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Statistical Extremes and Applications

✍ Scribed by Benjamin Epstein (auth.), J. Tiago de Oliveira (eds.)


Publisher
Springer Netherlands
Year
1984
Tongue
English
Leaves
690
Series
NATO ASI Series 131
Edition
1
Category
Library

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✦ Synopsis


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 emerΒ­ 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 ProbaΒ­ 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


Front Matter....Pages i-xii
Statistical Extremes: Theory and Applications, Motivation and Perspectives....Pages 1-2
Extremes in Dependent Random Sequences....Pages 155-165
Extremes in Continuous Stochastic Processes....Pages 167-180
Comparison Technique for Highly Dependent Stationary Gaussian Processes....Pages 181-195
Extremes in Hydrology....Pages 197-220
Application of Extreme Values in Structural Engineering....Pages 221-234
Extremes in Meteorology....Pages 235-252
Extreme Values in Insurance Mathematics....Pages 253-259
Introduction, Order Statistics, Exceedances. Laws of Large Numbers....Pages 3-17
Asymptotics; Stable Laws for Extremes; Tail Properties....Pages 19-29
Slow Variation and Characterization of Domains of Attraction....Pages 31-48
Introduction, Gumbel Model....Pages 49-80
Statistical Estimation of Parameters of the Weibull and Frechet Distributions....Pages 81-89
Univariate Extremes; Statistical Choice....Pages 91-107
Statistical Estimation in Extreme Value Theory....Pages 109-115
Probabilistic Aspects of Multivariate Extremes....Pages 117-130
Bivariate Models for Extremes; Statistical Decision....Pages 131-153
Use and Structure of Slepian Model Processes for Prediction and Detection in Crossing and Extreme Value Theory....Pages 261-284
Spline and Isotonic Estimation of the Pareto Function....Pages 285-296
Extremal Processes....Pages 297-309
Extreme Values for Sequences of Stable Random Variables....Pages 311-324
Large Deviations of Extremes....Pages 325-340
Uniform Rates of Convergence to Extreme Value Distributions....Pages 341-346
Rates of Convergence in Extreme Value Theory....Pages 347-352
Concomitants in a Multidimensional Extreme Model....Pages 353-364
A Short Cut Algorithm for Obtaining Coefficients of the Blue’s....Pages 365-371
Statistical Choice of Univariate Extreme Models. Part II....Pages 373-394
Doubly Exponential Random Number Generators....Pages 395-402
Probability Problems in Seismic Risk and Load Combinations for Power Plants....Pages 403-411
The Distribution of the Maximal Time Till Departure from a State in a Markov Chain....Pages 413-426
The Box-Jenkins Model and the Progressive Fatigue Failure of Large Parallel Element Stay Tendons....Pages 427-434
The Asymptotic Behaviour of the Maximum Likelihood Estimates for Univariate Extremes....Pages 435-442
On Upper and Lower Extremes in Stationary Sequences....Pages 443-460
Modelling Excesses over High Thresholds, with an Application....Pages 461-482
Stationary Min-Stable Stochastic Processes....Pages 483-489
Strong Approximations of Records and Record Times....Pages 491-496
High Percentiles Atmospheric SO 2 -Concentrations in Belgium....Pages 497-502
Extreme Response of the Linear Oscillator with Modulated Random Excitation....Pages 503-512
Frost Data: A Case Study on Extreme Values of Non-Stationary Sequences....Pages 513-520
Estimation of the Scale and Location Parameters of the Extreme Value (Gumbel) Distribution for Large Censored Samples....Pages 521-534
Asymptotic Behaviour of the Extreme Order Statistics in the Non Identically Distributed Case....Pages 535-547
Limit Distribution of the Minimum Distance between Independent and Identically Distributed d-Dimensional Random Variables....Pages 549-562
Approximate Values for the Moments of Extreme Order Statistics in Large Samples....Pages 563-578
Estimation of Parameters of Extreme Order Distributions of Exponential Type Parents....Pages 579-588
On Ordered Uniform Spacings for Testing Goodness of Fit....Pages 589-596
Inequalities for the Relative Sufficiency between Sets of Order Statistics....Pages 597-610
Pot-Estimation of Extreme Sea States and the Benefit of Using Wind Data....Pages 611-620
Threshold Methods for Sample Extremes....Pages 621-638
On Successive Record Values in a Sequence of Independent Identically Distributed Random Variables....Pages 639-650
Two Test Statistics for Choice of Univariate Extreme Models....Pages 651-668
On the Asymptotic Upcrossings of a Class of Non-Stationary Sequences....Pages 669-678
Back Matter....Pages 679-692

✦ Subjects


Statistics, general


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