Majorization and the lorenz order a brief introduction pdf download

Third, disparity in several attributes and multivariate majorization are. The lorenz curve, however, can be meaningfully used to compare arbitrary distributions rather than distributions concentrated on n points, as is the case with the majorization partial order. Sorry, we are unable to provide the full text but you may find it at the following locations. Multivariate convex orderings, dependence, and stochastic. The comparison of lorenz curve may be quite complicated.

If, quite unluckily, i happened to know the laws of these phenomena, i could achieve this goal only at the price of inextricable computations, and should renounce to answer you. The appearance of marshall and olkins 1979 book on inequalities with special emphasis on majorization generated a surge of interest in potential applications of majorization and schur convexity in a broad spectrum of fields. Majorization theorems for strongly convex functions. It is an introduction to the theory of majorization and related notions. A brief introduction, lecture notes in statistics, vol. Pdf download majorization and the lorenz order with. L vector with values of the ordinary lorenz curve l. On the lorenz ordering of order statistics from exponential populations and some applications. Theory of majorization and its applications, 2nd edition. As per the standard gastwirth 1971 definition of a lorenz.

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. It corresponds to a decomposition of the graph into vertex groups of increasing minimum degree. The main result in section 2 provides sufficient conditions for the lorenz order of two random variables which are distributed according to the fourparameter generalized beta density of the first kind gb. Ordinary differential equations and dynamical systems. The need for a multivariate version of lorenz s curve and his partial order. Download pdf introduction irreversibilitythe loss of order and the increase of disorderis a fundamental and ubiquitous feature of physics that is typically described through thermodynamics. The exposition of multivariate lorenz orderings sets it apart from existing treatments. Majorization in economic disparity measures sciencedirect. These properties make this order useful in applications. The journal of the american statistical association jasa has long been considered the premier journal of statistical science. Quantum majorization and a complete set of entropic. In this note we consider a multicriteria decision problem where the decision maker know the the state of the world but the set of consequences is multidimensional. For example, a wealth distribution is lorenz greater than another iff its lorenz curve lies below the other.

Science citation index reported jasa was the most highly cited journal in the mathematical sciences in 19912001, with 16,457 citations, more than 50% more than the next most highly cited journals. Animal behavior in this chapter, a brief introduction to the topic of animal behavior will be given, along with a description of its relevance to autonomous robots. Lavenda entropies of mixing eomand the lorenz order. Introduction in 1972, the meteorologist edward lorenz gave a talk at the 9th meeting of the american association for the advancement of science entitled does the flap of a butterflys wings in brazil set off a tornado in texas. Theory of majorization and its applications marshall and olkin,1979many researchers were unaware of the rich bodyof literature related to majorization that was scattered in journals in a wide variety of. Fixed points of graph peeling proceedings of the 20. Undeniably, many concepts of majorization have been reinvented and used in different fields of research such as dominance ordering or lorenz in economics, graph theory, and optimization. Two variability orders probability in the engineering. A new characterization ofrdas proportional to a univariate gini index for a particular linear combination of attributes relates it to the lorenz zonoid. The lorenz attractor, a paradigm for chaos 5 you are asking me to predict future phenomena. We suppose that a value function is specified over the attribute of the decision problem and we analyze some classes of. A brief introduction, the authors provide a straightforward development and explanation of majorization concepts, addressing historical development of the topics, and providing uptodate coverage of families of lorenz curves.

The focus of the present article is, however, on classical majorization. Measurement of inequality, 2000, in a b atkinson f bourguignon eds. This work was sponsored by the institute of ocean science and. Out of the wide body of literature on partial order relations over. We extend one of the main findings in bossmann et al. I have found the income distribution context to be quite convenient for discussion of inequality orderings. In this paper we argue that by appropriately choosing. Marat ibragimov1 and rustam ibragimov2 1 department of probability theory, tashkent state economics university, tashkent, uzbekistan 2 department of economics, harvard university, littauer center, 1875 cambridge st. Characterization of stochastic orders by lfunctionals characterization of stochastic orders by lfunctionals sordo, miguel. Zlibrary is one of the largest online libraries in the world that contains over 4,960,000 books and 77,100,000 articles. Entropy majorization, thermal adiabatic theorem, and. Read inequality and welfare evaluation of heterogeneous income distributions, the journal of economic inequality on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. A transfer a, b is called a pigoudalton transfer briefly, a pd transfer iff. This is a preliminary version of the book ordinary differential equations and dynamical systems.

However, a brief introduction to the fourier and laplace transforms is given in one of the appendices. For the time being, we will consider the case where y is a closed subspace of a normed linear space x. The majorization partial order on finite sets, described here, can be generalized to the lorenz ordering, a partial order on distribution functions. Intergenerational links, taxation, and wealth distribution. Recently, many articles that were published in an extensive variety of fields have been dedicated to the theory of majorization. Here, there and everywhere, statistical science, vol. The inequality principles of dalton, especially the transfer or robin hood principle, are given appropriate prominence. Thelorenz zonoidwas suggested as a multivariate generalization of the lorenz curve. The inequality principles of dalton, especially the transfer.

For this purpose, a new order, called the excess wealth order, is introduced and studied. Revising and expanding on an earlier monograph, majorization and the lorenz order. The pre sent set of notes is designed for a one quarter course introducing majorization and the lorenz order. Rvis, up to scaling, the volume of the lorenz zonoid plus a. These results will be exploited for the ordering of powerfunction order statistics in section 3. The lorenz order can, thus, be thought of as a useful generalization of the majorization order. The concept of majorization has shown a particular interest in the last decades, mainly due to its wide range of applicability in information and quantum theory, among others 1,2,3,4,5,6,7,8,9. The lorenz curve in economics and econometrics semantic. Naturally extensions of the majorization concept were possible and indeed many have been fruitfully introduced. Entropies of mixing eom and the lorenz order 87 in the case of the three parent distributions of extremev alue statistics, immaterial of whether we are considering the power distribution or its. Since a wide variety of conventions is in use this also serves to define the conventions and notations used in the text. In the last years, the majorization theory has been used in different research areas, as engineering, lorenz or dominance ordering in economics, optimization, networks, and graph theory.

The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or median, or curves like the hypotenuse of the right triangle where every lorenz curve falls into. This paper surveys selected applications of the lorenz curve and related stochastic orders in economics and econometrics, with a bias towards problems in statistical distribution theory. We show that the result holds for a stronger criterion of inequality comparison between distributions. Introduction prior to the appearance of the celebrated volume inequalities.

This is true for general distributions but becomes quite simple for some wellknown distributions, such as pareto distribution of. In short, the vector x majorizes y if the coordi nates of x are. The lorenz order in the space of distribution functions. Entropy free fulltext majorization and dynamics of. Majorization under constraints and bounds on the second. Natural hazards and disasters 3rd edition pdf download. This new order is based on the excess wealth transform which, in turn, is related to the lorenz curve and to the ttt total time on test. Majorization and the lorenz order with applications in applied.