Stochastic Orders in Reliability and Risk
Stochastic Orders in Reliability and Risk

Author: Haijun Li

Publisher: Springer Science & Business Media

Published: 2013-06-22

Total Pages: 459

ISBN-13: 1461468922

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Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications. These review/exploratory chapters present recent and current research on stochastic orders reported at the International Workshop on Stochastic Orders in Reliability and Risk Management, or SORR2011, which took place in the City Hotel, Xiamen, China, from June 27 to June 29, 2011. The conference’s talks and invited contributions also represent the celebration of Professor Moshe Shaked, who has made comprehensive, fundamental contributions to the theory of stochastic orders and its applications in reliability, queueing modeling, operations research, economics and risk analysis. This volume is in honor of Professor Moshe Shaked. The work presented in this volume represents active research on stochastic orders and multivariate dependence, and exemplifies close collaborations between scholars working in different fields. The Xiamen Workshop and this volume seek to revive the community workshop tradition on stochastic orders and dependence and strengthen research collaboration, while honoring the work of a distinguished scholar.

Stochastic Orders and Their Applications
Stochastic Orders and Their Applications

Author: Moshe Shaked

Publisher:

Published: 1994

Total Pages: 580

ISBN-13:

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Stochastic orders and inequalities are being used at an accelerated rate in many diverse areas of probability and statistics. This book provides the first unified, systematic, and accessible treatment of stochasticorders, addressing the growing importance of these orders with the presentation of numerous results that illustrate their usefulness and applicability. Ten insightful chapters emphasize the applications by specialists in probability and statistics, economics, operations research, and reliability theory. Applications include multivariate variability, epidemics, comparisons of risk and risk aversion, scheduling, and systems reliability theory.

Stochastic Orders
Stochastic Orders

Author: Moshe Shaked

Publisher: Springer Science & Business Media

Published: 2007-04-03

Total Pages: 482

ISBN-13: 0387346759

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This reference text presents 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. And the value of the other notions of stochastic orderings needs further exploration. This book is an ideal reference for those 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.

Advances in Distribution Theory, Order Statistics, and Inference
Advances in Distribution Theory, Order Statistics, and Inference

Author: N. Balakrishnan

Publisher: Springer Science & Business Media

Published: 2007-10-23

Total Pages: 515

ISBN-13: 0817644873

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The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.

Stochastic Comparisons with Applications
Stochastic Comparisons with Applications

Author: Subhash C. Kochar

Publisher: Springer Nature

Published: 2022-10-22

Total Pages: 280

ISBN-13: 303112104X

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This book emphasizes the use of stochastic orders as motivational tools for developing new statistical procedures. Stochastic orders have found useful applications in many disciplines, including reliability theory, survival analysis, risk theory, finance, nonparametric methods, economics and actuarial science. Written by a statistician, this volume clarifies the connection between stochastic orders and nonparametric methods. The importance of order statistics and spacings is well recognized. Classically, they mainly focus on the case when the observations are independent and identically distributed, however, several new developments have extended the comparison of order statistics to the case of non-identically distributed or non-independent observations. In addition to giving a detailed discussion of various topics in the general area of stochastic orders, a substantial part of the book is devoted to recent research on stochastic comparisons of order statistics and spacings, including a long chapter on dependence among them. The book will be useful for graduate students and researchers in statistics, economics, actuarial science and other related disciplines. In particular, with close to 300 references, it will be a valuable resource for reliability theorists, applied probabilists and statisticians. Readers are expected to have taken a first-year graduate level course in mathematical statistics or in applied probability.

Stochastic Orders and Applications
Stochastic Orders and Applications

Author: Karl Mosler

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 385

ISBN-13: 3642499724

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A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.

System and Bayesian Reliability
System and Bayesian Reliability

Author: Yu Hayakawa

Publisher: World Scientific

Published: 2001

Total Pages: 444

ISBN-13: 9789812799548

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This volume is a collection of articles on reliability systems and Bayesian reliability analysis. Written by reputable researchers, the articles are self-contained and are linked with literature reviews and new research ideas. The book is dedicated to Emeritus Professor Richard E Barlow, who is well known for his pioneering research on reliability theory and Bayesian reliability analysis. Contents: System Reliability Analysis: On Regular Reliability Models (J-C Chang et al.); Bounding System Reliability (J N Hagstrom & S M Ross); Large Excesses for Finite-State Markov Chains (D Blackwell); Ageing Properties: Nonmonotonic Failure Rates and Mean Residual Life Functions (R C Gupta); The Failure Rate and the Mean Residual Lifetime of Mixtures (M S Finkelstein); On Some Discrete Notions of Aging (C Bracquemond et al.); Bayesian Analysis: On the Practical Implementation of the Bayesian Paradigm in Reliability and Risk Analysis (T Aven); A Weibull Wearout Test: Full Bayesian Approach (T Z Irony et al.); Bayesian Nonparametric Estimation of a Monotone Hazard Rate (M-W Ho & A Y Lo); and other papers. Readership: Students, academics, researchers and professionals in industrial engineering, probability and statistics, and applied mathematics.

Order Statistics
Order Statistics

Author: Herbert A. David

Publisher: John Wiley & Sons

Published: 2004-03-22

Total Pages: 482

ISBN-13: 0471654019

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This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even when chapter and section headings are the same as in OSII, there are appreciable changes, mostly additions, with some obvious deletions. Parts of old Ch. 7, for example, are prime candidates for omission. Appendices are designed to help collate tables, computer algorithms, and software, as well as to compile related monographs on the subject matter. Extensive exercise sets will continue, many of them replaced by newer ones.

Modeling Uncertainty
Modeling Uncertainty

Author: Moshe Dror

Publisher: Springer

Published: 2019-11-05

Total Pages: 782

ISBN-13: 0306481022

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Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, is a volume undertaken by the friends and colleagues of Sid Yakowitz in his honor. Fifty internationally known scholars have collectively contributed 30 papers on modeling uncertainty to this volume. Each of these papers was carefully reviewed and in the majority of cases the original submission was revised before being accepted for publication in the book. The papers cover a great variety of topics in probability, statistics, economics, stochastic optimization, control theory, regression analysis, simulation, stochastic programming, Markov decision process, application in the HIV context, and others. There are papers with a theoretical emphasis and others that focus on applications. A number of papers survey the work in a particular area and in a few papers the authors present their personal view of a topic. It is a book with a considerable number of expository articles, which are accessible to a nonexpert - a graduate student in mathematics, statistics, engineering, and economics departments, or just anyone with some mathematical background who is interested in a preliminary exposition of a particular topic. Many of the papers present the state of the art of a specific area or represent original contributions which advance the present state of knowledge. In sum, it is a book of considerable interest to a broad range of academic researchers and students of stochastic systems.

Introduction to System Reliability Theory
Introduction to System Reliability Theory

Author: Jorge Navarro

Publisher: Springer Nature

Published: 2021-10-03

Total Pages: 181

ISBN-13: 3030869539

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This textbook provides the tools for a modern post-graduate introductory course on system reliability theory. It focuses on probabilistic aspects of the theory, including recent results based on signatures, stochastic orders, aging classes, copulas and distortion (or aggregation) functions. The reader requires on an introductory knowledge on probability theory and mathematics. The book serves both for graduate students in mathematics and for engineering students in various disciplines as well as students learning survival analysis, network reliability or simple game theory. Included also are brief introductions to the basic aspects of lifetime modelling, stochastic comparisons, aging classes, mixtures and copula theory. The book develops this knowledge with worked examples and supplies code for the program R so that students can explore its lessons and techniques.