Extreme Value Theory and Applications: Proceedings of the Conference on Extreme Value Theory and Applications, Volume 1 Gaithersburg Maryland 1993 (Mathematics and Its Applications)

It appears that we live in an age of disasters: the mighty Missis­ sippi and Missouri flood millions of acres, earthquakes hit Tokyo and California, airplanes crash due to mechanical failure and the seemingly ever increasing wind speeds make the storms more and more frightening. While all these may seem to be unexpected phenomena to the man on the street, they are actually happening according to well defined rules of science known as extreme value theory. We know that records must be broken in the future, so if a flood design is based on the worst case of the past then we are not really prepared against floods. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it might still suddenly fail if the aircraft has been in operation over an extended period of time. Our theory has by now penetrated the so­ cial sciences, the medical profession, economics and even astronomy. We believe that our field has come of age. In or~er to fully utilize the great progress in the theory of extremes and its ever increasing acceptance in practice, an international conference was organized in which equal weight was given to theory and practice. This book is Volume I of the Proceedings of this conference. In selecting the papers for Volume lour guide was to have authoritative works with a large variety of coverage of both theory and practice. Front Matter....Pages i-xiv Extreme Value Theory for Applications....Pages 1-14 Extremes in Engineering Applications....Pages 15-42 The Poisson-Weibull Flaw Model for Brittle Fiber Strength....Pages 43-59 Extreme Value Distributions for Linear and Non-Linear Systems and Applications to Marine Structures....Pages 61-76 Extreme Value Theory for Fibre Bundles....Pages 77-92 Extreme Value Statistics....Pages 93-122 Bayes Quantile Estimation and Threshold Selection for the Generalized Pareto Family....Pages 123-138 Novel Extreme Value Estimation Procedures: Application to Extreme Wind Data....Pages 139-158 On Testing the Exponential and Gumbel Distribution....Pages 159-174 XTREMES: Extreme Value Analysis and Robustness....Pages 175-187 Simulations for the Extreme Statistics....Pages 189-198 Analytical and Empirical Study of the Tails of Probability Distributions....Pages 199-209 Concomitants of Extreme Order Statistics....Pages 211-224 Multivariate Threshold Methods....Pages 225-248 Applications of Multivariate Extremes....Pages 249-268 Some Aspects of Spatial Extremes....Pages 269-282 Extremes: Limit Results for Univariate and Multivariate Nonstationary Sequences....Pages 283-304 Extreme Value Limit Theory with Nonlinear Normalization....Pages 305-318 Extreme Values and Choice Theory....Pages 319-336 Functional Laws of Small Numbers....Pages 337-354 Record Statistics from Point Process Models....Pages 355-370 Extremes and Exceedance Measures for Continuous Parameter Stationary Processes....Pages 371-388 A New Class of Random Fields and Their Extreme Values....Pages 389-402 Penultimate Behaviour of the Extremes....Pages 403-418 Weak Convergence of the Hill Estimator Process....Pages 419-431 On the Limiting Distribution of Fractional Parts of Extreme Order Statistics....Pages 433-446 On the Largest Prime Divisors of an Integer....Pages 447-462 Probing the Nature of the Brightest Galaxies Using Extreme Value Theory....Pages 463-470 Safety First Portfolio Selection, Extreme Value Theory and Long Run Asset Risks....Pages 471-487 Extremes in Non-Life Insurance....Pages 489-510 Back Matter....Pages 511-519

the Contributions In This Volume Represent A Selection Of The Papers Presented At The Conference On Extreme Value Theory And Applications Held In Gaithersburg, Maryland In 1993.
Recent Rapid Advancement In The Theory Of Extremes, In The Statistical Inference Of Extreme-related Problems And The Ever-increasing Acceptance Of The Theory In Applications Brought Together The Leading Experts In The Fields Of Model Building Statistics, Engineering And Business, Whose Authoritative Presentations On These Matters Are Published In This Volume. A Variety Of Engineering Applications Are Covered: Strength Due To Fatigue Failure, Bundle Strength Of Fibre, Longest Living Humans, Concomitants Of Extremes Such As Characteristics Of Offspring Of The Present Generation, Long-run Asset Risk, Reinsurance, High Winds, And Other Applications. The Theoreticians Address Model Building And The Newest Results Of Statistical Inference, Including Bayesian Methods. This Is The First Such Mix Of The Theory And Applications Of Extremes To Be Published.
For Statisticians, Mathematicians, Engineers And Business Professionals With A Basic Knowledge Of Probability And Statistics.