This second volume, similar to the first volume, discusses various inequalities and sharp bounds for some general forms of ordered data as well as some functions of them. In particular, different bounds and their sharpness are discussed for order statistics from identically distributed and exchangeable samples, order statistics from arbitrarily distributed variable, coherent and mixed reliability systems, record values and their extensions, generalized order statistics and finally mixtures of ordered distributions. An elaborate numerical evaluation and comparison of various bounds are also presented to illustrate their inherent differences and their accuracy and precision. Moreover, their applications to inference and reliability are also highlighted. This second and final volume provides an in-depth exposure to various mathematical inequalities and bounds established historically as well as in recent years and their applications to various forms of ordered data and some important functions of them like range, L-statistics and trimmed mean. It thus presents an up-to-date discussion of all results in this important area of mathematical and statistical research. The results described here are general and so would be useful in other areas of Probability and Statistics as well.

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 ofWarsaw, Poland, in 1982. He then completed his PhD thesis at the Institute of Mathematics, Polish Academy of Sciences in 1986. At present, he is a 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 with many about inequalities for ordered variables.