Statistical Extremes and Applications

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