Advances in Distribution Theory, Order Statistics, and Inference
Barry Arnold has made fundamental contributions to many different areas of statistics, including distribution theory, Bayesian inference, multivariate analysis, bounds and orderings, and characterization problems. Organized to honor Arnold’s significant c
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Series Editor N. Balakrishnan McMaster University Department of Mathematics and Statistics 1280 Main Street West Hamilton, Ontario L8S 4K1 Canada
Editorial Advisory Board Max Engelhardt EG&G Idaho, Inc. Idaho Falls, ID 83415 Harry F. Martz GroupA-lMSF600 Los Alamos National Laboratory Los Alamos, NM 87545 Gary C. McDonald NAO Research & Development Center 30500 Mound Road Box 9055 Warren, MI 48090-9055 Peter R. Nelson Department of Mathematical Sciences Clemson University Martin Hall Box 341907 Clemson, SC 29634-1907 Kazuyuki Suzuki Communication & Systems Engineering Department University of Electro Communications 1-5-1 Chofugaoka Chofu-shi Tokyo 182 Japan
Advances in Distribution Theory, Order Statistics, and Inference
N. Balakrishnan Enrique Castillo Jose Maria Sarabia Editors
Birkhauser Boston • Basel • Berlin
N. Balakrishnan McMaster University Department of Mathematics and Statistics 1280 Main Street West Hamilton, Ontario L8S 4K1 Canada
Enrique Castillo University of Cantabria Department of Applied Mathematics s/n Avenida de los Castros Santander 39005 Spain
Jose Maria Sarabia University of Cantabria Department of Economics s/n Avenida de los Castros Santander 39005 Spain
Mathematics Subject Classification: 62E10,62E15,62E20,62F03,62F10,62G30,62J05,62N01,62N02,62N05, 62P12, 62P20, 62P30 Library of Congress Control Number: 2006900999 ISBN-10: 0-8176-4361-3
e-ISBN: 0-8176-4487-3
ISBN-13: 978-0-8176-4361-4 Printed on acid-free paper. ©2006 Birkhauser Boston All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhauser Boston, c/o 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 in the United States of America. 987654321 www.birkhauser.com
(HP)
In Honor of Barry C. Arnold
BARRY C. ARNOLD
Contents
Preface Barry C. Arnold: Career and Accomplishments Publications Contributors List of Tables List of Figures
xix xxi xxiii xli xlvii li
PART I: DISCRETE DISTRIBUTIONS AND APPLICATIONS
1 Stochastic Comparisons of Bernoulli Sums and Binomial Random Variables P, J, Boland and H. Singh
3
1.1 Introduction 3 1.2 Stochastic Orders for Random Variables 5 1.3 Stochastic Order Comparisons for Sums of Bernoulh Random Variables 6 1.4 Graphical Insight for Two-Dimensional Stochastic Comparisons 8 References 11 2 Stopped Compound Poisson Process and Related Distributions C. Lefevre 2.1 Introduction 13 2.2 The Boundary Is Linear 15 2.3 The Boundary Is of Renewal Type 18 2.4 The Boundar
