Inequalities Theory Of Majorization And Its Applications

Author : Ingram Olkin,Albert W. Marshall
Publisher : Academic Press
Page : 569 pages
File Size : 43,5 Mb
Release : 2016-01-22
Category : Mathematics
ISBN : 9780080959979

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Inequalities by Ingram Olkin,Albert W. Marshall Pdf

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.

Author : Albert W. Marshall,Ingram Olkin,Barry C. Arnold
Publisher : Springer Science & Business Media
Page : 909 pages
File Size : 40,9 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780387682761

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Inequalities: Theory of Majorization and Its Applications by Albert W. Marshall,Ingram Olkin,Barry C. Arnold Pdf

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.

Author : Josip E. Peajcariaac,Y. L. Tong
Publisher : Academic Press
Page : 485 pages
File Size : 47,9 Mb
Release : 1992-06-03
Category : Mathematics
ISBN : 9780080925226

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Convex Functions, Partial Orderings, and Statistical Applications by Josip E. Peajcariaac,Y. L. Tong Pdf

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

Author : S. Ejaz Ahmed,Francisco Carvalho,Simo Puntanen
Publisher : Springer
Page : 190 pages
File Size : 45,9 Mb
Release : 2019-08-02
Category : Mathematics
ISBN : 9783030175191

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Matrices, Statistics and Big Data by S. Ejaz Ahmed,Francisco Carvalho,Simo Puntanen Pdf

This volume features selected, refereed papers on various aspects of statistics, matrix theory and its applications to statistics, as well as related numerical linear algebra topics and numerical solution methods, which are relevant for problems arising in statistics and in big data. The contributions were originally presented at the 25th International Workshop on Matrices and Statistics (IWMS 2016), held in Funchal (Madeira), Portugal on June 6-9, 2016. The IWMS workshop series brings together statisticians, computer scientists, data scientists and mathematicians, helping them better understand each other’s tools, and fostering new collaborations at the interface of matrix theory and statistics.

Author : Huan-nan Shi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 236 pages
File Size : 48,7 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110607840

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Schur-Convex Functions and Inequalities by Huan-nan Shi Pdf

This two-volume work introduces the theory and applications of Schur-convex functions. The first volume introduces concepts and properties of Schur-convex functions, including Schur-geometrically convex functions, Schur-harmonically convex functions, Schur-power convex functions, etc. and also discusses applications of Schur-convex functions in symmetric function inequalities.

Author : Karl Mosler,Marco Scarsini
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642499722

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Stochastic Orders and Applications by Karl Mosler,Marco Scarsini Pdf

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.

Author : Fuzhen Zhang
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 46,9 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387242736

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The Schur Complement and Its Applications by Fuzhen Zhang Pdf

This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. Coverage includes historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis.

Author : Olimpia Lombardi,Sebastian Fortin,Cristian López,Federico Holik
Publisher : Cambridge University Press
Page : 411 pages
File Size : 44,7 Mb
Release : 2019-04-11
Category : Science
ISBN : 9781108473477

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Quantum Worlds by Olimpia Lombardi,Sebastian Fortin,Cristian López,Federico Holik Pdf

Offers a comprehensive and up-to-date volume on the conceptual and philosophical problems related to the interpretation of quantum mechanics.

Author : Theodore Wilbur Anderson,Ingram Olkin
Publisher : IMS
Page : 502 pages
File Size : 47,7 Mb
Release : 1994
Category : Multivariate analysis
ISBN : 0940600358

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Multivariate Analysis and Its Applications by Theodore Wilbur Anderson,Ingram Olkin Pdf

Author : Claudi Alsina,Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 181 pages
File Size : 49,9 Mb
Release : 2009-12-31
Category : Mathematics
ISBN : 9781614442028

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When Less is More by Claudi Alsina,Roger B. Nelsen Pdf

Introduces the richness and variety of inequalities in mathematics using illustration and visualisation.

Author : Ludger Rüschendorf
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 53,5 Mb
Release : 2013-03-12
Category : Mathematics
ISBN : 9783642335907

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Mathematical Risk Analysis by Ludger Rüschendorf Pdf

The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications. The first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.

Author : Piotr Jaworski,Fabrizio Durante,Wolfgang Karl Härdle,Tomasz Rychlik
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 50,5 Mb
Release : 2010-07-16
Category : Mathematics
ISBN : 9783642124655

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Copula Theory and Its Applications by Piotr Jaworski,Fabrizio Durante,Wolfgang Karl Härdle,Tomasz Rychlik Pdf

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.

Author : Ibragimov Rustam,Prokhorov Artem
Publisher : World Scientific
Page : 304 pages
File Size : 55,6 Mb
Release : 2017-02-24
Category : Business & Economics
ISBN : 9789814689816

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Heavy Tails And Copulas: Topics In Dependence Modelling In Economics And Finance by Ibragimov Rustam,Prokhorov Artem Pdf

This book offers a unified approach to the study of crises, large fluctuations, dependence and contagion effects in economics and finance. It covers important topics in statistical modeling and estimation, which combine the notions of copulas and heavy tails — two particularly valuable tools of today's research in economics, finance, econometrics and other fields — in order to provide a new way of thinking about such vital problems as diversification of risk and propagation of crises through financial markets due to contagion phenomena, among others. The aim is to arm today's economists with a toolbox suited for analyzing multivariate data with many outliers and with arbitrary dependence patterns. The methods and topics discussed and used in the book include, in particular, majorization theory, heavy-tailed distributions and copula functions — all applied to study robustness of economic, financial and statistical models, and estimation methods to heavy tails and dependence.

Author : M. McGillivray
Publisher : Springer
Page : 270 pages
File Size : 50,6 Mb
Release : 2006-08-10
Category : Business & Economics
ISBN : 9780230625594

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Inequality, Poverty and Well-being by M. McGillivray Pdf

This book examines inequality, poverty and well-being concepts and corresponding empirical measures. Attempting to push future research in new and important directions, the book has a strong analytical orientation, consisting of a mix of conceptual and empirical analyses that constitute new and innovative contributions to the research literature.

Author : Gianni Betti,Achille Lemmi
Publisher : Routledge
Page : 369 pages
File Size : 40,7 Mb
Release : 2008-04-24
Category : Business & Economics
ISBN : 9781134068012

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Advances on Income Inequality and Concentration Measures by Gianni Betti,Achille Lemmi Pdf

This impressive collection from leading distributional analysts provides an overview of a wide range of economic, statistical and sociological relationships. The resulting book deserves its place on the bookshelf of serious mathematical economists everywhere.