1,408,322 research outputs found
Estimating Lorenz Curves Using a Dirichlet Distribution.
No full textThe Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares, estimation techniques that have good properties when the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology that recognises the cumulative proportional nature of the Lorenz curve data by assuming that the income proportions are distributed as a Dirichlet distribution. Five Lorenz-curve specifications are used to demonstrate the technique. Maximum likelihood estimates under the Dirichlet distribution assumption provide better-fitting Lorenz curves than nonlinear least squares and another estimation technique that has appeared in the literature.Gini coefficient; maximum likelihood estimation
Estimating Lorenz Curves Using a Dirichlet Distribution
No full textThe Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares assuming that the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology which recognizes the cumulative proportional nature of the Lorenz curve data by assuming that the proportion of income is distributed as a Dirichlet distribution. Five Lorenz-curve specifications were used to demonstrate the technique. Once a likelihood function and the posterior probability density function for each specification are derived we can use maximum likelihood or Bayesian estimation to estimate the parameters. Maximum likelihood estimates and Bayesian posterior probability density functions for the Gini coefficient are also obtained for each Lorenz-curve specification.
REVISITING THE ORDERED FAMILY OF LORENZ CURVES
No full textLorenz curve; Gini index Abstract: Sarabia et al. (1999) present a basic model to create ordered families of Lorenz curves, along with basic theorems that describe the conditions for the models to satisfy the definition of the Lorenz curve. Using these basic models, they suggest a family which includes several well-known Lorenz models as special cases. This paper first shows that their basic theorems can be generalized. The paper then proceeds to propose additional families of Lorenz models. Finally the performance of some of the models is compared and it is shown that more efficient Lorenz models are possible with the assistance of our generalized result of the Sarabia et al. (1999) basic model.
Averaging Lorenz Curves
No full textA large number of functional forms have been suggested in the literature for estimating Lorenz curves that describe the relationship between income and population shares. One way of choosing a particular functional form is to pick the one that best fits the data in some sense. Another approach, and the one followed here, is to use Bayesian model averaging to average the alternative functional forms. In this averaging process, the different Lorenz curves are weighted by their posterior probabilities of being correct. Unlike a strategy of picking the best-fitting function, Bayesian model averaging gives posterior standard deviations that reflect the functional form uncertainty. Building on our earlier work (Chotikapanich and Griffiths 2002), we construct likelihood functions using the Dirichlet distribution and estimate a number of Lorenz functions for Australian income units. Prior information is formulated in terms of the Gini coefficient and the income shares of the poorest 10% and poorest 90% of the population. Posterior density functions for these quantities are derived for each Lorenz function and are averaged over all the Lorenz functions.Gini coefficient; Bayesian inference; Dirichlet distribution.
Ranking Intersecting Lorenz Curves
No full textThis paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the best-off income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that places more emphasis on changes that occur in the lower part of the income distribution and the other that places more emphasis on changes that occur in the upper part of the income distribution. Both strategies turn out to depart from the Gini coefficient; one requires higher degree of downside and the other higher degree of upside inequality aversion than what is exhibited by the Gini coefficient. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of a given set of Lorenz curves. Moreover, it is demonstrated that the introduction of successively more general transfer principles than the Pigou-Dalton principle of transfers forms a helpful basis for judging the normative significance of higher degrees of Lorenz dominance. The dominance results for Lorenz curves do also apply to generalized Lorenz curves and thus provide convenient characterizations of the corresponding social welfare orderings.generalized Gini families of inequality measures, rank-dependent measures of inequality, Gini coefficient, partial orderings, Lorenz dominance, Lorenz curve, general principles of transfers
The Lorenz curve in economics and econometrics
No full textThis 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. These include characterizations of income distributions in terms of families of inequality measures, Lorenz ordering of multiparameter distributions in terms of their parameters, probability inequalities for distributions of quadratic forms, and Condorcet jury theorems.Lorenz curve, Lorenz order, majorization, income distribution, income inequality, statistical distributions, characterizations, Condorcet jury theorem.
TWO NEW EXPONENTIAL FAMILIES OF LORENZ CURVES
No full textWe present two new Lorenz curve families by using the basic model proposed by Sarabia, Castillo and Slottje (1999). We present estimations which show that the models in our new families are very efficient when applied to data on income distribution for a range of countries from Shorrocks (1983).Lorenz curve
Declaración de uso de inteligencia artificial en la escritura académica en la Fundación Universitaria Konrad Lorenz
No full textLa Declaración de Uso de Inteligencia Artificial (IA) para la Escritura Académica de la Fundación Universitaria Konrad Lorenz proporciona un marco normativo para el uso ético y responsable de tecnologías de IA en los procesos de enseñanza y aprendizaje. Este documento establece directrices claras sobre la autoría, integridad académica, y el respeto por los derechos de propiedad intelectual, asegurando que la IA complemente, pero no reemplace, el pensamiento crítico humano en la producción académica.La Fundación Universitaria Konrad Lorenz ha emitido una declaración para regular el uso de la inteligencia artificial (IA) en la escritura académica. Este documento subraya principios éticos y de transparencia, estableciendo que el uso de herramientas de IA debe ser complementario al razonamiento y creatividad humana. La declaración exige que los estudiantes y docentes declaren explícitamente su uso de IA, manteniendo la integridad académica y respetando la propiedad intelectual. Además, se incluyen restricciones sobre el uso de IA en evaluaciones y la confidencialidad de datos. La Fundación también se compromete a ofrecer capacitación sobre el uso ético y efectivo de la IA.The Fundación Universitaria Konrad Lorenz has issued a declaration to regulate the use of artificial intelligence (AI) in academic writing. This document emphasizes ethical principles and transparency, establishing that the use of AI tools must complement human reasoning and creativity. The declaration requires students and faculty to explicitly disclose their use of AI, maintaining academic integrity and respecting intellectual property. Additionally, it includes restrictions on the use of AI in assessments and the confidentiality of data. The Foundation also commits to providing training on the ethical and effective use of AI.1. Introducción2. Principios generales3. Directrices para el uso de IA4. Restricciones5. Responsabilidades6. Propuesta de declaración de uso de IA (Formato electrónico)Los OVAS son aplicaciones basadas en la web que funcionan en la mayoría de los navegadores de internet en computadores o dispositivos móviles que soporten HTML5. Lo que significa que no es necesario descargar ni instalar ningún software adicional.
Requisitos Básicos:
Conexión a internet Velocidad mínima de conexión: 3 Mb/seg. Preferible: Conexión Ethernet por cable o WIFI de 6 Mb/seg o superior.
Exploradores Web
• Apple Safari 7 o una versión posterior
• Google Chrome 50 o una versión posterior
• Microsoft Edge
• Microsoft Internet Explorer 11
• Mozilla Firefox 35 o una versión posterior
Sistemas operativos
• Windows 10
• Windows 8.x – Windows 7.x
• Mac OS X 10.8 y versiones posteriores
• iOS (versión más reciente)
• Android (versión más reciente)
Plugins adicionales:
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Requerimientos mínimos de hardware:
• Procesador Intel® a 1,3 GHz o superior.
• Memoria RAM 512 Mb.
• Parlantes o Audífonos.
• Teclado y Mouse.
• Resolución de pantalla: 1024 x 768 píxeles o superior
Una nueva visión Konradista
No full textEsta investigación se concentró en la percepción de satisfacción de los graduados de la Fundación Universitaria Konrad Lorenz en aspectos de su vida universitaria y laboral.This research focused on the perceived satisfaction of Konrad Lorenz University Foundation graduates with aspects of their university and work life.Profesional en MercadeoPregradoMarketin
Visualizing the transition to chaos in the Lorenz system
No full textThe Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This paper addresses the role of the global stable and unstable manifolds in organising the dynamics. More precisely, for the standard system parameters, the origin has a two-dimensional stable manifold and the other two equilibria each have a two-dimensional unstable manifold. The intersections of these manifolds in the three-dimensional phase space form heteroclinic connections from the nontrivial equilibria to the origin. A parameter-dependent visualization of these manifolds clarifies the transition to chaos in the Lorenz syste
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