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| Author | : Patrick Albin |
| Publisher | : |
| Total Pages | : 60 |
| Release | : 1988 |
| Genre | : |
| ISBN | : |
| Author | : Michael Falk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 513 |
| Release | : 2010-10-07 |
| Genre | : Mathematics |
| ISBN | : 3034800096 |
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
| Author | : Michael Falk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 396 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9783764324162 |
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.
| Author | : M. R. Leadbetter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461254493 |
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 | : J. Tiago de Oliveira |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 690 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401730695 |
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 | : D N Shanbhag |
| Publisher | : Gulf Professional Publishing |
| Total Pages | : 1028 |
| Release | : 2003-02-24 |
| Genre | : Mathematics |
| ISBN | : 9780444500137 |
This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.
| Author | : Jürg Hüsler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 290 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461236347 |
The urgent need to describe and to solve certain problems connected to extreme phenomena in various areas of applications has been of decisive influence on the vital development of extreme value theory. After the pioneering work of M. Frechet (1927) and of R.A. Fisher and L.R.C. Tippett (1928), who discovered the limiting distributions of extremes, the importance of mathematical concepts of extreme behavior in applications was impressively demonstrated by statisticians like E.J. Gumbel and W. Weibull. The predominant role of applied aspects in that early period may be highlighted by the fact that two of the "Fisher-Tippett asymptotes" also carry the names of Gumbel and Weibull. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more of interest for mathematically oriented research workers. This was one of the reasons to organize a conference on extreme value theory which was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987.
| Author | : Simeon Berman |
| Publisher | : CRC Press |
| Total Pages | : 315 |
| Release | : 2017-07-12 |
| Genre | : Mathematics |
| ISBN | : 1351415646 |
Sojourns and Extremes of Stochastic Processes is a research monograph in the area of probability theory. During the past thirty years Berman has made many contributions to the theory of the extreme values and sojourn times of the sample functions of broad classes of stochastic processes. These processes arise in theoretical and applied models, and are presented here in a unified exposition.
| Author | : |
| Publisher | : |
| Total Pages | : 812 |
| Release | : 1997 |
| Genre | : Mathematical statistics |
| ISBN | : |
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
| Author | : Ian F. Blake |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 440 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 146124904X |
The areas of communications, computer networks, and signal processing have undergone rapid development over the past several years. The advent of VLSI circuitry and increasingly sophisticated computer hardware and software techniques have made possible the construction of systems and signal proces sors for· communications applications not contemplated only a short time ago. The increasing complexity of communication systems, both by themselves and in land-based or satellite networks, has created a greater need for finding use ful mathematical techniques for their analysis. The rapidly evolving technolo gies involved continue to find exciting new areas for application, and it remains a challenge for researchers to keep abreast of developments. In this volume researchers from a broad cross section of the areas of communications, signal processing, and computer networks have been invited to contribute articles to assist readers in learning about the current state of research and future research directions in their area. The authors were not given tight guidelines for their contributions and thus the character and emphasis of each chapter differs. Although the scope of the areas considered is necessarily limited in a volume of this size, the coverage here is quite broad and it is hoped that the reader will find the contents of this volume to be interesting, useful, and informative.
