The book has emerged from a series of lectures on the occasion of the workshop on "Laws of small numbers: extremes and rare events", held at the Katholische Universität Eichstätt from October 20-27, 1991, organized by the Gesellschaft für mathematische Forschung in cooperation with the Deutsche Mathematiker-Vereinigung (DMV). The starting point of the book is the probabilistic modelling of rare events by suitably truncated empirical point processes which in turn can be approximated by Poisson point processes in several ways. Therefore, estimations of metric distances (of variational and Hellinger type, in particular) between distributions and point processes play a central role throughout the text. The approach chosen here is applied to extremes and other rare events of stochastic processes (of Gaussian type, in particular), statistical analysis in extreme value models and nonparametric regression analysis. The book includes a diskette with the statistical software system XTREMES, version 1.2, running on IBM-compatible PCs under MS-DOS, being developed by the Xtremes group at the University of Seigen, Germany.
The book is organized as follows:... A final appendix provides detailed guidelines for practical work with XTREMES.
The book is written in a very appealing and comprehensive style, with many illustrations and practical examples. It covers classical material as well as more advanced topics from recent research lines, to which the authors have contributed with several research papers. The program system XTREMES is worked out thoroughly and is easy to handle after a short time. A more recent Windows-version of XTREMES can also be obtained from the Xtremes group.