The Information Theory of Comparisons With Applications to Statistic
This book finds a broad domain of relevance in statistics and the social sciences. Its conceptual development is supported by applications to economics and income distribution, finance, education, demographics and actuarial science, political studies, psy
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The Information Theory of Comparisons With Applications to Statistics and the Social Sciences
The Information Theory of Comparisons
Roger Bowden
The Information Theory of Comparisons With Applications to Statistics and the Social Sciences
123
Roger Bowden Kiwicap Research Ltd. Kelburn, Wellington New Zealand
ISBN 978-981-13-1549-7 ISBN 978-981-13-1550-3 https://doi.org/10.1007/978-981-13-1550-3
(eBook)
Library of Congress Control Number: 2018947773 © Springer Nature Singapore Pte Ltd. 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
Every now and then, research interests that have hitherto been tucked away in the recesses of the mind suddenly converge and come to the fore. So, it is with the present contribution. Any social scientist has constantly to face up to the problem of comparing distributions, whether across people, across nations, over time or how they might impact on the survival of a financial entity. And the audience being what it typically is, one has to present such comparisons and contrasts with as much impact as possible, but also with as much brevity as limited time, and even more limited attention (in the media for instance), typically allows. It had always struck me how little the standard metrics really inform such comparisons. Likewise, I had been reasonably familiar with information theory, from the time of my Manchester Ph.D. thesis on the spectral domain and later, from the work on income distribution of scholars like Henri Theil. But it did seem to me at the time that the standard entropy metric, as it stood, told one remarkably little. Yet, the fascination remained, just as I think it still does with so many researchers
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