Majorization And The Lorenz Order A Brief Introduction
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Majorization And The Lorenz Order A Brief Introduction
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Author : Barry C. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Majorization And The Lorenz Order A Brief Introduction written by Barry C. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
My interest in majorization was first spurred by Ingram aIkin's proclivity for finding Schur convex functions lurking in the problem section of every issue of the American Mathematical Monthly. Later my interest in income inequality led me again to try and "really" understand Hardy, Littlewood and Polya' s contributions to the majori zation literature. I have found the income distribution context to be quite convenient for discussion of inequality orderings. The pre sent set of notes is designed for a one quarter course introducing majorization and the Lorenz order. The inequality principles of Dalton, especially the transfer or Robin Hood principle, are given appropriate prominence. Initial versions of these notes were used in graduate statistics classes taught at the Colegio de Postgraduados, Chapingo, Mexico and the University of California, Riverside. I am grateful to students in these classes for their constructive critical commentaries. My wife Carole made noble efforts to harness my free form writ ing and punctuation. Occasionally I was unmoved by her requests for clarification. Time will probably prove her right in these instances also. Peggy Franklin did an outstanding job of typing the manu script, and patiently endured requests for innumerable modifications.
Majorization And The Lorenz Order With Applications In Applied Mathematics And Economics
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Author : Barry C. Arnold
language : en
Publisher: Springer
Release Date : 2018-07-27
Majorization And The Lorenz Order With Applications In Applied Mathematics And Economics written by Barry C. Arnold and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-27 with Mathematics categories.
This book was written to serve as a graduate-level textbook for special topics classes in mathematics, statistics, and economics, to introduce these topics to other researchers, and for use in short courses. It is an introduction to the theory of majorization and related notions, and contains detailed material on economic applications of majorization and the Lorenz order, investigating the theoretical aspects of these two interrelated orderings. Revising and expanding on an earlier monograph, Majorization and the Lorenz Order: A Brief Introduction, the authors provide a straightforward development and explanation of majorization concepts, addressing historical development of the topics, and providing up-to-date coverage of families of Lorenz curves. The exposition of multivariate Lorenz orderings sets it apart from existing treatments of these topics. Mathematicians, theoretical statisticians, economists, and other social scientists who already recognize the utility of the Lorenz order in income inequality contexts and arenas will find the book useful for its sound development of relevant concepts rigorously linked to both the majorization literature and the even more extensive body of research on economic applications. Barry C. Arnold, PhD, is Distinguished Professor in the Statistics Department at the University of California, Riverside. He is a Fellow of the American Statistical Society, the American Association for the Advancement of Science, and the Institute of Mathematical Statistics, and is an elected member of the International Statistical Institute. He is the author of more than two hundred publications and eight books. José María Sarabia, PhD, is Professor of Statistics and Quantitative Methods in Business and Economics in the Department of Economics at the University of Cantabria, Spain. He is author of more than one hundred and fifty publications and ten books and is an associate editor of several journals including TEST, Communications in Statistics, and Journal of Statistical Distributions and Applications.
Inequalities Theory Of Majorization And Its Applications
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Author : Albert W. Marshall
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-25
Inequalities Theory Of Majorization And Its Applications written by Albert W. Marshall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Mathematics categories.
This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. ... This work is a valuable resource!” (Mathematical Reviews). “The authors ... present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of ... Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.
An Introduction To Stochastic Orders
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Author : Felix Belzunce
language : en
Publisher: Academic Press
Release Date : 2015-09-29
An Introduction To Stochastic Orders written by Felix Belzunce and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-29 with Mathematics categories.
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
Stochastic Orders And Applications
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Author : Karl Mosler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Orders And Applications written by Karl Mosler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Modeling Computation And Optimization
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Author : S. K. Neogy
language : en
Publisher: World Scientific
Release Date : 2009
Modeling Computation And Optimization written by S. K. Neogy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
This volume provides recent developments and a state-of-the-art review in various areas of mathematical modeling, computation and optimization. It contains theory, computation as well as the applications of several mathematical models to problems in statistics, games, optimization and economics for decision making. It focuses on exciting areas like models for wireless networks, models of Nash networks, dynamic models of advertising, application of reliability models in economics, support vector machines, optimization, complementarity modeling and games.
Stochastic Models In Reliability Network Security And System Safety
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Author : Quan-Lin Li
language : en
Publisher: Springer Nature
Release Date : 2019-10-21
Stochastic Models In Reliability Network Security And System Safety written by Quan-Lin Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-21 with Computers categories.
This book is dedicated to Jinhua Cao on the occasion of his 80th birthday. Jinhua Cao is one of the most famous reliability theorists. His main contributions include: published over 100 influential scientific papers; published an interesting reliability book in Chinese in 1986, which has greatly influenced the reliability of education, academic research and engineering applications in China; initiated and organized Reliability Professional Society of China (the first part of Operations Research Society of China) since 1981. The high admiration that Professor Cao enjoys in the reliability community all over the world was witnessed by the enthusiastic response of each contributor in this book. The contributors are leading researchers with diverse research perspectives. The research areas of the book iclude a broad range of topics related to reliability models, queueing theory, manufacturing systems, supply chain finance, risk management, Markov decision processes, blockchain and so forth. The book consists of a brief Preface describing the main achievements of Professor Cao; followed by congratulations from Professors Way Kuo and Wei Wayne Li, and by Operations Research Society of China, and Reliability Professional Society of China; and further followed by 25 articles roughly grouped together. Most of the articles are written in a style understandable to a wide audience. This book is useful to anyone interested in recent developments in reliability, network security, system safety, and their stochastic modeling and analysis.
Advances In Statistics Theory And Applications
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Author : Indranil Ghosh
language : en
Publisher: Springer Nature
Release Date : 2021-04-01
Advances In Statistics Theory And Applications written by Indranil Ghosh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Mathematics categories.
This edited collection brings together internationally recognized experts in a range of areas of statistical science to honor the contributions of the distinguished statistician, Barry C. Arnold. A pioneering scholar and professor of statistics at the University of California, Riverside, Dr. Arnold has made exceptional advancements in different areas of probability, statistics, and biostatistics, especially in the areas of distribution theory, order statistics, and statistical inference. As a tribute to his work, this book presents novel developments in the field, as well as practical applications and potential future directions in research and industry. It will be of interest to graduate students and researchers in probability, statistics, and biostatistics, as well as practitioners and technicians in the social sciences, economics, engineering, and medical sciences.
Advances In Knowledge Discovery And Data Mining
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Author : Ming-Syan Cheng
language : en
Publisher: Springer
Release Date : 2003-08-01
Advances In Knowledge Discovery And Data Mining written by Ming-Syan Cheng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-01 with Computers categories.
Knowledge discovery and data mining have become areas of growing significance because of the recent increasing demand for KDD techniques, including those used in machine learning, databases, statistics, knowledge acquisition, data visualization, and high performance computing. In view of this, and following the success of the five previous PAKDD conferences, the sixth Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD 2002) aimed to provide a forum for the sharing of original research results, innovative ideas, state-of-the-art developments, and implementation experiences in knowledge discovery and data mining among researchers in academic and industrial organizations. Much work went into preparing a program of high quality. We received 128 submissions. Every paper was reviewed by 3 program committee members, and 32 were selected as regular papers and 20 were selected as short papers, representing a 25% acceptance rate for regular papers. The PAKDD 2002 program was further enhanced by two keynote speeches, delivered by Vipin Kumar from the Univ. of Minnesota and Rajeev Rastogi from AT&T. In addition, PAKDD 2002 was complemented by three tutorials, XML and data mining (by Kyuseok Shim and Surajit Chadhuri), mining customer data across various customer touchpoints at- commerce sites (by Jaideep Srivastava), and data clustering analysis, from simple groupings to scalable clustering with constraints (by Osmar Zaiane and Andrew Foss).
Continuous Univariate Distributions Volume 2
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Author : Norman L. Johnson
language : en
Publisher: John Wiley & Sons
Release Date : 1995-05-08
Continuous Univariate Distributions Volume 2 written by Norman L. Johnson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05-08 with Mathematics categories.
Comprehensive reference for statistical distributions Continuous Univariate Distributions, Volume 2 provides in-depth reference for anyone who applies statistical distributions in fields including engineering, business, economics, and the sciences. Covering a range of distributions, both common and uncommon, this book includes guidance toward extreme value, logistics, Laplace, beta, rectangular, noncentral distributions and more. Each distribution is presented individually for ease of reference, with clear explanations of methods of inference, tolerance limits, applications, characterizations, and other important aspects, including reference to other related distributions.