Sharp Inequalities for Ordered Random Variables in Statistics and Reliability

Professor N. Balakrishnan is a Distinguished University Professor in the Department of Mathematics and Statistics at McMaster University, Hamilton, Canada.  He is a Fellow of the Royal Society of Canada, a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and a recipient of an honorary doctoral degree from the National and Kapodistrian University of Athens, Greece. He is an author of many well-known books and research monographs in Statistics including the well-known four encyclopedic volumes on Statistical Distributions published by John Wiley & Sons.  He is currently the Editor-in-Chief of three series of Communications in Statistics as well as Mathematical Methods of Statistics.Professor Tomasz Rychlik received the M.Sc. Degree in applied mathematics at the Faculty of Applied Mathematics and Technical Physics of the Technical University of Warsaw, Poland, in 1982. He defended his PhD thesis on robust statistics at the Institute of Mathematics, Polish Academy of Sciences in 1986. Now he is Professor of Mathematics at the Institute of Mathematics, Polish Academy of Sciences. His research interests contain probabilistic inequalities, reliability theory, and stochastic orders. He has published over 120 papers. Most of them were devoted to inequalities for ordered random variables.

“Written by two renowned researchers in the field of stochastic processes, the present book is an excellent review on the inequalities and bounds related to the standard order statistics. … Numerous recent results due to the authors of this monograph are included. Some numerical evaluations adequately illustrate the theoretical results. The results presented in this book have important applications in reliability theory. The reading of the theorems and their proofs is particularly instructive and enjoyable.” (Eugen Paltanea, zbMATH 1568.60001, 2025) “The book is an excellent compilation on the classic and recent results on sharp bounds for the classic order statistics (from IID samples).” (Jorge Navarro, Mathematical Reviews, May, 2025)

• - Introduction and Notation.- Analytic Inequalities and Other Tools.- Deterministic Bounds.- General, Symmetric and Life IID Samples.- Sampling from Finite Populations.- IID Samples from Shape Restricted Families.