Statistical Extremes and Applications: (131 NATO Science Series C)

The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer­ ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba­ bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.

Table of Contents:
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 theProgressive 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.- Modelling Excesses over High Thresholds, with an Application.- Stationary Min-stable Stochastic Processes.- Strong Approximations of Records and Record Times.- High Percentiles Atmospheric SO2-Concentrations in Belgium.- Extreme Response of the Linear Oscillator with Modulated Random Excitation.- Frost Data: A Case Study on Extreme Values of Non-Stationary Sequences.- Estimation of the Scale and Location Parameters of the Extreme Value (Gumbel) Distribution for Large Censored Samples.- Asymptotic Behaviour of the Extreme Order Statistics in the Non-Identically Distributed Case.- Limit Distribution of the Minimum Distance between Independent and Identically Distributed d-Dimensional Random Variables.- Approximate Values for the Moments of Extreme Order Statistics in Large Samples.- Estimation of Parameters of Extreme Order Distributions of Exponential Type Parents.- On Ordered Uniform Spacings for Testing Goodness of Fit.- Inequalities for the Relative Sufficiency between Sets of Order Statistics.- POT-Estimation of Extreme Sea States and the Benefit of Using Wind Data.- Threshold Methods for Sample Extremes.- On Successive Record Values in a Sequence of Independent Identically Distributed Random Variables.- Two Test Statistics for Choice of Univariate Extreme Models.- On the Asymptotic Uperossings of a Class of Non-Stationary Sequences.- Author Index.

Review :
`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)