Lorenz curve and gini coefficient pdf

Lorenz curve and gini coefficient pdf
Gini Coefficient. BIBLIOGRAPHY. The Gini coefficient is the most popular measure of inequality in use today. The measurement is named for its developer, Corrado Gini (1884 – 1965), and is based on the Lorenz curve (Sen 1997; Xu 2004).
Journal of Statistical and Econometric Methods, vol.1, no.2, 2012, 31-38 ISSN: 2241-0384 (print), 2241-0376 (online) Scienpress Ltd, 2012 Estimation of Gini coefficients using Lorenz curves
Gini coefficient. Lorenz curves may be constructed from grouped data using Lorenz curves may be constructed from grouped data using interpolation techniques (Gastwirth, 1976) or may be presumed to follow a particular
Calculus I — Introduction to the Gini coefficient The Gini coefficient (or Gini index) is a commonly-used measure of inequality devised by Italian economist Corrado Gini in 1912. In this assignment, we study income inequality in the United States using the Gini coefficient. The Gini coefficient is defined using the Lorenz function)𝐿( , which describes the distribution of some resource in
The Gini coefficient is a numerical measure of distributional inequality. The idea behind the Gini coefficient is fairly simple. We’ve labeled the area between the Lorenz curve and the diagonal line area A and the remaining area under the diagonal to the right of and below the Lorenz curve area B .
18/06/2014 · For a discrete probability function f(y). the free encyclopedia The Gini coefficient is the area between the line of perfect equality and the observed Lorenz curve. is represented by the horizontal axis. and for i = 1 to n: Note that the statement that the Lorenz curve gives the portion of the wealth or income held by a given portion of the population is only strictly true at the points
Tying the Lorenz Curve and Gini Coefficient with Development The Gini Coefficient. They can also compare a country’s Gini Coefficient over years which may illustrate a trend of income distribution.0) and (100.100). Economists can compare the Gini Coefficient of one country with the Gini Coefficient of another country in a particular year. In order to narrow the gap between the rich and the
A complete handout about the Lorenz curve including various applications, including an Excel spreadsheet graphing Lorenz curves and calculating Gini coefficients as well as coefficients of variation. LORENZ 3.0 is a Mathematica notebook which draw sample Lorenz curves and calculates Gini coefficients and Lorenz asymmetry coefficients from data in an Excel sheet.
These are the important key points of lecture notes of Social Stratification are: Gini Index, Gini Coefficient, Inequality In a Society, Lorenz Curve, Small Economy, Income, Economy, Cumulative Income, Imaginary Economy,…
One, the Lorenz curve for a given population with respect to a given resource, represents the cumulative percentage of the resource as a function of the cumulative percentage of the population that shares that percentage of the resource. The second curve is the line y = x which is the Lorenz curve for a population which shares the resource equally. The Gini coefficient can be interpreted as
Proposition 5.1 implies that if one takes the Lorenz curve and applies a monotonic transformation to the horizontal axis (i.e., portraying the curve as a function of X rather than of p), then the square of the coefficient of variation has a geometrical representation that resembles the one for the Gini coefficient.
The Gini Coefficient represents the area of concentration between the Lorenz curve and the line of perfect equality as it expresses a proportion of the area enclosed by the triangle defined by the line of perfect equality and the line of perfect inequality. The closer the coefficient …

Lorenz Curve Wikipedia The Free Encyclopedia Gini

Measuring Resource Inequality The Gini Coefficient
Calculate the Gini Coefficient by taking the ratio of the area inside the Lorenz Curve and dividing the area by the area under the line of perfect equality. Since the area under the line of perfect equality is 0.5, one actually multiplies. This fact explains why countries might have a large Gini Coefficient.
LORENZGI.DOC Page 1 (of 2) 04/06/2016 Lorenz Curve and Gini Coefficient 1 Lorenz curve (LC) and income distribution Households (HH) / persons
Using Lorenz Curve and Gini Coefficient to Reflect the Inequality Degree of S&T Publications H. Kretschmer & F. Havemann (Eds.): Proceedings of WIS 2008, Berlin
The Gini Coefficient is equal to the area between the actual income distribution curve and the line of perfect income equality, scaled to a number between 0 and 100. The Gini coefficient is the Gini index expressed as a number between 0 and 1.
Interpreting Lorenz Curves and Gini Coefficients It was noted in the introduction that Lorenz Curves and Gini Coefficients can be used to gain insights into …
56 Modelling Lorenz curves Figure 1 shows that the Gini coefficient tends towards 1, when . 0
6.3.b.) in the second distribution incomes double and population size remains constant – in this case the Lorenz curve, GINI coefficient, and coefficient of variation will be identical to part a.

The concept of the Gini coefficient was introduced in 1912 by a statistician and sociologist Gini. First we introduce the concept of the Lorenz curve which is the cumulative distribution function of either income or wealth.
The main objective of the study is to compare the Newton–Cotes methods such as the Trapezium rule, Simpson 1/3 rule and Simpson 3/8 rule to estimate the area under the Lorenz curve and Gini coefficient of income using polynomial function with degree 5. Comparing the Gini coefficients of income computed from the Polynomial function with degree 5 for the Trapezium, Simpson 1/3 and …
Page 1 of 1 1 Syllabus Reference: 2.3 Lorenz Curve and the Gini Coefficient (Max Otto Lorenz, 1905) B: Lorenz Curve 45 100 a
Chapter 6. Inequality Measures Summary The Gini is derived from the Lorenz curve, which sorts the population from poorest to richest, and shows the cumulative proportion of the population on the horizontal axis and the cumulative proportion of expenditure (or income) on the vertical axis. While the Gini coefficient has many desirable properties – mean independence, population size
Measuring Inequality: The Origins of the Lorenz Curve and the Gini Coefficient Michael Schneider Devised almost a century ago, both the Lorenz curve and the Gini coefficient are

The Gini coefficient, G, is the ratio of the area between the line of equality (y = x) and the Lorenz curve (A), to the total area under the line of equality (A + B). Caption Lorenz diagram, defined as the cumulative proportion of the total N2O flux plotted against the cumulative proportion of the population.
The more nearly equal a country’s income distribution, the closer its Lorenz curve to the 45 degree line and the lower its Gini index, e.g., a Scandinavian country with an index of 25. The more unequal a country’s income distribution, the farther its Lorenz curve from the 45 degree line and the higher its Gini index, e.g., a Sub-Saharan country with an index of 50. If income were distributed
Creating a Lorenz Curve in Excel . GEOG 326 Winter 2011 Section Handout . 1. Enter original data for case study . Region % Population
GINI COEFFICIENT AND LORENZ CURVE EPUB (Pdf Plus.)
Gini coefficient summarizes the income distribution measured according to Lorenz Curve with a figure. The coefficient is the division of area between the Lorenz Curve and the line of perfect equality (A) by the area which lies beneath the line of equality (A+B).
14/04/2014 · Gini, ROC, AUC (and Accuracy) In economics, it is common to read in newspaper about gini coefficient (Gini was taken from Italian sociologist who introduce this method). Often it is used by the government to report the economic condition of a country.
The Gini coefficient is a ratio between 0 and 1, where 0 implies that each individual receives the same ‘income’ and 1 imply that only one individual receives all the ‘income’ (Benson, 1970 5 ).
A Lorenz curve must have the following properties: The time evolution of the mode of the pdf and of the Gini coefficient shown in Fig. 5 suggests that the estimated uncertainties are realistic and also that both the mode and the Gini coefficient varied linearly with time during the period 2003–2007. Chi-square tests of the fit of straight lines to the data give P(χ 2) = 11% and P(χ 2
Findings: Firstly, the standardized Gini coefficient can still be related to the Lorenz curve. Secondly, changes in standardized Gini coefficients can be decomposed into respectively the change in the distribution of health outcomes and the change in the average health outcomes.
This R code writes the function to plot the Lorenz curves and calculate the following statistics: Biased and unbiased forms of the Gini coefficient and the Lorenz asymmetry coeffcient as described
The Gini coefficient requires you to construct a Lorenz curve that would look like this: A Then you have to determine what fraction of the triangle is made up of area A. Fraction of population . Fraction of income. How to Solve it More Simply . You can solve it geometrically, which would involve solving for the areas of several triangle and trapezoids and adding them up. Here is an alternative
152 PORTFOLIO R ISK M ANAGEMENT U SING THE L ORENZ C URVE S PRING 2014 Portfolio Risk Management Using the Lorenz Curve HAIM S HALIT HAIM S HALIT is a professor of
23/09/2014 · There is an earlier video titled Lorenz Curve in Excel. That video does not include the Gini Index. It focuses on how to construct a Lorenz curve from raw data in Excel. – coefficient of linear expansion pdf 28/07/2016 · The main objective of the study is to compare the Newton–Cotes methods such as the Trapezium rule, Simpson 1/3 rule and Simpson 3/8 rule to estimate the area under the Lorenz curve and Gini coefficient of income using polynomial function with degree 5. Comparing the Gini coefficients of income
Table of Contents 1 Introduction 306 2 Definitions and properties 308 2.1 The Lorenz curve 308 2.2 Application to the distribution of length of life 308
Estimation of the Gini coefficient for the lognormal distribution of income using the Lorenz curve Kwasi A. Darkwah*, Ezekiel N. N. Nortey and Anani Lotsi
20/07/2008 · The Lorenz curve is a graphical tool that is widely used to characterize the concentration of a measure in a population, such as wealth. It is frequently the case that the measure of interest used to rank experimental units when estimating the empirical Lorenz curve, and the corresponding Gini
The Lorenz curve reveals the percentage of income (A+B). A higher Gini coefficient represents a more unequal distribution. According to World Bank data, between 1981 and 2013, the Gini index
The Gini coefficient is the (shaded) area between the Lorenz curve that would exist in a perfectly egalitarian society (the dashed line) and the Lorenz curve that does exist, divided by the area under the Lorenz curve that would exist in a perfectly egalitarian society. The coefficients are thus normalized to run from zero in a perfectly egalitarian society, to one in a society in which the
The econometrics of inequality and poverty Chapter 4: Lorenz curves, the Gini coefficient and parametric distributions Michel Lubrano October 2017
Primary income data yields the most exact estimates of the Gini coefficient. Using Lorenz curves, the Gini coefficient is defined as the ratio of the area between the diagonal and the Lorenz curve
The Gini coefficient is a numerical measure of inequality, which can be easily related to the Lorenz curve. That leaves the remaining The ratio between the areas X and Y on the graph is known as the Gini coefficient.
The gini index is the ratio of the area below the ‘equality line’ (an area which is exactly 0.5) minus the area below the Lorenz curve to the area below the ‘equality line’. If the area below a specific Lorenz curve is given by 0.20, the gini coefficient will be (0.5-0.20)/(0.5) = 0.6.
Fitting Lorenz curves ScienceDirect
The Gini coefficient is defined as a ratio of the areas on the Lorenz curve diagram. If the area between the line of perfect equality and Lorenz curve is A, and
Charting Income Inequality 5 The Lorenz Curve Table 2 – Calculating Lorenz Curves 1 individual 1 3 5 DISCUSSION 5.1 The Lorenz Curve to describe inequality The Lorenz Curve is a very useful way to calculate income inequality. Figure 3, below, shows the shape of Lorenz Curves in the case of the three income distributions A, B and C, with the same total income. Example 1: Case is that of an
The same diagram (Lorenz Curve) is used to show the relative inequality in the distribution of income at the world level. Whereas the GINI-Coefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level.
3/08/2016 · Lorenz curve and Gini coefficient In economics, the Lorenz curve [ 26 ] is often used to explain and measure the heterogeneity of the wealth distribution. It is a graphical representation of the cumulative distribution function of the empirical probability distribution.
Abstract. The Lorenz curve and Gini coefficient are applied here to measure and graph disproportionality in outcomes for multiseat elections held in 2017.
if lc = TRUE (plot of Lorenz curve), add.lc specifies if a new Lorenz curve is plotted (add.lc = “FALSE”) or the plot is added to an existing Lorenz curve plot (add.lc = “TRUE”) Details The Gini coefficient (Gini 1912) is a popular measure of statistical dispersion, especially used for analyzing inequality or concentration.
This paper is concerned with distributions of income and the ordering of related Lorenz curves. By introducing appropriate preference relations on the set of Lorenz curves, two alternative axiomatic characterizations of Lorenz curve orderings are proposed.
The Gini coefficient is a well-known measure of income inequality. It corresponds to the percentage of area below the 45(^circ ) line that is between the 45(^circ ) line and the Lorenz curve on a graph of cumulative income versus cumulative population. In this paper, new interpretations of the
Plotted as a Lorenz curve, complete equality would be a straight diagonal line with a slope of 1 (the area between this curve and itself is 0, so the Gini coefficient is 0). A coefficient of 1
and nonlinear least squares estimates for the Gini coefficient are obtained for each Lorenz-curve specification. Finally, we examine which estimation technique
Lorenz Curve Investopedia

Lorenz curve Wikipedia
inequality, the Lorenz Curve. Extended version of the Gini Index with different weighting schemes are also discussed. The use of the Gini Index and of its generalised versions is explained through a step-by-step procedure and numerical examples. 2. INTRODUCTION Objectives The objective of this module is to introduce readers to the use of both the Gini Index and the Generalised Gini Index, to
A Study of the Estimation of the Gini Coefficient of Income Using Lorenz Curve Kwasi A. Darkwah 1* , Ezekiel N. N. Nortey 1 , Felix O. Mettle 1 and Isaac Baidoo 1 1 Department of Statistics, School of Physical and Mathematical Sciences, College of Basic and …
(iv) Measuring inequality: Using the Lorenz Curve and Gini Coefficient 1. Introduction Almost thirty years ago, the author of this brief attended a lecture addressing the economics of inequality. At the start, the class was invited to imagine the implications of individual wealth being reflected in our personal height. Assume that by government decree, everyone has to march past a fixed point
Lorenz curve coincides with the diagonal in Figure 2) and 1 perfect inequality. If the Gini coefficient for If the Gini coefficient for some variable (e.g., income) in a country has increased over time, it means that the distribution of that
The Lorenz curve is a graphical device used to represent distributional inequality. The Gini coefficient is a numerical measure of inequality based on the Lorenz curve.
In section 4 we carry out the measurement of the income inequality using the Lorenz curve and the Gini-coefficient while in section 5 we carry out the empirical study of the relationship between income inequality and poverty. Section 6 summarizes the findings, draws conclusions and makes policy recommendations.
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