Lorenz Curve Research Papers - Academia.edu (original) (raw)

This paper shows how the Lorenz curve can be used, together with models of disease risk, to allocate scarce resources so as to optimize a health benefit. Consider the example of breast cancer mortality. If there were sufficient resources to provide all women with mammograms, a certain maximal number of lives could be saved. Suppose, however, that only a fraction of that amount of money is available for prevention activities. Suppose that a questionnaire could be given to assess a woman's risk of dying of breast cancer. Depending on the amount of money available, on the ratio of the cost of a questionnaire to the cost of a mammogram, and on the Lorenz curve of the distribution of risks of breast cancer mortality, I calculate the proportion of women who should be given questionnaires, the proportion of women given the questionnaires who should be given mammograms because they have high risks, and the proportion of women not given questionnaires who should be assigned to receive ma...

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- Bioinformatics, Mathematics, Life Sciences, Medicine

In which representation is speech most sparse? Time-scale? Time-frequency? Which window generator and length should be used to create the sparsest decomposition? To answer these questions, we propose the Gini index, which is twice the area between the Lorenz curve and the 45 degree line, as a measure of signal sparsity. The Gini index, introduced in 1912, is one of the most common measures of income or wealth distribution and is used to measure the inequity, or sparseness, of wealth distribution. Numerous decompositions of the speech signals in the TIMIT database are used to determine the most sparse standard representation for speech.

- by Scott Rickard
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- Wealth Distribution, Lorenz Curve

A general method for building parametric-functional families of Lorenz curves, generated from an initial Lorenz curve (which satisfies some regularity conditions) is presented. It is shown that these families can be ordered in a manner which leads to a hierarchy of Lorenz curves. The method starts from a generating Lorenz curve¸(p) and builds the family by increasing the number of parameters, which can be easily interpreted in terms of the elasticities of¸(p). The method is applied to a family we term the Pareto family, since they use the Pareto Lorenz curves as their generating curves. The family is shown to contain an important number of classical Lorenz curves used in the existing literature. Several properties of this family are analyzed, these include the population function, inequality measures and Lorenz orderings. A general method for the estimation of these family is given and applied to the Pareto family. Finally, an application is presented for data from various countries. The results are very robust across data sources. The Pareto models fit very well in a number of applications.

- by Daniel Slottje
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- Econometrics, Inequality, Boolean Satisfiability, Lorenz Curve

The power distribution is defined as the inverse of the Pareto distribution. We study in full detail a distribution so-called the beta power distribution. We obtain analytical forms for its probability density and hazard rate functions. Explicit expressions are derived for the moments, probability weighted moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, moments of order statistics, entropy and reliability. We estimate the parameters by maximum likelihood. The practicability of the model is illustrated in two applications to real data. y 0 ω a−1 (1 − ω) b−1 dω is the incomplete beta function is the complete beta function. The unknown positive parameters a and b are shape parameters which introduce skewness and vary tail weights.

- by Gauss Cordeiro
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- Applied Mathematics, Statistics, Maximum Likelihood, Reliability

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan, sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

- by Gauss Cordeiro
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- Mathematics, Statistics, Statistical Computing, Density-functional theory

A treatment of the mathematical properties is provided for the Lindley distribution. The properties studied include: moments, cumulants, characteristic function, failure rate function, mean residual life function, mean deviations, Lorenz curve, stochastic ordering, entropies, asymptotic distribution of the extreme order statistics, distributions of sums, products and ratios, maximum likelihood estimation and simulation schemes. An application to waiting time data at a bank is described.

- by M. Ghitany
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- Mathematical Sciences, Maximum Likelihood, Physical sciences, Exponential distribution

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution.

- by Bander Al-Zahrani and +2
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- Statistics, Primary, Maximum Likelihood, Random sampling

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution.

- by Vitor Marchi and +2
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- Statistics, Primary, Maximum Likelihood, Random sampling

The aim of this article is to develop a tourism (Carrying Capacity Indicator) for protected areas that could assist regional planners and park managers to promote an equitable form of the spatial distribution of visitors environmentally sensitive area, various indicators have been proposed, with regard to ecologically sustainable tourism. In this paper, we examine the unequal distribution of visitors to a protected area that causes significant additional environmental pressure on some sub-areas. This additional pressure, which may exceed the landscape's carrying capacity, cannot be measured by the commonly used indices that represent an average for the whole area. Our objective is to depict the variability of pressure intensity within a protected area. For this purpose we introduce an indicator adjusted to the Gini co-efficient resulting from the Lorenz curve, used by economists to measure the unequal distribution of income. The proposed indicator is applied to the Mount Olympus National Park, Greece.

- by Stella Kostopoulou
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- Environmental Management, Anatolia, Tourism, Environmental Assessment
- by Joao Pedro Azevedo
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- Lorenz Curve

In this paper we argue that a better understanding of the relationship between inequality and growth can be obtained by shifting the analysis from the space of final achievements to the space of opportunities. To this end, we introduce the Opportunity Growth Incidence Curve (OGIC) that can be used to evaluate the income dynamics of specific groups of the population and to infer the role of growth in the evolution of inequality of opportunity over time. By employing a rank dependent social welfare function we provide a rigorous normative justification for the use of the OGIC: We obtain suitable dominance conditions and we show how they can be interpreted in terms of OGIC dominance. We also propose an index that can be used to measure the impact of growth in terms of opportunity redistribution. Finally, we provide two empirical illustrations, for Italy and for Brazil, which show the potentials of the tools we have introduced.

- by Flaviana Palmisano
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- Economics, Development Economics, Econometrics, Public Economics
- by Nguyen Quan
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- Applied Economics, World Economics, Lorenz Curve

The purpose of this paper is two-fold: to measure the degree of earnings inequality in tourism employees in South Korea, using the Gini coefficient and the Lorenz curve; and to examine the level of earnings based on median earnings. The results show that tourism generates a moderately equal distribution of earnings. In general, tourism performs earnings distribution better than secondary and tertiary industries, but it performs poorly as compared with primary industry. The results also indicate that tourism is more likely to improve living standards for the lower income class than secondary and tertiary industries.The analysis of median earnings, however, indicates that tourism is a low wage industry. The labor-intensive nature of the tourism industry absorbing many unskilled and semi-skilled workers might be attributed to its low wage structure. It is interesting to note that tourism was found to be advantageous to female workers in terms of earnings inequality and the level of earnings.

- by Choong-ki Lee
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- Marketing, Tourism Management, South Korea, Tourism

The opportunity for site-specific management of crops depends on both the magnitude and spatial structure of yield variation. This study explored the applicability of Lorenz curves and Gini coefficients (G) to characterise the magnitude of the variation in grain yield. Maize crops were grown in farmers fields in a semi-arid region of central Argentina. Major sources of yield variation between and within paddocks included season, soil type and topography, rate of nitrogen fertiliser (nil to 132 kg N ha À1 ), and the interactions among these factors. Nitrogen treatments were applied in a complete block strip trial (strip size $ 700 m Â 9:8 m) with three replicates. Data were collected with an AgLeader TM yield monitor, and GIS software was used to create 9:8 m Â 9:8 m grids over the observations. Average yield in 0.7-2.8 ha field sections ranged from 1.6 to 7.0 t ha À1 . Gini coefficient ranged from 0.027 to 0.191 whereas its theoretical limits are 0 for a perfectly uniform population, and 1 for a theoretical population of infinite size where all units but one yield 0. Conditions conducive to high yield, e.g. adequate availability of nitrogen and water, reduced crop yield inequality, as quantified with G. The agronomic relevance of G was summarised in an inverse relationship with yield. Lorenz curves seemed particularly apt to present crop heterogeneity in terms of inequality, and to highlight the relative contribution of low-and high-yielding sections of the field to total paddock yield. Lorenz curves and Gini coefficients provide a potentially useful extension tool, a complement to yield maps and other statistical indices of yield variation, and further contact points between site-specific management, economics and ecology. #

- by V. Sadras
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- Population ecology, Seasonality, Maize, Field Crops

This study explored inequality of agricultural resources among states in India using the Lorenz curve and Gini coefficient. The shape of the Lorenz Curve shows inequality in operational holding, livestock population, irrigation and per capital income at current prices (2012 2013) among states in the country.
Irrigation inequality was highest with Gini-coefficient value of 0.66 followed by 0.6 for agricultural landholding size. Livestock inequality had a value of 0.54 whereas per capita income at current prices (2012 2013) reported the least inequality among states with a Gin coefficient value of 0.2.

- by Melkamu Mada
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- Poverty, India, Inequality, Gini Coefficient

In recent years successive Brazilian governments have actively pursued economic and social policies aimed at reducing poverty and promoting social equality and inclusion. In the field of energy, this has meant introducing and implementing programs aimed at expanding the supply of safe and reliable energy to the poorest sectors of Brazilian society, including those living in remote rural areas. This paper draws attention on the findings of extensive field research to evaluate the impact of rural electrification on energy poverty in the context of government policies aimed at promoting energy equity. The authors re-examine the concept of an energy poverty line, seeking to fine tune its application to Brazilian social and economic realities, and then apply an analytical framework (Lorenz Curve, Gap Poverty, Gap Quadratic, Gini Coefficient and Sen Index) to evaluate the effectiveness of recent efforts in Brazil to expand access to electricity. One of the main conclusions of this study is that is that rural electrification leads to a significant reduction of the energy poverty level and a consequent improvement in energy equity.

- by Marcos Freitas
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- Social Policy, Energy Policy, Multidisciplinary, Government Policy
- by Eugen Hristev
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- Local Development, Good Governance, Welfare, Labor Market

ÖZET Bu makale gelir dağılımı ile ekonomik büyüme arasındaki karşılıklı ilişkiler üzerine mevcut literatürü kalkınma açısından analitik olarak incelemektedir. Ayrıca yakın geçmişteki gelir dağılımı trendlerini değerlendirmektedir. Çalışmamız büyümenin gelir dağılımı üzerinde her hangi bir yönde sistemli etkisi olmadığını göstermektedir. Buna karşın gelir dağılımı birçok mekanizma aracılığı ile ekonomik büyümeyi etkileyebilmektedir. Ampirik çalışma gelişmekte olan ülkeler için bu yönde anlamlı kanıtlar sunmaktadır.

- by Oded Galor
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- Economic Growth, Inequality, Lorenz Curve

With the ready accessibility of bibliometric data and the availability of ready-to-use tools for generating bibliometric indicators for evaluation purposes, there is the danger of inappropriate use. Here we present standards of good practice for analyzing bibliometric data and presenting and interpreting the results. Comparisons drawn between research groups as to research performance are valid only if (1) the scientific impact of the research groups or their publications are looked at by using box plots, Lorenz curves, and Gini coefficients to represent distribution characteristics of data (in other words, going beyond the usual arithmetic mean value), (2) different reference standards are used to assess the impact of research groups, and the appropriateness of the reference standards undergoes critical examination, and (3) statistical analyses comparing citation counts take into consideration that citations are a function of many influencing factors besides scientific quality.

- by Hans-Dieter Daniel
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- Applied Ethics, Research evaluation, Science Ethics, Perforation

- by Bander Al-Zahrani
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- Statistics, Primary, Maximum Likelihood, Random sampling

The paper provides an evaluation of the redistribution effects stemming from the changes to the personal income tax introduced in the last decade. The analysis confirms that between 1989 and 2001 the net average tax rate increased for all taxpayers and, above all, for one-earner couples. The reason is twofold: a) the progressivity of the tax makes larger the burden on these households of changes in income brackets and tax rates; b) the absence of dependent relatives does not allow the compensation of higher taxes with increased tax ...

- by Chiara Rapallini
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- Stochastic dominance, Income Distribution, Social Welfare, Tax Burden

Poly-b-hydroxybutyrate (PHB) is a natural polymer that can be depolymerized into water-soluble short-chain fatty acid monomers. These monomers can act as microbial control agents. In this study, the effects of partially replacing the diet of Siberian sturgeon fingerlings with 2% and 5% PHB were investigated. Replacing 2% of the diet with PHB improved weight gain, specific growth rate (SGR) and survival in the sturgeon fingerlings during the 10-week experimental period. Community-level physiological profiling and PCR-denaturing gradient gel electrophoresis (PCR-DGGE) were used to analyze the microbial community diversity and community organization in the sturgeon gastrointestinal tract. DGGE analysis revealed that PHB affected the intestinal microbial species richness and diversity. The highest species richness was observed with 2% PHB. DNA sequencing of the dominant bands in 2% and 5% PHB treatments revealed that PHB stimulated bacteria belonging to the genera Bacillus and Ruminococcaceae. Principal component analysis, Lorenz curves and the Shannon index of Biolog™ Ecoplate data revealed that aerobic metabolic potential of the bacterial community was different in the PHB-treated fishes as compared with the control situation. Overall, our results indicate that PHB act as microbial control agents and replacement of 2% of Siberian sturgeon fingerling diet with PHB has beneficial effects.

- by Tom Defoirdt
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- Principal Component Analysis, Siberia, Aquaculture, Biological Sciences

The study used primary data from 100 households following multistage random sampling process. To address income and resource inequality of household in the study area, the study used Lorenz curve and Gin-coefficient. Grapical and analytical results showed existence of high income and resource inequality in the district. In the district irrigated land and farm land inequality have highest Gin-coefficient. Livestock and income relatively diffused better than other resource. The result found that in Bikaner district 48.1 percent of agricultural land, 42.8 percent of livestock, 61.3 percent of irrigated land and 52.3 percent of farm incomes were distributed unequally.

- by Dinesh Kumar and +1
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- Bikaner, Lorenz Curve

To Professor Joseph L. Gastwirth whose creativity and fondness for indices have been matchlessly inspiring L-statistics play prominent roles in various research areas and applications, including development of robust statistical methods, measuring economic inequality and insurance risks. In many applications the score functions of L-statistics depend on parameters (e.g., distortion parameter in insurance, risk aversion parameter in econometrics), which turn the L-statistics into functions that we call L-functions. A simple example of an L-function is the Lorenz curve. Ratios of L-functions play equally important roles, with the Zenga curve being a prominent example. To illustrate real life uses of these functions/curves, we analyze a data set from the Bank of Italy year 2006 sample survey on household budgets. Naturally, empirical counterparts of the population L-functions need to be employed and, importantly, adjusted and modified in order to meaningfully capture situations well beyond those based on simple random sampling designs. In the processes of our investigations, we also introduce the L-process on which statistical inferential results about the population L-function hinges. Hence, we provide notes and references facilitating ways for deriving asymptotic properties of the L-process.

- by Madan Puri and +2
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- Gini Index, Indexation, Lorenz Curve

En el presente trabajo se analiza la influencia de las curvas de Lorenz, el Principio de Transferencias y las relaciones de mayoración entre vectores de renta sobre las medidas de desigualdad. De esta forma, se pasa revista al desarrollo... more

Analysing the impact of agricultural performance on foreign trade concentration and competitiveness defines an important step in identifying the opportunities, challenges and proactive measures in designing a functional and marked based agricultural model. The scope of this study is to investigate the evolution of Romania’s the foreign trade competitiveness and its concentration on main destinations during 2007–2016. In this context, in the paper are identified and investigated some of the competitiveness’ mutations arisen from the Romania’s trade flows concentration and restructuration in relation with 26 of the European Union member states. It was used a unique dataset on agro -food trade output and concentration across EU countries to construct measures of trade competitiveness. The results obtained suggest the existence of a dual relationship of the Romanian agriculture competitiveness and its dependence on the EU economic area, by the concentration of the commercial relationships.

- by Luminita Chivu
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- Agricultural Economics, Convergence, Applied Economics, Business and Management

Distribution of income has been an important area of research in both economics and sports economics literature. However, the sports economics literature regarding European football lacks empirical studies associated with the relationship between revenue generation and competitive balance. This study analyzes the revenue sharing structure in Europe's top 5 football leagues along with its effects on competitive balance. Trends in the distribution of revenue are illustrated with the help of Lorenz curves and the coefficient of variations of revenue shares. There is significant evidence that there have been severe distortions in the distribution of revenue in European football, and it has been influential in the competition. The revenue shares of the top 5 leagues' have changed substantially over the last two decades which led to the utter dominance of European football by few clubs. The increasing inequality, in revenue generation and sharing, has affected the competitive balance adversely. The rising financial domination of the giants in European football is widening the gap between them and the lower profile teams hence decreasing the uncertainty of games, which might have adverse effects on the demand for football.

- by Selçuk Özaydın
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- Sports economics, Lorenz Curve, Distribution of revenue

This study evaluates long-term structural adjustments in fresh grapefruit packing under aggregate market pressures, including those from retail concentration. While individual firms enter and exit, Markov-model results are indicative of an industry near equilibrium with little expectation of change in the distribution of firm sizes given existing patterns of sector adjustment. Estimation of Lorenz curves and corresponding Gini coefficients fully

- by Suzanne Thornsbury
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- Supply Chain, Crop Production, Firm Size, Food Distribution

Several polyhedral risk measures have been recently introduced leading to Linear Programming (LP) models for portfolio optimization. In this paper we study LP solvable portfolio optimization models based on the tail Gini's mean difference risk measurement. We use combinations of the Conditional Value at Risk (CVaR) measures to get some approximations to the tail Gini's mean difference with the advantage of being computationally much simpler than the Gini's measure itself. We introduce the weighted CVaR (WCVaR) measures defined as simple combinations of a very few CVaR measures with specific type of weights settings which relates the WCVaR measure to the tail Gini's mean difference. This allows us to use a few tolerance levels as only parameters specifying the entire WCVaR measures while the corresponding weights are automatically predefined by the requirements of the corresponding tail Gini's measure. All the studied models are SSD consistent and LP computable. We analyze both the theoretical properties of the models and their performances on the real-life data.

... sources are utilised by a bacterial community [6]. Two analytical approaches are used ... BIOLOG microtiter plates [6]. However, comparisons made between communities from different soil samples ... use data from an experiment using... more

- by Raymond Correll and +1
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- Microbiology, Medical Microbiology, Functional diversity, Analysis of Variance

This paper explains how to build Lorenz Curves for income distributions and discusses their use for inequality measurement. A short conceptual background, a step-by-step procedure and a simple numerical example illustrate how to calculate and draw Lorenz Curves. A discussion on the use of Lorenz Curves to represent inequality is also provided. It highlights that the Lorenz Curve is one of the most used ways of representing income distributions in empirical works thanks to its immediate comparability with a “natural” benchmark, the Equidistribution line, representing the most egalitarian distribution. The concepts of Lorenz dominance and intersection of Lorenz Curves are also discussed. Furthermore, the appendix provides a detailed presentation of the properties of the Lorenz Curves.

- by Paolo Liberati
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- Mathematics, Economics, Poverty, Income Distribution

- by Ronald Ward
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- Supply Chain, Crop Production, Firm Size, Food Distribution

This paper compiles the risk measures associated with the Lorenz curve. The Lorenz curve is the main tool in economics for measuring income distribution and inequality. For the past decades some of the Lorenz curve spin-offs have been used in risk analysis and finance. In particular, the Lorenz curve addresses the concepts of second degree stochastic dominance, Gini's mean difference, Conditional Value-at-Risk, and the extended Gini in portfolio theory and in investment practice. Because the Lorenz curve can be estimated from asset returns, the risk measures are easy to implement and use.. JEL Codes G32 D81 G11

- by Haim Shalit
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- Risk Management, Stochastic dominance, Risk Analysis, Working Papers

For the first time, a five-parameter distribution, the so-called beta Burr XII distribution, is defined and investigated. The new distribution contains as special sub-models some wellknown distributions discussed in the literature, such as the logistic, Weibull and Burr XII distributions, among several others. We derive its moment generating function. We obtain, as a special case, the moment generating function of the Burr XII distribution, which seems to be a new result. Moments, mean deviations, Bonferroni and Lorenz curves and reliability are provided. We derive two representations for the moments of the order statistics. The method of maximum likelihood and a Bayesian analysis are proposed for estimating the model parameters. The observed information matrix is obtained. For different parameter settings and sample sizes, various simulation studies are performed and compared in order to study the performance of the new distribution. An application to real data demonstrates that the new distribution can provide a better fit than other classical models. We hope that this generalization may attract wider applications in reliability, biology and lifetime data analysis.

- by edwin ortega
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- Econometrics, Statistics, Data Analysis, Bayesian Analysis
- by Kanwal Bilal
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- Income inequality, Research Paper, Cross Section, Per Capita Income

In estimating a density function for the duration of unemployment, we consider two departures from what would be ideal conditions. If the so-called digit preference e!ect produces local distortion in observed samples, we can apply a maximum entropy density estimation method. To establish the functional form of the density, we maximize entropy subject to moment restrictions. The global shape of the density is determined by the lower ordered sample moments which are not a!ected much by the digit preference e!ect. As a by-product of this method, we can establish the local transition structure of the digit preference e!ect. As a second case of departure from an ideal condition, we consider coarse sample observations where unemployment duration was observed only for 4, 10, 14, 26, and 52 weeks. Once the unemployment duration density is derived, quintile behavior over time, the Lorenz curve, and the Gini coe$cient for the distribution of unemployment duration can be obtained. Finally, we discuss the rami"cations of only focusing on the headcount ratio of unemployment when other information is available.

- by Daniel Slottje
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- Econometrics, Density Estimation, Maximum entropy, Functional Form

The actual distribution of world income across countries is extremely unequal, much higher than the within country inequality faced by most countries. The question studied in this paper is: how do international policies on aid, trade and... more

- by David Rosenblatt
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- Development Economics, International Trade, Immigration, Economic Growth

We propose a statistical index for measuring the fluctuations of a stochastic process ξ. This index is based on the generalized Lorenz curves and (modified) Gini indices of econometric theory. When ξ is a fractional Brownian motion with Hurst index α ∈ (0, 1), we develop a complete picture of the asymptotic theory of our index. In particular, we show that the asymptotic behavior of our proposed index depends critically on whether α ∈ (0, 3 4), α = 3 4 , or α ∈ (3 4 , 1). Furthermore, in the first two cases, there is a Gaussian limit law, while the third case has an explicit limit law that is in the second Wiener chaos.

- by Youri Davydov
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- Mathematics, Stochastic Process, Econometrics, Statistics

Value Added Tax (VAT) has been introduced in India in place of Sales Tax with effect from April 1, 2005. These taxes are in the domain of different state governments within the federal set up in India. Although VAT is widely acclaimed to be a better system than the sales taxes on grounds of efficiency and tax collection, there is no study undertaken which has addressed the direction of this tax reform from the angle of its possible impact on poverty reduction. This paper analyses this question with the help of concentration curves, Lorenz curve and consumption dominance curves of various orders. The conclusions reached from six major states in India, namely Bihar, Gujarat, Karnataka, Madhya Pradesh, Maharashtra and West Bengal using National Sample Survey Unit Level data for the 55 th round is that there are scopes of improvement in the design of VAT reform with respect to some items predominantly consumed by the relatively poorer groups.

- by DR. SUDIP KUMAR SINHA
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- Econometrics, Tax reform, Indian Economic problems, Applied Economics

We show that a theory of earnings and wealth inequality based on the optimal choices of ex-ante identical households who face uninsured idiosyncratic shocks to their endowments of efficiency labor units accounts for the U.S. earnings and wealth inequality almost exactly. Relative to previous work, we make three major changes to the way in which this basic theory is implemented:

- by Javier Diaz
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- Economics, Political Economy, Wealth Distribution, Political
- by Fazli Rabbi
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- Human Geography, Rural Development, Sustainable, Human Capital

- by Maria-Pia Victoria-Feser
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- Lorenz Curve

Abstract: The present study attempts to analyze income and resource inequality of household in Nagaur district. The study used primary data from 100 households following multistage random sampling process. To address income and resource inequality of household in the study area, the study used Lorenz curve and Gin-coefficient. Grapical and analytical results showed existence of high income and resource inequality in the district. In the district, irrigated land is owned by few people but farm land is relatively owned by many people. Income and farm land relatively diffused better than other resource. The Gin-coefficient result found that in Nagaur district 29.5 percent of agricultural land, 39.9 percent of livestock, 73.5 percent of irrigated land and 34.1 percent of incomes were distributed unequally.

- by Vikash Kumar and +1
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- India, Rajasthan, Lorenz Curve

In this paper we examine empirically the market for local amenities in the Paris metropolitan region. We find first that there is considerable inequality in the spatial distribution of these local amenities, including accessibility, environmental and social indicators. We use a spatial representation and Lorenz curves to examine the degree of inequality in these amenities, and this provides evidence that some amenities (or disamenities) are much more inequitably distributed than others. The most extremely unequally distributed amenities are noise (due to its concentration near airports), "Redevelopment Areas", presence of water (lakes and rivers) and forests, and presence of train and subway stations. Some indicators, such as the "Poulit accessibility" measure, were by contrast remarkably constant over the region. We recognize that local amenities should be capitalized into the housing market, and explore the willingness to pay of households for these amenities within the Paris region using alternative specifications of a location choice model. One of the core questions we examine is the spatial scale of the amenity effects and how this is captured in a location choice context. By estimating models at both a commune and at a grid cell level, we obtain new insights into how households in the Paris region trade off amenities against each other and against housing cost. We find that the residential location choice model fits the data moderately better at the smaller scale of the grid cell compared to the commune.

- by Nathalie Picard
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- Spatial Representation, Spatial Scale, Housing Market, Spatial Distribution

and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

- by Gauss Cordeiro
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- Mathematics, Statistics, Applied Economics, Extreme Value Theory

Distribution of income is among the most important issues in welfare economics. Economic literature provides different ways to measure income inequality. Most common inequality indices provide information about the income distribution and analyze the inequality of income allocation without any reference to the amount of money needed to reduce the income inequality.In this paper, we design a model to estimate the Lorenz curve function parameters. By this approach, any census summary data can be used to measure the distribution of income. We also introduce a new fiscal-compensation-based index for reduction of the degree of inequality. Using this index, we show how much transfer payment is needed to achieve the desired distribution of income consistent with the perceived economic goals of the society.

- by Bijan Bidabad
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- Economics, Welfare Economics, Statistics, Income Distribution