Majorization And The Lorenz Order

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Majorization and the Lorenz Order: A Brief Introduction

Author : Barry C. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 1461573793
Total Pages : 130 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Majorization and the Lorenz Order: A Brief Introduction by : Barry C. Arnold

Download or read book Majorization and the Lorenz Order: A Brief Introduction written by Barry C. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Barry C. Arnold
Publisher : Springer
ISBN 13 : 3319937731
Total Pages : 283 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Majorization and the Lorenz Order with Applications in Applied Mathematics and Economics by : Barry C. Arnold

Download or read book Majorization and the Lorenz Order with Applications in Applied Mathematics and Economics written by Barry C. Arnold and published by Springer. This book was released on 2018-07-27 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Albert W. Marshall
Publisher : Springer Science & Business Media
ISBN 13 : 0387682767
Total Pages : 919 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Inequalities: Theory of Majorization and Its Applications by : Albert W. Marshall

Download or read book Inequalities: Theory of Majorization and Its Applications written by Albert W. Marshall and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inequalities

Author : Ingram Olkin
Publisher : Academic Press
ISBN 13 : 0080959970
Total Pages : 590 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Inequalities by : Ingram Olkin

Download or read book Inequalities written by Ingram Olkin and published by Academic Press. This book was released on 2014-06-28 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of inequalities." For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.Anyone wishing to employ majorization as a tool in applications can make use of the theorems; for the most part, their statements are easily understood.

Stochastic Orders and Decision Under Risk

Author : Karl C. Mosler
Publisher : IMS
ISBN 13 : 9780940600263
Total Pages : 414 pages
Book Rating : 4.6/5 (2 download)

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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:

An Introduction to Stochastic Orders

Author : Felix Belzunce
Publisher : Academic Press
ISBN 13 : 0128038268
Total Pages : 175 pages
Book Rating : 4.1/5 (28 download)

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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

Modeling Income Distributions and Lorenz Curves

Author : Duangkamon Chotikapanich
Publisher : Springer Science & Business Media
ISBN 13 : 0387727965
Total Pages : 322 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Modeling Income Distributions and Lorenz Curves by : Duangkamon Chotikapanich

Download or read book Modeling Income Distributions and Lorenz Curves written by Duangkamon Chotikapanich and published by Springer Science & Business Media. This book was released on 2008-09-16 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jean-Jacques Rousseau wrote in the Preface to his famous Discourse on Inequality that “I consider the subject of the following discourse as one of the most interesting questions philosophy can propose, and unhappily for us, one of the most thorny that philosophers can have to solve. For how shall we know the source of inequality between men, if we do not begin by knowing mankind?” (Rousseau, 1754). This citation of Rousseau appears in an article in Spanish where Dagum (2001), in the memory of whom this book is published, also cites Socrates who said that the only useful knowledge is that which makes us better and Seneca who wrote that knowing what a straight line is, is not important if we do not know what rectitude is. These references are indeed a good illustration of Dagum’s vast knowledge, which was clearly not limited to the ?eld of Economics. For Camilo the ?rst part of Rousseau’s citation certainly justi?ed his interest in the ?eld of inequality which was at the centre of his scienti?c preoccupations. It should however be stressed that for Camilo the second part of the citation represented a “solid argument in favor of giving macroeconomic foundations to microeconomic behavior” (Dagum, 2001). More precisely, “individualism and methodological holism complete each other in contributing to the explanation of individual and social behavior” (Dagum, 2001).

An Introduction to the Formalism of Quantum Information with Continuous Variables

Author : Carlos Navarrete-Benlloch
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681744066
Total Pages : 147 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis An Introduction to the Formalism of Quantum Information with Continuous Variables by : Carlos Navarrete-Benlloch

Download or read book An Introduction to the Formalism of Quantum Information with Continuous Variables written by Carlos Navarrete-Benlloch and published by Morgan & Claypool Publishers. This book was released on 2016-01-01 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information is an emerging field which has attracted a lot of attention in the last couple of decades. It is a broad subject which extends from the most applied questions (e.g. how to build quantum computers or secure cryptographic systems) to the most theoretical problems concerning the formalism and interpretation of quantum mechanics, its complexity, and its potential to go beyond classical physics. This book is an introduction to quantum information with special emphasis on continuous-variable systems (such as light) which can be described as collections of harmonic oscillators. It covers a selection of basic concepts, focusing on their physical meaning and mathematical treatment. It starts from the very first principles of quantum mechanics, and builds up the concepts and techniques following a logical progression. This is an excellent reference for students with a full semester of standard quantum mechanics and researchers in closely related fields.

Contributions to Probability and Statistics

Author : Leon J. Gleser
Publisher : Springer Science & Business Media
ISBN 13 : 1461236789
Total Pages : 512 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Contributions to Probability and Statistics by : Leon J. Gleser

Download or read book Contributions to Probability and Statistics written by Leon J. Gleser and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in honor of the sixty-fifth birthday of Professor Ingram Olkin of Stanford University. Part I contains a brief biography of Professor Olkin and an interview with him discussing his career and his research interests. Part II contains 32 technical papers written in Professor Olkin's honor by his collaborators, colleagues, and Ph.D. students. These original papers cover a wealth of topics in mathematical and applied statistics, including probability inequalities and characterizations, multivariate analysis and association, linear and nonlinear models, ranking and selection, experimental design, and approaches to statistical inference. The volume reflects the wide range of Professor Olkin's interests in and contributions to research in statistics, and provides an overview of new developments in these areas of research.

Multivariate Dispersion, Central Regions, and Depth

Author : Karl Mosler
Publisher : Springer Science & Business Media
ISBN 13 : 1461300452
Total Pages : 303 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Multivariate Dispersion, Central Regions, and Depth by : Karl Mosler

Download or read book Multivariate Dispersion, Central Regions, and Depth written by Karl Mosler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has many applications to stochastic comparison problems in economics and other fields. It covers theory of lift zonoids and demonstrates its usefulness in multivariate analysis, an informal introduction to basic ideas, and a comprehensive investigation into the theory, as well as various applications of the lift zonoid approach and may be separately studied. Readers are assumed to have a firm grounding in probability at the graduate level.

Advances on Income Inequality and Concentration Measures

Author : Gianni Betti
Publisher : Routledge
ISBN 13 : 113406800X
Total Pages : 473 pages
Book Rating : 4.1/5 (34 download)

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Book Synopsis Advances on Income Inequality and Concentration Measures by : Gianni Betti

Download or read book Advances on Income Inequality and Concentration Measures written by Gianni Betti and published by Routledge. This book was released on 2008-04-24 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This impressive collection from some of today‘s leading distributional analysts provides an overview a wide range of economic, statistical and sociological relationships that have been opened up for scientific study by the work of two turn-of-the-20th-century economists: C. Gini and M. O. Lorenz. The authors include such figues as Barry A

Pareto Distributions

Author : Barry C. Arnold
Publisher : CRC Press
ISBN 13 : 1466584858
Total Pages : 435 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Pareto Distributions by : Barry C. Arnold

Download or read book Pareto Distributions written by Barry C. Arnold and published by CRC Press. This book was released on 2015-03-10 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition over 30 years ago, the literature related to Pareto distributions has flourished to encompass computer-based inference methods. Pareto Distributions, Second Edition provides broad, up-to-date coverage of the Pareto model and its extensions. This edition expands several chapters to accommodate recent result

Income and Wealth Distribution, Inequality and Poverty

Author : Camilo Dagum
Publisher : Springer Science & Business Media
ISBN 13 : 364284250X
Total Pages : 427 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Income and Wealth Distribution, Inequality and Poverty by : Camilo Dagum

Download or read book Income and Wealth Distribution, Inequality and Poverty written by Camilo Dagum and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the following issues: the analysis, estimation and assessment of alternatived models of income distribution, the specification and evaluation of income inequality measures the analysis and measurement of poverty and its rationale, the scope and methodological power of the social accounting matrix (SAM) in the analysis of the functional and personal distribution of income and the family income multiplier, the study of the source and reliability of income distribution data, the decomposition of income inequality measures, the asymptotic distributions and inferential analysis of income inequalities, and an inquiry on the income distribution and income inequality of Eastern European Countries under socialism. New models on income and wealth distribution are specified and their corresponding properties and goodness of fit are discussed. A multivariate approach to the measurement of poverty is developed and applied, and a compact survey of the literature is presented. The book can be used as a text in advanced undergraduate and graduate courses dealing with the theory, model specifications, methods and applications of income and wealth distribution, income inequality and poverty assessment in measurement and the use of SAMs in the analysis of income distribution.

Hydro-Environmental Analysis

Author : James L. Martin
Publisher : CRC Press
ISBN 13 : 1138000868
Total Pages : 5742 pages
Book Rating : 4.1/5 (38 download)

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Book Synopsis Hydro-Environmental Analysis by : James L. Martin

Download or read book Hydro-Environmental Analysis written by James L. Martin and published by CRC Press. This book was released on 2013-12-04 with total page 5742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on fundamental principles, Hydro-Environmental Analysis: Freshwater Environments presents in-depth information about freshwater environments and how they are influenced by regulation. It provides a holistic approach, exploring the factors that impact water quality and quantity, and the regulations, policy and management methods that are necessary to maintain this vital resource. It offers a historical viewpoint as well as an overview and foundation of the physical, chemical, and biological characteristics affecting the management of freshwater environments. The book concentrates on broad and general concepts, providing an interdisciplinary foundation. The author covers the methods of measurement and classification; chemical, physical, and biological characteristics; indicators of ecological health; and management and restoration. He also considers common indicators of environmental health; characteristics and operations of regulatory control structures; applicable laws and regulations; and restoration methods. The text delves into rivers and streams in the first half and lakes and reservoirs in the second half. Each section centers on the characteristics of those systems and methods of classification, and then moves on to discuss the physical, chemical, and biological characteristics of each. In the section on lakes and reservoirs, it examines the characteristics and operations of regulatory structures, and presents the methods commonly used to assess the environmental health or integrity of these water bodies. It also introduces considerations for restoration, and presents two unique aquatic environments: wetlands and reservoir tailwaters. Written from an engineering perspective, the book is an ideal introduction to the aquatic and limnological sciences for students of environmental science, as well as students of environmental engineering. It also serves as a reference for engineers and scientists involved in the management, regulation, or restoration of freshwater environments.

Stochastic Orders

Author : Moshe Shaked
Publisher : Springer Science & Business Media
ISBN 13 : 0387346759
Total Pages : 482 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Stochastic Orders by : Moshe Shaked

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.

Stochastic Orders and Applications

Author : Karl Mosler
Publisher : Springer Science & Business Media
ISBN 13 : 3642499724
Total Pages : 385 pages
Book Rating : 4.6/5 (424 download)

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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.

Partitions

Author : Frank Hwang
Publisher : World Scientific
ISBN 13 : 9812770151
Total Pages : 363 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Partitions by : Frank Hwang

Download or read book Partitions written by Frank Hwang and published by World Scientific. This book was released on 2012 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The OC clusteringOCO problem, which has recently received a lot of attention, is a special case of optimal partitioning. This book is the first attempt to collect all theoretical developments of optimal partitions, many of them derived by the authors, in an accessible place for easy reference. Much more than simply collecting the results, the book provides a general framework to unify these results and present them in an organized fashion. Many well-known practical problems of optimal partitions are dealt with. The authors show how they can be solved using the theory OCo or why they cannot be. These problems include: allocation of components to maximize system reliability; experiment design to identify defectives; design of circuit card library and of blood analyzer lines; abstraction of finite state machines and assignment of cache items to pages; the division of property and partition bargaining as well as touching on those well-known research areas such as scheduling, inventory, nearest neighbor assignment, the traveling salesman problem, vehicle routing, and graph partitions. The authors elucidate why the last three problems cannot be solved in the context of the theory."