Fundamentals of Order and Rank Statistics

This book is devoted to the fundamentals of order and rank statistics. Primarily focusing on theoretical properties, it also discusses practical aspects, including interesting applications of step and impulse functions for the distribution of random variables, magnitudes, and signs. New concepts are introduced, such as independent and semi-identically distributed random vectors and probability density-mass functions. This book also presents an investigation of relative magnitudes in order statistics, and of correlation coefficients among signs, ranks, and magnitudes.

The basic concepts are described in clear terms, and step-by-step details are provided for most of the presented mathematical results. The exposition is accompanied by numerous examples and more than 100 exercises, for which a complete solution manual is available.

Providing a useful reference, and requiring only a basic understanding of probability and random variables, the book will appeal to a wide readership.

Iickho Song received the BSE and MSE degrees in electronics engineering from Seoul National University, Seoul, Korea, in 1982 and 1984, respectively, and the MSE and Ph.D. degrees in electrical engineering from the University of Pennsylvania, Philadelphia, PA, USA, in 1985 and 1987, respectively. In March 1988, Dr. Song joined the School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, Korea, where Dr. Song is currently a Professor. Dr. Song was an International Visiting Professor at the University of Science and Technology of China, Hefei, Anhui, China, in 2023.
The research interests of Dr. Song include communications theory, signal detection theory, and statistical signal processing. Dr. Song is a Fellow of the IEEE, IET, and KICS.

So Ryoung Park received the BS degree in electronics engineering from Yonsei University, Seoul, Korea, in 1997, and the MSE and Ph.D. degrees in electrical engineering from Korea Advanced Institute of Science and Technology, Daejeon, Korea, in 1999 and 2002, respectively. In March 2003, Dr. Park joined the School of Information, Communications, and Electronics Engineering, the Catholic University of Korea, Bucheon, Korea, where Dr. Park is currently a Professor.

The research interests of Dr. Park include detection and estimation theory, statistical signal processing, and wireless communications. Dr. Park is a Senior Member of the IEEE.

Wenyi Zhang received the bachelor’s degree in automation from Tsinghua University, Beijing, China, in 2001, and the master’s and Ph.D. degrees in electrical engineering from the University of Notre Dame, Notre Dame, IN, USA, in 2003 and 2006, respectively. Dr. Zhang is currently a Professor with the Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China. Prior to that, Dr. Zhang was with the University of Southern California, Los Angeles, CA, USA, as a postdoctoral research associate, and the Corporate Research and Development, Qualcomm Incorporated, San Diego, CA, USA.

The research interests of Dr. Zhang include wireless communications, information theory, and signal detection/estimation. Dr. Zhang is a Senior Member of the IEEE.

Seungwon Lee received the Ph.D. degree in electrical engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2018. From 2018 to 2020, Dr. Lee was with the School of Electrical Engineering, KAIST as a Postdoctoral Research Fellow. Since 2020, Dr. Lee has been with the Modem Development Team, SOC Development, System LSI Business Department, Samsung Electronics, Hwaseong-si, Gyeonggido Korea.

The research interests of Dr. Lee include mobile communications, detection and estimation theory, and statistical signal processing. Dr. Lee is a Senior Member of the IEEE.