Continuous Bivariate Distributions Second Edition
Random variables are rarely independent in practice and so many multivariate distributions have been proposed in the literature to give a dependence structure for two or more variables. In this book, we restrict ourselves to the bivariate distributions fo
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N. Balakrishnan · Chin-Diew Lai
Continuous Bivariate Distributions Second Edition
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N. Balakrishnan Department of Mathematics & Statistics McMaster University 1280 Main St. W. Hamilton ON L8S 4K1 Canada [email protected]
Chin-Diew Lai Institute of Fundamental Sciences Massey University 11222 Private Bag Palmerston North New Zealand [email protected]
ISBN 978-0-387-09613-1 e-ISBN 978-0-387-09614-8 DOI 10.1007/b101765 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009928494 c Springer Science+Business Media, LLC 2009 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my loving mother, Lakshmi, and lovely memories of my father, Narayanaswamy N.B.
To Ai Ing, Joseph, Eugene, Serena, my brother Chin-Yii, and my parents C.D.L.
Preface
This volume, which is completely dedicated to continuous bivariate distributions, describes in detail their forms, properties, dependence structures, computation, and applications. It is a comprehensive and thorough revision of an earlier edition of “Continuous Bivariate Distributions, Emphasizing Applications” by T.P. Hutchinson and C.D. Lai, published in 1990 by Rumsby Scientific Publishing, Adelaide, Australia. It has been nearly two decades since the publication of that book, and much has changed in this area of research during this period. Generalizations have been considered for many known standard bivariate distributions. Skewed versions of different bivariate distributions have been proposed and applied to model data with skewness departures. By specifying the two conditional distributions, rather than the simple specification of one marginal and one conditional distribution, several general families of conditionally specified bivariate distributions have been derived and studied at great length. Finally, bivariate distributions generated by a variety of copulas and their flexibility (in terms of accommodating association/correlation) and structural properties have received considerable attention. All these developments and advances necessitated the present volume and have thus resulted in a substantially different version than the last edition, both in terms of coverage and topics of discussion. In a volume of this size and wide coverage, there will inevitably be some mist
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