Table Of ContentEXTREME VALUE THEORY AND APPLICATIONS
Extreme Value Theory
and Applications
Proceedings of the Conference on
Extreme VaIue Theory and Applications, Volume 1
Gaithersburg Maryland 1993
Edited by
Janos Galambos
Department ofM athematics, Temple University,
Philadelphia, Pennsylvania, U.S.A.
James Lechner
National Institute of Standards and Technology,
Gaithersburg, Maryland, U.S.A.
and
Emil Simiu
National Institute of Standards and Technology,
Gaithersburg, Maryland, U.S.A.
Technical editing by
Nicholas Macri
Department of Mathematics, Temple University,
Philadelphia, Pennsylvania, U.S.A.
KLUWER ACADEMIC PUBLISHERS
DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging-in-Publication Data
Conference on Extreme Value Theory and Applications (1993 :
Gaithersburg. Md.)
Proceedings of the Conference on Extreme Value Theory and
Applications. Gaithersburg. Maryland. 1993 / edited by Janos
Galambos. James Lechner. and Emil Simiu.
p. cm.
Includes index.
Contents: v. 1. Extreme value theory and applications
ISBN 0-7923-2865-5 (v. 1 : aCid-free)
1. Extreme value theory~-Congresses. I. Galambos. Janos.
II. Lechner. James. III. Silliu. Emil. IV. Title.
OA273.6.C65 1993
519.2·4--dc20 94-15439
ISBN-13: 978-1-4613-3640-2 e-ISBN-13: 978-1-4613-3638-9
001: 10.1007/978-1-4613-3638-9
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TABLE OF CONTENTS
PREFACE ........................................................... ix
J.
RECOLLECTIONS of E. Gumbel
Churchill Eisenhart .............................................. xiii
INAUGURAL ADDRESS
Extreme Value Theory for Applications
janos Galambos ........•......................................... 1
CHAPTER I: ENGINEERING APPLICATIONS
Extremes in engineering applications
Enrique Castillo ................................................. 15
The Poisson-Weibull flaw model for brittle fiber strength
Howard M. Taylor ............................................... 43
Extreme value distributions for linear and non-linear systems and
applications to marine structures
Alaa E. Mansour ................................................. 61
Extreme value theory for fibre bundles
Pranab K. Sen ................................................... 77
CHAPTER II: UNIVARIATE STATISTICAL INFERENCE
Extreme value statistics
Laurens de Haan ................................................ 93
Bayes quantile estimation and threshold selection for the Generalized Pareto
family
james Pickands III .............................................. 123
Novel extreme value estimation procedures: Application to extreme wind
data
john Gross, Alan Heckert, james Lechner and Emil Simiu .......... 139
On testing the exponential and Gumbel distribution
Frank Marohn .................................................. 159
vi TABLE OF CONTENTS
CHAPTER III: COMPUTER PROGRAMS, COMPUTATIONS
XTREMES: Extreme value analysis and robustness
Rolph-Dieter Reiss, Sylvia Hassmann and Michael Thomas ......... 175
Simulations for the extreme statistics
Masaaki Sibuya ................................................ 189
Analytical and empirical study of the tails of probability distributions
janos Galambos and Nicholas Macri ............................. 199
CHAPTER IV: MULTIVARIATE THEORY AND APPLICATIONS
Concomitants of extreme order statistics
Herbert A. David ............................................... 211
Multivariate threshold methods
Richard L. Smith ............................................... 225
Applications of multivariate extremes
jonathan Tawn ................................................. 249
Some aspects of spatial extremes
Stuart Coles ................................................... 269
CHAPTER V: NONCLASSICAL MODELS
Extremes: Limit results for univariate and multivariate nonstationary
sequences
jurg Husler .................................................... 283
Extreme value limit theory with nonlinear normalization
Elisaveta Pancheva ............................................. 305
CHAPTER VI: POINT PROCESSES AND EXTREMES
Extreme values and choice theory
Sidney I. Resnick and Rishin Roy ................................. 319
Functional laws for small numbers
Michael Falk and Rolf-Dieter Reiss ............................... 337
TABLE OF CONTENTS vii
Record statistics from point process models
H. N. Nagaraja ...•.......•............•........•...•........... 355
CHAPTER VII: CONTINUOUS TIME
Extremes and exceedance measures for continuous parameter stationary
processes
M. R. Leadbetter ......•••.•.........•............•............. 371
A new class of random fields and their extreme values
Simeon M. Berman .•...•..................••................... 389
CHAPTER VIII: SPECIAL TOPICS FOR THE CLASSICAL MODEL
Penultimate behaviour of the extremes
M. Ivette Gomes ............................................... 403
Weak convergence of the Hill estimator process
David M. Mason and Tatyana S. Turova .......................... 419
On the limiting distribution of fractional parts of extreme order statistics
Roel j. G. Wilms .......••........................•............. 433
CHAPTER IX: PROBABILISTIC NUMBER THEORY
On the largest prime divisors of an integer
jean-Marie De Koninck .•....................•...............•.. 447
CHAPTER X: ASTRONOMY
Probing the nature of the brightest galaxies using extreme value theory
Suketu P. Bhavsar ............................................... 463
CHAPTER XI: BUSINESS
Safety first portfolio selection, extreme value theory and long run asset risks
L. de Haan, D. W. jansen, K. Koedijk and C. G. de Vries ...•....... 471
Extremes in non-life insurance
jan Beir/ant, jozef L. Teugels and Petra Vynckier ................... 489
SUBJECT INDEX ................................................. 511
PREFACE
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. All papers have been refereed and we are
grateful to the large number of scientists froin allover the world for giv
ing their time and taking the responsibility for evaluating the papers of
the conference.
The conference was held on the campus of the National Institute of
Standards and Technology (NIST) in Gaithersburg, Maryland, with its
Statistical Engineering Division (SED) acting as host. The organization
was a cooperative effort by Temple University (Philadelphia, Pennsylva
nia) and NIST. The conference had no external funding, and thus the
generous support from NIST was fundamental to its success. Additional
ix
x PREFACE
help is being provided by the publication of Volumes II and III at NIST,
which volumes will be directly available from NIST through SED. The
whole international community should be particularly grateful to Dr.
Robert Lundegard, Chief of SED, whose virtual unlimited support was
the single most important factor in bringing the conference into exis
tence. Whenever the Organizing Committee had any kind of difficulty
Bob was always there to help. Since Dr. Lundegard's retirement coin
cides with the publication of our Proceedings, we wish him great joy and
happiness for the'coming years.
The Organizing Committee consisted of Janos Galambos (Chair
man), James Lechner, Stefan Leigh (Director of Local Arrangements)
James Pickands III, Emil Simiu, and Grace Yang. Stefan's enthusiasm
and tireless work was critical to the success of the Conference.
There were three special sessions at the Conference. These were:
The Centennial Session for Emil Gumbel. Churchill Eisenhart
introduced the Session and Emil Simiu spoke in detail on the life and
work of Gumbel.
The Memorial Session for Josef Tiago de Oliveira. On behalf
of the International Community, Janos Galambos remembered Tiago
who was a close friend to many at the Conference and who was on the
initial list of invited speakers. M. Ivette Gomes gave a detailed account
of his work.
The 80th Birthday Session for B. V. Gnedenko. Janos Galam
bos summarized the work of Gnedenko, not only in his role as the founder
of modern extreme value theory but also his contributions to the central
limit problem, limit theorems with random sample size and reliability
theory.
Except for Eisenhart's Recollections of Gumbel, which record the
strong ties Gumbel had to NIST, the contributions to these special ses
sions are not reproduced in these Proceedings.
The Conference was opened by Dr. Robert Lundegard who, in his
relaxed manner and humorous style, expressed the deep understanding
of extreme value theory's role in several engineering fields. We all wish
that others in the government's responsible positions would be as sup
portive to our field as has been Dr. Lundegard. Not only we, but society
as a whole would benefit from it. The Conference ended with a panel
discussion on the future of extreme value theory and its applications.
The Panel was chaired by Janos Galambos, and its members were En
rique Castillo, Laurens de Haan, Lucien Le Cam and Richard 1. Smith.
PREFACE xi
The discussions were lively, spirited and enjoyable.
Both we and the contributors to this volume are grateful to Dr.
Nicholas Macri, the Technical Editor of Volume I, for so generously as
sisting us with his skill in the production of this book. Our thanks also
go to Mr. John R. Martindale, the scientific editor at Kluwer's Nor
well office who was always anxious to help during the preparation and
production of this volume.
The Editors
