Laws of Small Numbers : Extremes and Rare Events

Laws of small numbers concern rare events, i.e., events having but a small probability of occurrence.

It is reasonable to describe such events as truncated empirical point processes, and a point process of rare events can be approximated by a Poisson process.

This approach is applied to the following topics: extremes and rare events of stochastic processes, with special emphasis given to Gaussian processes; Poisson point processes; statistics in extreme value models; and nonparametric regression analysis.

This book comes with the statistical software system XTREMES, version 1.2, an interactive menu-driven system which runs on IBM-compatible PCs under MS-DOS and is designed for dealing with various questions in extreme value analysis.

The beginner should appreciate the introduction to the fields mentioned above, and the expert the comprehensive account of recent results and developments.