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Dirichlet and Related Distributions Dirichlet and Related Distributions: Theory, Methods and Applications, First Edition. Kai Wang Ng, Guo-Liang Tian and Man-Lai Tang. © 2011 John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd. ISBN: 978-0-470-68819-9 WILEY SERIES IN PROBABILITY AND STATISTICS Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors David J. Balding, Noel A.C. Cressie, Garrett M. Fitzmaurice, Harvey Goldstein, Geert Molenberghs, David W. Scott, Adrian F.M. Smith, Ruey S. Tsay, Sanford Weisberg Editors Emeriti Vic Barnett, Ralph A. Bradley, J. Stuart Hunter, J.B. Kadane, David G. Kendall, Jozef L. Teugels A complete list of the titles in this series can be found on http://www.wiley.com/ WileyCDA/Section/id-300611.html. Dirichlet and Related Distributions Theory, Methods and Applications Kai Wang Ng • Guo-Liang Tian Department of Statistics and Actuarial Science The University of Hong Kong, Hong Kong Man-Lai Tang Department of Mathematics, Hong Kong Baptist University Kowloon Tong, Hong Kong This edition first published 2011 © 2011 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Ng, Kai Wang, author. Dirichlet and Related Distributions : Theory, Methods and Applications / Kai Wang Ng, Guo-Liang Tian, Man-Lai Tang. p. cm. – (Wiley Series in Probability and Statistics) Includes bibliographical references and index. ISBN 978-0-470-68819-9 (hardback) 1. Distribution (Probability theory) 2. Dirichlet problem. I. Tian, Guo-Liang, author. II. Tang, Man-Lai, author. III. Title. QA276.7.N53 2011 519.2’4–dc22 2010053428 A catalogue record for this book is available from the British Library. Print ISBN: 978-0-470-68819-9 ePDF ISBN: 978-1-119-99586-9 oBook ISBN: 978-1-119-99578-4 ePub ISBN: : 978-1-119-99841-9 Mobi ISBN: 978-1-119-99842-6 Typeset in 10.25/12pt, Times Roman, by Thomson Digital, Noida, India To May, Jeanne, Jason and his family To Yanli, Margaret and Adam To Daisy and Beatrice Contents Preface xiii Acknowledgments xv List of abbreviations xvii List of symbols xix List of figures xxiii List of tables xxv 1 Introduction 1.1 Motiva