Stochastic Orders
Stochastic ordering is a fundamental guide for decision making under uncertainty. It is also an essential tool in the study of structural properties of complex stochastic systems. This reference text presents a comprehensive coverage of the various notion
- PDF / 3,451,625 Bytes
- 482 Pages / 441 x 666 pts Page_size
- 36 Downloads / 184 Views
Moshe Shaked J. George Shanthikumar
Stochastic Orders
Moshe Shaked Department of Mathematics University of Arizona Tucson, AZ 85721 [email protected] J. George Shanthikumar Department of Industrial Engineering and Operations Research University of California, Berkeley Berkeley, CA 94720 [email protected]
Library of Congress Control Number: 2006927724 ISBN-10: 0-387-32915-3 ISBN-13: 978-0387-32915-4 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com
To my wife Edith and to my children Tal, Shanna, and Lila M.S. To my wife Mellony and to my children Devin, Rajan, and Sohan J.G.S.
To my wife Edith and to my children Tal Shanna Lila
To my wife Mellony and to my children Devin Rajan Sohan
Preface
Stochastic orders and inequalities have been used during the last 40 years, at an accelerated rate, in many diverse areas of probability and statistics. Such areas include reliability theory, queuing theory, survival analysis, biology, economics, insurance, actuarial science, operations research, and management science. The purpose of this book is to collect in one place essentially all that is known about these orders up to the present. In addition, the book illustrates some of the usefulness and applicability of these stochastic orders. This book is a major extension of the first six chapters in Shaked and Shanthikumar [515]. The idea that led us to write those six chapters arose as follows. In our own research in reliability theory and operations research we have been using, for years, several notions of stochastic orders. Often we would encounter a result that we could easily (or not so easily) prove, but we could not tell whether it was known or new. Even when we were sure that a result was known, we would not know right away where it could be found. Also, sometimes we would prove a result for the purpose of an application, only to realize later that a stronger result (stronger than what we needed) had already been derived elsewhere. We also often have had difficulties giving a reference for one source that contained everything about stochastic orders that we needed in a particular paper. In order to avoid such difficulties we wrote the first six chapters in Shaked and Shanthikumar [515]. Since 1994 the theory of stochastic orders
Data Loading...
