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This book introduces a new approach, denoted RMM, for an empirical modeling of a response variation, relating to both systematic variation and random variation. In the book, the developer of RMM discusses the required properties of empirical modeling and evaluates how current approaches conform to these requirements. In addition, he explains the motivation for the development of the new methodology, introduces in detail the new approach and its estimation procedures, and shows how it may provide an excellent alternative to current approaches for empirical modeling (like Generalized Linear Modeling, GLM). The book also demonstrates that a myriad of current relational models, developed independently in various engineering and scientific disciplines, are in fact special cases of the RMM model, and so are many current statistical distributions, transformations and approximations.
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Response Modeling Methodology This page intentionally left blank Series on Quality, Reliability and Engineering Statistics Response Modeling Methodology Empirical Modeling for Engineering and Science Haim Shore Ben-Gurian University of the Negev, Israel We World Scientific NEW JERSEY · LONDON · SINGAPORE · BEIJING · SHANGHAI · HONG KONG · TAIPEI · CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Series on Quality, Reliability and Engineering Statistics — Vol. 8 RESPONSE MODELING METHODOLOGY (RMM) Empirical Modeling for Engineering and Science Copyright © 2005 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-256-102-1 Printed in Singapore. 'HGLFDWHG WR P\ SDUHQWV +DYD DQG 'DQLHO ZKRVH OLYHV KDYH KHURLFDOO\ GHILHG DGYHUVLW\ Y This page intentionally left blank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