Download or read book Convex Ordering Among Functions with Applications to Reliability and Mathematical Statistics written by Wai Chan and published by . This book was released on 1983 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hardy, Littlewood and Polya (1934) introduced the notion of one function being convex with respect to a second function and developed some inequalities concerning the means of the functions. We use this notion to establish a partial order called convex-ordering among functions. In particular, the distribution functions encountered in many parametric families in reliability theory are convex-ordered. We have formulated some inequalities which can be used for testing whether a sample comes from F or G, when F and G are within the same convex family. Performance characteristics of different coherent structures can also be compared with respect to this partial ordering. For example, we will show that the reliability of a k+l-out-of-n system is convex with respect to the reliability of a k-out-of-n system. When F is convex with respect to G, the tail of the distribution F is heavier than that of G; therefore, our convex ordering implies stochastic ordering. The ordering is also related to total positivity and monotone likelihood ratio families. This provides us a tool to obtain some useful results in reliability and mathematical statistics.
Download or read book Convex Functions Partial Orderings and Statistical Applications written by Josip E. Peajcariaac and published by Academic Press. This book was released on 1992-06-03 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research-level book presents up-to-date information concerning recent developments in convex functions and partial orderings and some applications in mathematics, statistics, and reliability theory. The book will serve researchers in mathematical and statistical theory and theoretical and applied reliabilists. Presents classical and newly published results on convex functions and related inequalities Explains partial ordering based on arrangement and their applications in mathematics, probability, statsitics, and reliability Demonstrates the connection of partial ordering with other well-known orderings such as majorization and Schur functions Will generate further research and applications
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.
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 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.
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:
Download or read book Topics in Statistical Dependence written by Henry W. Block and published by IMS. This book was released on 1990 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research in Progress written by United States. Army Research Office and published by . This book was released on 1984 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1977- consist of two parts: Chemistry, biological sciences, engineering sciences, metallurgy and materials science (issued in the spring); and Physics, electronics, mathematics, geosciences (issued in the fall).
Download or read book Research in Progress written by and published by . This book was released on 1988 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Convex Functions and Their Applications written by Constantin P. Niculescu and published by Springer. This book was released on 2018-06-08 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
Download or read book Linear Algebra with Applications written by Steve Kirkland and published by Manipal Universal Press. This book was released on 2014-12-20 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed articles.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Easy Path to Convex Analysis and Applications written by Boris Mordukhovich and published by Springer Nature. This book was released on 2022-05-31 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.
Download or read book Bulletin Institute of Mathematical Statistics written by Institute of Mathematical Statistics and published by . This book was released on 1992 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Uncertainty And Optimality Probability Statistics And Operations Research written by Jagadis Chandra Misra and published by World Scientific. This book was released on 2002-11-05 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with different modern topics in probability, statistics and operations research. It has been written lucidly in a novel way. Wherever necessary, the theory is explained in great detail, with suitable illustrations. Numerous references are given, so that young researchers who want to start their work in a particular area will benefit immensely from the book.The contributors are distinguished statisticians and operations research experts from all over the world.
Download or read book Convex Functions written by Jonathan M. Borwein and published by Cambridge University Press. This book was released on 2010-01-14 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.
