Synopses & Reviews
The theory of extreme values has become a broad subject which is difficult to cover by a few authors. It is the purpose of this book to lay out in an expository way the broad spectrum of extremes by contributions, some of which are reviewing recent developments and some are including original ideas and results. 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 interesting to mathematically oriented research workers. This was one of the reasons a conference on extreme value theory was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987. The book is split into three parts with a total number of nine sections. The topics covered include probabilistic theory, statistical theory of extreme values, and multivariate extremes and records.
Synopsis
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.
Table of Contents
Contents: Univariate Extremes: Probability Theory: Limit Laws and Expansions. Strong Laws. Records. Exceedances. Characterizations.- Univariate Extremes: Statistics: Estimation. Test Procedures. Sufficiency of Extremes in Parametric Models.- Multivariate Extremes.- Author Index.- Subject Index.