Characterizations of Univariate Continuous Distributions
Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with ap
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Mohammad Ahsanullah
Characterizations of Univariate Continuous Distributions
Atlantis Studies in Probability and Statistics Volume 7
Series editor Chris P. Tsokos, Tampa, USA
Aims and scope of the series The series ‘Atlantis Studies in Probability and Statistics’ publishes studies of high quality throughout the areas of probability and statistics that have the potential to make a significant impact on the advancement in these fields. Emphasis is given to broad interdisciplinary areas at the following three levels: (I) Advanced undergraduate textbooks, i.e., aimed at the 3rd and 4th years of undergraduate study, in probability, statistics, biostatistics, business statistics, engineering statistics, operations research, etc.; (II) Graduate-level books, and research monographs in the above areas, plus Bayesian, nonparametric, survival analysis, reliability analysis, etc.; (III) Full Conference Proceedings, as well as selected topics from Conference Proceedings, covering frontier areas of the field, together with invited monographs in special areas. All proposals submitted in this series will be reviewed by the Editor-in-Chief, in consultation with Editorial Board members and other expert reviewers. For more information on this series and our other book series, please visit our website at: www.atlantis-press.com/Publications/books AMSTERDAM—PARIS—BEIJING ATLANTIS PRESS Atlantis Press 29, avenue Laumière 75019 Paris, France
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Mohammad Ahsanullah
Characterizations of Univariate Continuous Distributions
Mohammad Ahsanullah Department of Management Sciences Rider University Lawrenceville, NJ USA
ISSN 1879-6893 ISSN 1879-6907 (electronic) Atlantis Studies in Probability and Statistics ISBN 978-94-6239-138-3 ISBN 978-94-6239-139-0 (eBook) DOI 10.2991/978-94-6239-139-0 Library of Congress Control Number: 2017934309 © Atlantis Press and the author(s) 2017 This book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher. Printed on acid-free paper
To my grand children, Zakir, Samil, Amil and Julian.
Preface
Characterization of distributions plays an important role in statistical science. Using the basic properties of data, characterizations provide the type of distributions of that data set. Significant findings in this area have been published over the last several decades, and this book serves to be an extensive compilation of many important characterizations of univariate continuous distributions. Chapter 1 presents basic properties common to all univariate continuous distributions, while Chap. 2 discusses the properties of some select important distributions. Chapter 3 discusses ways to use independent copies of random variables to characterize distributions. Chapters 4–6 characterize distributions using order statistics, record v
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