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Tiago de Oliveira J. (ed.) Statistical Extremes and Applications

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Tiago de Oliveira J. (ed.) Statistical Extremes and Applications
Amsterdam: Springer, 1984. — 690 p.
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.
Contents :
Front Matter
Statistical Extremes: Theory and Applications, Motivation and Perspectives
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
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
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
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
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
Modelling Excesses over High Thresholds, with an Application
Stationary Min-Stable Stochastic Processes
Strong Approximations of Records and Record Times
High Percentiles Atmospheric SO 2 -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 Upcrossings of a Class of Non-Stationary Sequences
Back Matter
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