Stochastic Orders: (Springer Series in Statistics)

Stochastic ordering is a fundamental guide for decision making under uncertainty. It is also an essential tool in the study of structural properties of complex stochastic systems. This reference text presents a comprehensive coverage of the various notions of stochastic orderings, their closure properties, and their applications. Some of these orderings are routinely used in many applications in economics, finance, insurance, management science, operations research, statistics, and various other fields of study. And the value of the other notions of stochastic orderings still needs to be explored further. This book is an ideal reference for anyone interested in decision making under uncertainty and interested in the analysis of complex stochastic systems. It is suitable as a text for advanced graduate course on stochastic ordering and applications.

Table of Contents:
Univariate Stochastic Orders.- Mean Residual Life Orders.- Univariate Variability Orders.- Univariate Monotone Convex and Related Orders.- The Laplace Transform and Related Orders.- Multivariate Stochastic Orders.- Multivariate Variability and Related Orders.- Stochastic Convexity and Concavity.- Positive Dependence Orders.

Review :
From the reviews: "This book is a wide, well written and clearly organized extension of the first six chapters of the author’s book ‘Stochastic orders and their applications’ … . In addition the book illustrates some of the usefulness and applicability of the theory and now it is the most complete monograph in this field. … The book will be useful for a wide spectrum of researchers in the area of probability, statistics, operations research, actuarial mathematics, economics, etc." (Jaroslaw Bartoszewicz, Zentralblatt MATH, Vol. 1111 (8), 2007) "A comprehensive coverage of various notions of stochastic orderings and their closure properties. The authors have done an excellent job in the coverage of the material. The book is written in a theorem-proof format … . has a bibliography with 578 items indicating the wide coverage. Selected material from the book can be used for a course in stochastic orders … . is an ideal reference for those interested in learning about various types of stochastic orders to analyze complex stochastic systems." (B. L. S. Prakasa Rao, Mathematical Reviews, Issue 2008 g) "This book is a major extension of some of the materials presented in authors’ earlier book on the topic. … this is a timely reference book for the targeted researcher. It has an up-to-date reference section, with 578 entries. The book could be adopted as a text for advanced graduate course on the subject. … a nicely written and well-structured book, with excellent review sections. … The book’s infrastructure makes it an ideal candidate as an advanced-level textbook in a host of disciplines … ." (Technometrics, Vol. 50 (3), August, 2008) “…Since 1994, research in stochastic orders has grown considerably, leading the authors to update their earlier book. …Although the book is a reference, it is enjoyable to read. The material is presented at a level that makes the book accessible to a broad audience.…results are presented as theorems. The authors have taken care in deciding which results to prove.  Rather than giving general or arcane proofs, they prove their theorems using tools familiar to persons working in operations research, statistics, and engineering. As a result, the reader quickly gains an appreciation of why particular results work… . This book is a must for anyone whose research involves stochastic orders. ...” ((Journal of the American Statistical Association, September 2009, Vol. 104, No. 487) “This book presents a comprehensive review of stochastic orders. … this is the book that everyone interested in stochastic orders must have on their desk. … Its lucid writing style, plentiful examples, and moderate mathematical exposition make all the material accessible, not only to applied probabilists, but also to most engineers, economists, actuaries, and so on. … I recommend this book without reservation to anyone interested in stochastic order relations and their applications.” (Michel Denuit, SIAM Review, Vol. 53 (1), 2011)