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Stochastic Orderings For Order Statistics And Reliability Systems
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Book Synopsis Stochastic Orderings for Order Statistics and Reliability Systems by : N Balakrishnan
Download or read book Stochastic Orderings for Order Statistics and Reliability Systems written by N Balakrishnan and published by Birkhäuser. This book was released on 2017-07-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book specifically devoted to the topic of stochastic orderings for order statistics. Combining classical and recent results, the work is a comprehensive overview of ordering properties for order statistics and related concepts. Special emphasis is placed on the connections between order statistics and coherent systems, applying results to reliability and survival studies. The work is an excellent reference for advanced undergraduates, graduate students, and researchers in statistics, mathematics, computer science, engineering, and medicine. The book may serve as a supplementary textbook for courses on ordering for order statistics and ordering coherent systems.
Book Synopsis Stochastic Orders and Applications by : Karl Mosler
Download or read book Stochastic Orders and Applications written by Karl Mosler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Orders written by Moshe Shaked and published by Springer Science & Business Media. This book was released on 2007-04-03 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Orders and Their Applications by : Moshe Shaked
Download or read book Stochastic Orders and Their Applications written by Moshe Shaked and published by . This book was released on 1994 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Orders in Reliability and Risk by : Haijun Li
Download or read book Stochastic Orders in Reliability and Risk written by Haijun Li and published by Springer Science & Business Media. This book was released on 2013-06-22 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Orders and Decision Under Risk by : Karl C. Mosler
Download or read book Stochastic Orders and Decision Under Risk written by Karl C. Mosler and published by IMS. This book was released on 1991 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Comparisons with Applications by : Subhash C. Kochar
Download or read book Stochastic Comparisons with Applications written by Subhash C. Kochar and published by Springer Nature. This book was released on 2022-10-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Stochastic Orders by : Felix Belzunce
Download or read book An Introduction to Stochastic Orders written by Felix Belzunce and published by Academic Press. This book was released on 2015-09-29 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics. The book provides a general background on this topic for students and researchers who want to use it as a tool for their research. In addition, users will find detailed proofs of the main results and applications to several probabilistic models of interest in several fields, and discussions of fundamental properties of several stochastic orders, in the univariate and multivariate cases, along with applications to probabilistic models. - Introduces stochastic orders and its notation - Discusses different orders of univariate stochastic orders - Explains multivariate stochastic orders and their convex, likelihood ratio, and dispersive orders
Book Synopsis Stochastic Orders in Heterogeneous Samples with Applications by : Maochao Xu
Download or read book Stochastic Orders in Heterogeneous Samples with Applications written by Maochao Xu and published by . This book was released on 2010 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistics literature has mostly focused on the case when the data available is in the form of a random sample. In many cases, the observations are not identically distributed. Such samples are called heterogeneous samples. The study of heterogeneous samples is of great interest in many areas, such as statistics, econometrics, reliability engineering, operation research and risk analysis. Stochastic orders between probability distributions is a widely studied concept. There are several kinds of stochastic orders that are used to compare different aspects of probability distributions like location, variability, skewness, dependence, etc. In this dissertation, most of the work is devoted to investigating the properties of statistics based on heterogeneous samples with the aid of stochastic orders. We will see the effect of the change in the stochastic properties of various functions of observations as their parameters change. The theory of majorization will be used for this purpose. First, order statistics from heterogeneous samples will be investigated. Order statistics appear everywhere in statistics and related areas. The k-out-of-n systems are building blocks of a coherent system. The lifetime of such a system is the same as that of the (n-k+1)th order statistic in a sample size of n. Stochastic comparisons between order statistics have been studied extensively in the literature in case the parent observations are independent and identically distributed. However, in practice this assumption is often violated as different components in a system may not have the same distribution. Comparatively less work has been done in the case of heterogeneous random variables, mainly because of the reason that their distribution theory is very complicated. Some open problems in the literature have been solved in the dissertation. Some new problems associated with order statistics have been investigated in the thesis. Next, stochastic properties of spacings based on heterogeneous observations are studied. Spacings are of great interest in many areas of statistics, in particular, in the characterizations of distributions, goodness-of-fit tests, life testing and reliability models. In particular, the stochastic properties of the sample range are investigated in detail. Applications in reliability theory are highlighted. The relative dependence between extreme order statistics will be investigated in Chapter 4. In particular, the open problem discussed in Dolati, et al. (2008) is solved in this Chapter. In the last Chapter, convolutions of random variables from heterogeneous samples will be investigated. Convolutions have been widely used in many areas to model many practical situations. For example, in reliability theory, it arises as the lifetime of a redundant standby system; in queuing theory, it is used to model the total service time by an agent in a system; in insurance, it is used to model total claims on a number of policies in the individual risk model. I will compare the dispersion and skewness properties of convolutions of different heterogeneous samples. The tail behavior of convolutions are investigated as well. The work in this dissertation has significant applications in many diverse areas of applied probability and statistics. For example, statistics based on order statistics and spacings from heterogeneous samples arise in studying the robust properties of statistical procedures; the work on order statistics will also provide a better estimation of lifetime of a coherent system in reliability engineering; convolution results will be of great interest in insurance and actuarial science for evaluating risks.
Book Synopsis Stochastic Ageing and Dependence for Reliability by : Chin Diew Lai
Download or read book Stochastic Ageing and Dependence for Reliability written by Chin Diew Lai and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a panoramic view of theory and applications of Ageing and Dependence in the use of mathematical methods in reliability and survival analysis. Ageing and dependence are important characteristics in reliability and survival analysis. They affect decisions with regard to maintenance, repair/replacement, price setting, warranties, medical studies, and other areas. Most of the works containing the topics covered here are theoretical in nature. However, this book offers applications, exercises, and examples. It serves as a reference for professors and researchers involved in reliability and survival analysis.
Book Synopsis Stochastic Comparisons of Order Statistics, with Applications in Reliability by : Jee S. Kim
Download or read book Stochastic Comparisons of Order Statistics, with Applications in Reliability written by Jee S. Kim and published by . This book was released on 1987 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper surveys recent advances in stochastic comparisons of order statistics along with reliability applications. Section 2 presents inequalities for linear combinations of order statistics from restricted families. Comparisons of linear combinations of order statistics from distributions F and G are obtained for/G F convex and for/G F starshaped. These results yield conservative upper and lower tolerance limits. For G exponential and F IFR or IFRA, stochastic comparisons are presented for the total time on test, used in life testing. Section 3 presents stochastic comparisons of order statistics from underlying heterogeneous distributions. Given two sets of independent components (possibly unlike), majorization conditions are given which insure that any k-out-of-n system constructed from components in the first set will have reliability at least as great as that of a corresponding system constructed from components in the second set. Since the ordered failure times of the components represent order statistics from heterogeneous distributions, the order statistics from one set of underlying distributions (F1, ..., Fn) can be compared stochastically with those from another set (F1, ..., Fn).
Book Synopsis Reliability Engineering by : Mangey Ram
Download or read book Reliability Engineering written by Mangey Ram and published by CRC Press. This book was released on 2019-10-14 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 50 years, the theory and the methods of reliability analysis have developed significantly. Therefore, it is very important to the reliability specialist to be informed of each reliability measure. This book will provide historical developments, current advancements, applications, numerous examples, and many case studies to bring the reader up-to-date with the advancements in this area. It covers reliability engineering in different branches, includes applications to reliability engineering practice, provides numerous examples to illustrate the theoretical results, and offers case studies along with real-world examples. This book is useful to engineering students, research scientist, and practitioners working in the field of reliability.
Book Synopsis Advances in Distribution Theory, Order Statistics, and Inference by : N. Balakrishnan
Download or read book Advances in Distribution Theory, Order Statistics, and Inference written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis System and Bayesian Reliability by : Yu Hayakawa
Download or read book System and Bayesian Reliability written by Yu Hayakawa and published by World Scientific. This book was released on 2001 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Order Statistics by : Herbert A. David
Download or read book Order Statistics written by Herbert A. David and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to System Reliability Theory by : Jorge Navarro
Download or read book Introduction to System Reliability Theory written by Jorge Navarro and published by Springer Nature. This book was released on 2021-10-03 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modeling Uncertainty by : Moshe Dror
Download or read book Modeling Uncertainty written by Moshe Dror and published by Springer. This book was released on 2019-11-05 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
