Statistical Extremes and Applications

A - Core Course.- Inaugural Address: Statistical Extremes: Theory and Applications, Motivation and Perspectives.- Introduction, Order Statistics, Exceedances. Laws of Large Numbers.- Asymptotics; Stable Laws for Extremes. Tail Properties.- Slow Variation and Characterization of Domains of Attraction.- Introduction, Gumbel Model.- Statistical Estimation of Parameters of the Weibull and Frechet Distributions.- Univariate Extremes; Statistical Choice.- Statistical Estimation in Extreme Value Theory.- Probabilistic Aspects of Multivariate Extremes.- Bivariate Models for Extremes; Statistical Decision.- Extremes in Dependent Random Sequences.- Extremes in Continuous Stochastic Processes.- Comparison Technique for Highly Dependent Stationary Gaussian Processes.- Extremes in Hydrology.- Application of Extreme Values in Structural Engineering.- Extremes in Meteorology.- Extreme Values in Insurance Mathematics.- B - Specific Lectures.- Use and Structure of Slepian Model. Processes for Prediction and Detection in Crossing and Extreme Value Theory.- Spline and Isotonic Estimation of the Pareto Function.- Extremal Processes.- Extreme Values for Sequences of Stable Random Variables.- C - Workshops.- Large Deviations of Extremes.- Uniform Rates of Convergence to Extreme Value Distributions.- Rates of Convergence in Extreme Value Theory.- Concomitants in a Multidimensional Extreme Model.- A Short Cut Algorithm for Obtaining Coefficients of the BLUE's.- Statistical Choice of Univariate Extreme Models. Part II.- Doubly Exponential Random Number Generators.- Probability Problems in Seismic Risk and Load Combinations for Power Plants.- D - Contributed Papers.- The Distribution of the Maximal Time till Departure from a State in a Markov Chain.- The Box-Jenkins Model and the Progressive Fatigue Failure of Large Parallel Element Stay Tendons.- The Asymptotic Behaviour of the Maximum Likelihood Estimates for Univariate Extremes.- On Upper and Lower Extremes in Stationary Sequences.-

`According to the preface, 'the purpose of (this) NATO Advanced Science Institute ... was to obtain a complete perspective of the field, also with a series of promising directions of research and some recent results'. This purpose seems to me to have been admirably fulfilled, and the organisers, speakers and editor deserve great credit for this; anyone seriously interested in the subject will certainly wish to have this volume available.' Metrika, 33:2 (1986)