Comparing Distributions
Comparing Distributions refers to the statistical data analysis that encompasses the traditional goodness-of-fit testing. Whereas the latter includes only formal statistical hypothesis tests for the one-sample and the K-sample problems, this book presents
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Olivier Thas
Comparing Distributions
Springer Series in Statistics Advisors: P. Bickel, P. Diggle, S. Fienberg, U. Gather, I. Olkin, S. Zeger
For other titles published in this series, go to http://www.springer.com/series/692
Olivier Thas
Comparing Distributions
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Olivier Thas Department of Applied Mathematics Biometrics, and Process Control Ghent University Coupure Links 653 B-9000 Gent Belgium [email protected]
ISSN: 0172-7397 ISBN: 978-0-387-92709-1 ISBN: 978-0-387-92710-7 (eBook) DOI: 10.1007/978-0-387-92710-7 Library of Congress Control Number: 2009935174 c Springer Science+Business Media, LLC 2010 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.com
To Ingeborg and my parents
Preface
This book is mainly about goodness-of-fit testing, particularly about tests for the one- and the two- and K-sample problems. In the one-sample problem we need to test the hypothesis that the sample observations have a hypothesised distribution, whereas the two-sample problem is concerned with testing the equality of the distributions of two independent samples. Both testing problems are almost as old as statistical science itself. For instance, the well-known Pearson chi-squared test for testing goodness-of-fit to a discrete multinomial distribution, was proposed back in 1900 by Karl Pearson, who is generally recognised as one of the fathers of statistics. Another important test is the smooth test for testing uniformity which was proposed in 1937 by Jerzy Neyman, another founder of modern statistics. The Kolmogorov– Smirnov test dates from the same period, and in the middle of the century the Anderson–Darling and Cram´er–von Mises tests were published. The roots of the two-sample problem also date back to the first half of the twentieth century. Frank Wilcoxon published his nonparametric rank test in 1945, and if we consider the Student-t test also as a two-sample test, though under very restrictive parametric assumptions, then we even have to go back to 1908. Despite the age of many of these methods, they are still very often used in daily statistical practice, and they are taught in almost any basic statistics course. These older methods are also frequently referred to in the contemporary statistical literature. Moreover, goodness-of-fit is still a very active research domain, and many of the newer techniqu
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