Search results for "Lorenz curve"

Computing Difficulties for Deriving Poverty Indices from Some Functional Forms of Lorenz Curves

2014

We examine three families of classical one-parameter functional forms for estimating a Lorenz curve: the power form (Pareto, elementary form), the exponential form (Gupta, elementary form) and fractional form (Rohde). For the first time, we systematically study these functions not for their ability to be estimated but on the point of view of the possibility of deriving poverty indices, which implies first determining the headcount ratio (i.e., the percentage of poor). We show that computing difficulties have been largely underestimated. Two forms, the most simple ones, pose no problem: the elementary power and exponential forms. However, the Pareto functional form poses problem with a restr…

Median vs. Mean in Poverty Alleviation

2011

When evaluating poverty, the relative poverty line may be taken as a percentage of either normalized median or normalized mean income. It is proved that, for any family of non-intersecting Lorenz curves, when the poverty line is set relative to the normalized median income, reducing poverty become less costly in proportion to the total income when inequality is great and increasing; a counter-example proves that such a change may be associated with greater poverty. However, when the poverty line is set relative to the normalized mean income, the relative cost of poverty alleviation always increases with inequality and poverty, as expected. One concludes that the poverty line should be taken…

Nonparametric estimation of quantile versions of the Lorenz curve

2018

Estimators of quantile versions of the Lorenz curve are proposed. The pointwise consistency and asymptotic normality of the estimators is proved. The efficiency of the estimators is also studied in simulations

Developing and Comparing Indices to Evaluate Community Knowledge Building in an Educational Research Course

2022

This paper implements a novel approach to analyzing the degree of Collective Cognitive Responsibility (CCR) in a Knowledge Building community, based on socioeconomic and scientometric measures. After engaging in Knowledge Forum (KF) discussions for one semester, 36 students identified impactful ideas in their portfolios, which were then used to develop their impact scores. These scores were then transformed and plotted along the Lorenz Curve and the Gini coefficient to visualize the degree of equidistribution of recognition in the community and, by extension, the degree of collective responsibility shared by members of the community. Additionally, students were classified into member roles …

Nonparametric estimation of quantile versions of the Lorenz curve

2018

Inference for Lorenz curve orderings

1999

In this paper we consider the issue of performing statistical inference for Lorenz curve orderings. This involves testing for an ordered relationship in a multivariate context and making comparisons among more than two population distributions. Our approach is to frame the hypotheses of interest as sets of linear inequality constraints on the vector of Lorenz curve ordinates, and apply order-restricted statistical inference to derive test statistics and their sampling distributions. We go on to relate our results to others which have appeared in recent literature, and use Monte Carlo analysis to highlight their respective properties and comparative performances. Finally, we discuss in gener…

About some difficulties with the functional forms of Lorenz curves

2022

We study to what extent some functional form assumption on the Lorenz curve are amenable to calculating headcount poverty, or poverty threshold, the key concept to determine a poverty index. The difficulties in calculating it have been underestimated. We must choose some functional forms for the Lorenz concentration curve. We examine three families of one-parameter functional forms to estimate Lorenz curves: power (elementary and Pareto), exponential (elementary and Gupta) and fractional (Rohde). Computing these numerical functions may be difficult and impose some restrictions on their domain of definition, may impose to use some numerical approximation methods. The elementary power and exp…

Measuring Social Mobility

1993

Abstract The paper considers the ranking of mobility matrices in a simple Markov model of social mobility. The approach is the dynamic counterpart ot the "static" inequality ranking of income distributions by the Lorenz curve. The derived partial ordering is motivated by welfare considerations, is shown to be equivalent to same intuitive mobility concepts, and is used to screen some immobility indices. The equivalence of the ranking with the "permanent income" Lorenz ordering gives support to the claim that this approach is the natural extension of Kolm′s [The optimal production of social justice, in "Public Economics (J. Margolis and H. Guitton, Eds.), MacMillan, London, 1969], Atkinson′s …