Author: A. A. BalkemaPublisher:
ISBN:
Category :
Languages : en
Pages : 13
Book Description
A Convergence Rate in Extreme-value Theory
Author: A. A. BalkemaExtreme Value Theory
Author: Laurens de HaanPublisher: Springer Science & Business Media
ISBN: 0387344713
Category : Mathematics
Languages : en
Pages : 421
Book Description
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
Second Order Regular Variation Ans Rates of Convergence in Extreme Value Theory
Author: Laurens F. M. de HaanPublisher:
ISBN:
Category :
Languages : en
Pages : 29
Book Description
Second Order Regular Variation and Rates of Convergence in Extreme Value Theory
Author: L. de HaanExtreme Value Theory and Applications
Author: J. GalambosPublisher: Springer Science & Business Media
ISBN: 1461336384
Category : Mathematics
Languages : en
Pages : 526
Book Description
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.
Normal Approximation by Stein’s Method
Author: Louis H.Y. ChenPublisher: Springer Science & Business Media
ISBN: 3642150071
Category : Mathematics
Languages : en
Pages : 411
Book Description
Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Extreme Value Methods with Applications to Finance
Author: Serguei Y. NovakPublisher: CRC Press
ISBN: 1439835748
Category : Mathematics
Languages : en
Pages : 402
Book Description
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.
Extreme Value Theory
Author: Jürg HüslerPublisher: Springer Science & Business Media
ISBN: 1461236347
Category : Mathematics
Languages : en
Pages : 290
Book Description
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.
Probability Theory and Extreme Value Theory
Author: Madan Lal PuriPublisher: Walter de Gruyter
ISBN: 3110917823
Category : Mathematics
Languages : en
Pages : 760
Book Description
Approximations in Extreme Value Theory
Author: Richard L. SmithPublisher:
ISBN:
Category :
Languages : en
Pages : 35
Book Description
Following a survey of rates of convergence in extreme value theory, a new class of approximations is developed and compared with existing approximations based on the extreme value distributions. Convergence in Hellinger distance is established, this distance measure being chosen because of its statistical applications. Numerical examples confirm the superiority of the new approximation. Keywords: Extreme value theory, Generalised extreme value distribution, Generlised Pareto distribution, Hellinger distance, Rates of convergence, Regular variation with reminder, Total variation distance.