Majorization And The Lorenz Order A Brief Introduction
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Majorization And The Lorenz Order
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Author : Barry C. Arnold
language : en
Publisher:
Release Date : 1987
Majorization And The Lorenz Order written by Barry C. Arnold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Distribution (Probability theory) categories.
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.
Majorization And The Lorenz Order
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Author : Barry C Arnold
language : en
Publisher:
Release Date : 1987-11-05
Majorization And The Lorenz Order written by Barry C Arnold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-11-05 with categories.
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.
Smoothness Priors Analysis Of Time Series
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Author : Genshiro Kitagawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Smoothness Priors Analysis Of Time Series written by Genshiro Kitagawa 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.
Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
Income And Wealth Distribution Inequality And Poverty
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Author : Camilo Dagum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Income And Wealth Distribution Inequality And Poverty written by Camilo Dagum 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 Business & Economics categories.
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.
Matrix Theory And Applications
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Author : Charles R. Johnson
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Matrix Theory And Applications written by Charles R. Johnson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
This volume contains the lecture notes prepared for the AMS Short Course on Matrix Theory and Applications, held in Phoenix in January, 1989. Matrix theory continues to enjoy a renaissance that has accelerated in the past decade, in part because of stimulation from a variety of applications and considerable interplay with other parts of mathematics. In addition, the great increase in the number and vitality of specialists in the field has dispelled the popular misconception that the subject has been fully researched.