A simple method for estimating the Lorenz curve

AbstractGiven many popular functional forms for the Lorenz curve do not have a closed-form expression for the Gini index and no study has utilized the observed Gini index to estimate parameter(s) associated with the corresponding parametric functional form, a simple method for estimating the Lorenz curve is introduced. It utilizes three indicators, namely, the Gini index and the income shares of the bottom and the top in order to calculate the values of parameters associated with the specified functional form which has a closed-form expression for the Gini index. No error minimization technique is required in order to estimate the Lorenz curve. The data on the Gini index and the income shares of four countries that have a different level of income inequality, economic, sociological, and regional backgrounds from the United Nations University-World Income Inequality Database are used to illustrate how the simple method works. The overall results indicate that the estimated Lorenz curves fit the actual observations practically well. This simple method could be useful in the situation where the availability of data on income distribution is low. However, if more data on income distribution are available, this study shows that the specified functional form could be used to directly estimate the Lorenz curve. Moreover, the estimated values of the Gini index calculated based on the specified functional form are virtually identical to their actual observations.

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Functional Form for Estimating the Lorenz Curve

American Finance & Banking Review ◽

10.46281/amfbr.v4i1.286 ◽

2019 ◽

Vol 4 (1) ◽

pp. 17-21

Author(s):

Bijan Bidabad ◽

Behrouz Bidabad

Keyword(s):

Income Distribution ◽

Lorenz Curve ◽

Functional Form ◽

Cumulative Data ◽

The Lorenz Curve

A flexible Lorenz curve which offers different curvatures allowed by the theory of income distribution is introduced. The intrinsically autoregressive nature of the errors in cumulative data of the Lorenz curve is also under consideration.

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Ranking and Selection Procedure for Gini Index

Bulletin of Mathematical Sciences and Applications ◽

10.18052/www.scipress.com/bmsa.3.1 ◽

2013 ◽

Vol 3 ◽

pp. 1-14

Author(s):

Saeed Baghban Kohne Rooz ◽

Mohammad Moradi ◽

Hossein Jabbari Khamnei

Keyword(s):

Income Inequality ◽

Lorenz Curve ◽

Gini Index ◽

Selection Procedure ◽

Ranking And Selection ◽

Income Distributions ◽

Different Populations ◽

The Lorenz Curve

Gini index, which is derived from the Lorenz curve of income inequality and shows income inequality in different populations, can be applied to ranking and selectionpopulations. Many procedures are available for ordering and ranking income distributions where the ordering is not linear. However, the researchers often are not interested in ordering the populations but selecting the best (or worst) of available populations indicating a lower (or higher) level of disparities in incomes within the population. Madhuri S. Mulekar (2005) discussed the estimation of overlap ofincome distributions and selection in terms of Gini Measure of income inequality. In this paper, we simulate populations ranking and selection based on Gini index of income inequality for case that the variances are equal but known in income distributions and for case that the variances are unequal but known in income distributions.

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Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽

10.1109/access.2021.3096419 ◽

2021 ◽

pp. 1-1

Author(s):

Yassine Zouaoui ◽

Larbi Talbi ◽

Khelifa Hettak ◽

Naresh K. Darimireddy

Keyword(s):

Closed Form ◽

Closed Form Expression ◽

Form Expression

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Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

ACM SIGMETRICS Performance Evaluation Review ◽

10.1145/3453953.3453974 ◽

2021 ◽

Vol 48 (3) ◽

pp. 91-96

Author(s):

Shigeo Shioda

Keyword(s):

Distribution Function ◽

Probability Density Function ◽

Closed Form ◽

Probability Density ◽

Infinite Number ◽

Stable Distribution ◽

Random Variable ◽

Cauchy Distribution ◽

Closed Form Expression ◽

Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

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Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

Journal of High Energy Physics ◽

10.1007/jhep06(2021)063 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Vivek Kumar Singh ◽

Rama Mishra ◽

P. Ramadevi

Keyword(s):

Closed Form ◽

Topological Strings ◽

Chebyshev Polynomials ◽

Fibonacci Numbers ◽

Infinite Family ◽

Closed Form Expression ◽

Two Dimensional ◽

Laurent Polynomials ◽

Form Expression ◽

Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

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