Ordered Random Variables: Theory and Applications
Ordered Random Variables have attracted several authors. The basic building block of Ordered Random Variables is Order Statistics which has several applications in extreme value theory and ordered estimation. The general model for ordered random variables
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Muhammad Qaiser Shahbaz Mohammad Ahsanullah Saman Hanif Shahbaz Bander M. Al-Zahrani
Ordered Random Variables: Theory and Applications
Atlantis Studies in Probability and Statistics Volume 9
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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Muhammad Qaiser Shahbaz Mohammad Ahsanullah Saman Hanif Shahbaz Bander M. Al-Zahrani
Ordered Random Variables: Theory and Applications
Muhammad Qaiser Shahbaz Department of Statistics King Abdulaziz University Jeddah Saudi Arabia
Saman Hanif Shahbaz Department of Statistics King Abdulaziz University Jeddah Saudi Arabia
Mohammad Ahsanullah Department of Management Sciences Rider University Lawrenceville, NJ USA
Bander M. Al-Zahrani Department of Statistics King Abdulaziz University Jeddah Saudi Arabia
ISSN 1879-6893 ISSN 1879-6907 (electronic) Atlantis Studies in Probability and Statistics ISBN 978-94-6239-224-3 ISBN 978-94-6239-225-0 (eBook) DOI 10.2991/978-94-6239-225-0 Library of Congress Control Number: 2016951690 © Atlantis Press and the author(s) 2016 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 Father, Mother and my Wife Saman Muhammad Qaiser Shahbaz To my Father, Mother and my Wife, Masuda Mohammad Ahsanullah To my Father, Mother and my Husband Shahbaz Saman Hanif Shahbaz To my parents Bander Al-Zahrani
Preface
Ordered random variables have attracted several researchers due to their applicability in many areas, like extreme values. These variables occur as a natural choice when deali
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