TECH NATL INST. OF STAND & United States Department of Commerce Technology Administration National Institute of Standards and Technology ^^^'^ REFERENCI PUBLICATIONS NIST Special Publication 866 Extreme Value Theory and Applications Proceedings of the Conference on Extreme Value Theory and Applications, Volume 3 Gaithersburg, Maryland, May 1993 Janos Galambos, James Lechner and Emil Simiu, Editors Charles Hagwood, Technical Editor CEOnnCNEIIC FIELD CNHNOIESLns) or IGnfOS TEnn- ipa;.o alt. !>09.o (icn) Figure 1 JacK-up plalfonn wiih cajililcvcr. Figure 10 Geomagnetic Field Contour Map On MOS-1 Orbit 'Vy\K \ (Cnimbcl). ,y( i ) = c\p(-c\|i(- v j). .v £ IR Type II U'n-chc/): = exp(-v~"), v > 0. a X) Type III [Wcihiill): = e\p(-(-v)«), ,v < 0, a > 0 1 n 1 (JLSl Threshold, ft95 b 7he National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering and performs related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. Major technical operating units and their principal activities are listed below. For more information contact the Public Inquiries Desk, 301-975-3058. 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'Some elements at Boulder, CO 80303. NIST Special Publication 860 Extreme Value Theory and Applications Proceedings of the Conference on Extreme Value Theory and Applications, Volume 3 Gaithersburg, Maryland, May 1993 Janos Galambos, James Lechner and Emil Simiu, Editors Charles Hagwood, Technical Editor Statistical Engineering Division Computing and Applied Mathematics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899-0001 August 1994 U.S. Department of Commerce Ronald H. Brown, Secretary Technology Administration Mary L. Good, Under Secretary for Technology National Institute of Standards and Technology Arati Prabhakar, Director National Institute of Standards U.S. Government Printing Office For sale by the Superintendent and Technology Washington: 1994 of Documents Special Publication 866 U.S. Government Printing Office Natl. Inst. Stand. Technol. Washington, DC 20402 Spec. Publ. 866 231 pages (Aug. 1994) CODEN: NSPUE2 PREFACE It appears that we live in an age of disasters: the Mississippi and the Missouri rivers flood millions of acres, earthquakes bit Tokyo and California, airplanes crash due to mechanical failure, and powerful windstorms cause increasingly costly damage. While 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. For many phenomena records must be broken in the future, so if a design is based on the worst case of the past then we are not really prepared for the future. Materials will fail due to fatigue: even if the body of an aircraft looks fine to the naked eye, it might suddenly fail if the aircraft has been in operation over an extended period of time. Extreme value theory has by now penetrated the social sciences, the medical profession, economics, and even astronomy. We believe this field has come of age. To utilize and stimulate progress in the theory of extremes and promote its application, an international conference was organized in which equal weight was given to theory and practice. The Proceedings are published in three Volumes. Volume I, pubhshed by Klewer Academic Publishers, contains papers of general interest in extreme value theory and practice. Volume II, a special issue of the NIST Journal of Research, contains papers deemed by the Committee to be most directly relevant to NIST's mission. Volume III (this volume) contains papers selected for their important contribution to a number of specialized topics. All papers have been refereed and we are grateful to the many scientists from all over the world for serving as referees. 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. It was organized by Temple University, Philadelphia, Pennsylvania, and NIST. The conference had no external funding, and NIST's support was fundamental to its success. We are particularly grateful to Dr. Robert Lundegard, Chief of SED, whose support was the single most important factor in making the conference happen. The support of NIST's Building and Fire Research Laboratory is also acknowledged with thanks. The Organizing Committee consisted of Janos Galambos (Chairman), James Lechner, Stefan Leigh (Director of Local Arrangements), James Pickands III, Emil Simiu, and Grace Yang. Stefan's enthusiasm and tireless work was essential for the success of the Conference. The Conference included three special sessions: The Centennial Session for Emil Gumbel. Churchill Eisenhart introduced the Session. His personal recollections of Gumbel are included in Volume I of the Proceedings. Emil Simiu then spoke on Gumbel 's life and work. iii The Memorial Session for Josef Tiago de Oliveira. Janos Galambos remembered Tiago, a close friend to many Conference participants, who was on the initial hst of invited speakers. M. Ivette Gomes gave a detailed account of his work. The 80th Birthday Session for B. V. Gnedenko. Janos Galambos summarized the work of Gnedenko as the founder of modern extreme value theory and his contributions to the central limit problem, hmit theorems with random sample size and renewal theory. Preceding the Conference, a Short Course was presented. Prof. Galambos gave an introductory lecture on general principles of extreme value theory, and Prof. Castillo presented a four-hour course on "Engineering Analysis of Extreme Value Data." Prof. Castillo's notes were distributed to all Conference participants. The Conference was opened by Dr. Robert Lundegard who emphasized extreme value theory's role in several scientific and engineering fields. It 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 Enrique Castillo, Laurens de Haan, Lucien Le Cam and Richard L. Smith. Finally, special thanks are extended to Shirley G. Bremer and Kaye Wade of the Statistical Engineering Division at NIST, for their tireless and efficient work on preparation for the Conference, including the typing of the Abstracts volume distributed at registration. The Editors iv TABLE OF CONTENTS On The Record Values From Univariate Distributions 1 Ahsanullah, M., Rider College, Lawerenceville, NJ Composite Sampling And Extreme Values 7 Argon, E.D., Gore, S.D.,and Patil, G.P., The Pennsylvania State University, University Park, PA Extremal Sojourn Times For Markov Chains 19 Arnold, B.C., University of California, Riverside, CA Bootstrapping Extremes Of I.I, D. Random Variables 23 Athreya, K.B., and Fukuchi,