Extreme Value Distributions
The aim of the book is to give a through account of the basic theory of extreme value distributions. The book cover a wide range of materials available to date. The central ideas and results of extreme value distributions are presented. The book rwill be
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Mohammad Ahsanullah
Extreme Value Distributions
Atlantis Studies in Probability and Statistics Volume 8
Series editor Chris P. Tsokos, Tampa, USA
Aims and scope of the series The series ‘Atlantis Studies in Probability and Statistics’ publishes studies of high quality throughout the areas of probability and statistics that have the potential to make a significant impact on the advancement in these fields. Emphasis is given to broad interdisciplinary areas at the following three levels: (I) Advanced undergraduate textbooks, i.e., aimed at the 3rd and 4th years of undergraduate study, in probability, statistics, biostatistics, business statistics, engineering statistics, operations research, etc.; (II) Graduate-level books, and research monographs in the above areas, plus Bayesian, nonparametric, survival analysis, reliability analysis, etc.; (III) Full Conference Proceedings, as well as selected topics from Conference Proceedings, covering frontier areas of the field, together with invited monographs in special areas. All proposals submitted in this series will be reviewed by the Editor-in-Chief, in consultation with Editorial Board members and other expert reviewers. For more information on this series and our other book series, please visit our website at: www.atlantis-press.com/Publications/books AMSTERDAM—PARIS—BEIJING ATLANTIS PRESS Atlantis Press 29, avenue Laumière 75019 Paris, France
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Mohammad Ahsanullah
Extreme Value Distributions
Mohammad Ahsanullah Department of Management Sciences Rider University Lawrenceville, NJ USA
ISSN 1879-6893 ISSN 1879-6907 (electronic) Atlantis Studies in Probability and Statistics ISBN 978-94-6239-221-2 ISBN 978-94-6239-222-9 (eBook) DOI 10.2991/978-94-6239-222-9 Library of Congress Control Number: 2016947032 © Atlantis Press and the author(s) 2016 This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher. Printed on acid-free paper
Preface
Extreme values are extremely interesting. The maximum or minimum of large number observations when normalized can only converge to three types of extreme value distributions, Gumbel, Frechet and Weibull. Thus the maximum and minimum order statistics of n observations when normalized converges to the extreme value distributions as n tends to infinity. The local maximum or minimum (records) of a sequence of independent and identically distributed random variables are useful to estimate the parameters of the extreme value distributions. In Chap. 1 of this book some distributional properties of the largest and smallest order statistics from some important distributions are presented. In Chap. 2 some basic properties of record values and inferences based on the distributional properties are given. In Chap. 3 the necessary and sufficient conditions
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