Characterizations of Probability Distributions A Unified Approach wi
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675 Janos Galambos Samuel Kotz
Characterizations of Probability Distributions A Unified Approach with an Emphasis on Exponential and Related Models
Springer-Verlag Berlin Heidelberg New York 1978
Authors Janos Galambos Samuel Katz Temple University College of Liberal Arts Department of Mathematics Philadelphia, PA 19122/USA
AMS Subject Classifications (1970): 62ElO, 62 H05
ISBN 3-540-08933-0 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-08933-0 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin Heidelberg 1978 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
PREFACE The stimulus for this research project was supplied during the 1974 Calgary Conference on Characterizations of Distributions organized by G,P. Patil; both of us were active participants in this conference and could not help but notice the multitude of results on characterizations widely scattered in the literature. Our aim in writing this monograph is twofold. One is to bring together the results in this useful and rapidly growing field in order to encourage further fruitful research in this area. We also have in mind a somewhat different objective, which in our opinion, is not less important and urgent at this time of rapid and unprecedented growth in periodical literature. The field of characterizations was independently developed in different branches of applied probability and pure mathematics which inevitably resulted in a certain amount of duplication of efforts. Moreover the terminology used in different subdisciplines by various authors is not the same. Our second aim is therefore to unify the existing theory. We found that seemingly unrelated matheamtical theorems turned out to be part of the same general theory. We therefore tried to discover the unifying thread which passes through the majority of the papers written in the past one and a half decades in the field of characterizations of statistical distributions (in particular those dealing with the exponential distribution, both univariate and multivariate, and its monotonic transformations, which is the subject of this monograph). However, we should point out that there are still a number of as yet unsolved problems, for example, those stemming from Rossberg's results which require additional investigation. This monograph contains no overlap with existing books on characterizations, since earlier books concentrated mainly on normality, which we do not discuss in our book. Moreover, as a rule, results dealing with exponential distribution
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