelling and Risk Analysis

Statistical Modelling and Risk Analysis

Author: Christos P. Kitsos

Publisher: Springer Nature

Published: 2024-01-13

Total Pages: 230

ISBN-13: 3031398645

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This volume covers the latest results on novel methods in Risk Analysis and assessment, with applications in Biostatistics (which is providing food for thought since the first ICRAs, covering traditional areas of RA, until now), Engineering Reliability, the Environmental Sciences and Economics. The contributions, based on lectures given at the 9th International Conference on Risk Analysis (ICRA 9), at Perugia, Italy, May 2022, detail a wide variety of daily risks, building on ideas presented at previous ICRA conferences. Working within a strong theoretical framework, supporting applications, the material describes a modern extension of the traditional research of the 1980s. This book is intended for graduate students in Mathematics, Statistics, Biology, Toxicology, Medicine, Management, and Economics, as well as quantitative researchers in Risk Analysis.


Records

Records

Author: Barry C. Arnold

Publisher: John Wiley & Sons

Published: 2011-09-20

Total Pages: 342

ISBN-13: 1118150406

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The first and only comprehensive guide to modern record theory andits applications Although it is often thought of as a special topic in orderstatistics, records form a unique area, independent of the study ofsample extremes. Interest in records has increased steadily overthe years since Chandler formulated the theory of records in 1952.Numerous applications of them have been developed in such far-flungfields as meteorology, sports analysis, hydrology, and stock marketanalysis, to name just a few. And the literature on the subjectcurrently comprises papers and journal articles numbering in thehundreds. Which is why it is so nice to have this book devotedexclusively to this lively area of statistics. Written by an exceptionally well-qualified author team, Recordspresents a comprehensive treatment of record theory and itsapplications in a variety of disciplines. With the help of amultitude of fascinating examples, Professors Arnold, Balakrishnan,and Nagaraja help readers quickly master basic and advanced recordvalue concepts and procedures, from the classical record valuemodel to random and multivariate record models. The book follows arational textbook format, featuring witty and insightful chapterintroductions that help smooth transitions from one topic toanother and challenging chapter-end exercises, which expand on thematerial covered. An extensive bibliography and numerous referencesthroughout the text specify sources for further readings onrelevant topics. Records is a valuable professional resource forprobabilists and statisticians, in addition to appliedstatisticians, meteorologists, hydrologists, market analysts, andsports analysts. It also makes an excellent primary text forcourses in record theory and a supplement to order statisticscourses.