A General Definition of the Lorenz Curve

Gastwirth, Joseph L.

doi:10.2307/1909675

Cited by 528 publications

(244 citation statements)

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“…(see Gastwirth (1971)). It is convenient to introduce the decumulative distribution function (ddf) -also known as the survival function -of x ∈ S (D) defined by DF (s; x) : = 1−F (s; x), for all s ∈ (−∞, +∞).…”

Section: The Frameworkmentioning

confidence: 99%

Elitism and stochastic dominance

Moyes

Bazen

2011

Soc Choice Welf

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RésuméLa dominance stochastique est traditionellement associée à la mesure du risque et de l'inégalité et repose sur la concavité de la fonction d'utilité. Nous prétendons que l'approche en terme de dominance stochastique a des implications qui vont au-delà de la mesure du risque et de l'inégalité pour peu que l'on procède à certains ajustements. Nous appliquons ici la dominance stochastique à la mesure de l'élitisme, notion qui peut d'une certaine manière être considérée comme le contraire de l'égalitarisme. Alors que les critères de dominance stochastique habituels accordent plus de valeur aux distributions qui sont à la fois moins inégales et plus efficientes, nos critères garantissent qu'une distribution sera d'autant mieux classée qu'une autre qu'elle est à la fois plus efficiente et plus inégale. Afin d'illustrer notre approche, nous proposons deux exemples : (i) la comparaison d'une vingtaine de départements d'économie en Europe du point de vue de la performance scientifique, et (ii) la comparaison de différents pays sur la base de la notion d'affluence par opposition à celle de pauvreté.Mots Clé : Fonction de Distribution Décumulative, Stochastic Dominance, Transfers Régressifs, Élitisme, Performance Scientifique, Affluence. Elitism and Stochastic DominanceAbstract Stochastic dominance has been typically used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adaptations be made. We apply in the paper the stochastic dominance approach to the measurement of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more efficient distributions, our criteria ensure that, the more unequal and the more efficient the distribution, the higher it is ranked. Two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments, and (ii) comparisons of affluence as opposed to poverty between countries.Journal of Economic Literature Classification Number: D31, D63.

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Section: The Frameworkmentioning

confidence: 99%

Elitism and stochastic dominance

Moyes

Bazen

2011

Soc Choice Welf

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“…Also these have been extensively used in the study of inequality of distributions. Let X be a non-negative random variable with distribution function F. The Lorenz curve corresponding to the random variable X, denoted by L(p), is defined (Gastwirth, 1971) We assume that the mean  is finite and positive. If the distribution which is being studied is the income of a certain population, then L(p) denotes the fraction of the total income received by the 100p%of the population which has the lowest income.…”

Section: Introductionmentioning

confidence: 99%

Semi-Parametric Estimation of Lorenz Curve and Gini-index in an Exponential Distribution

Pillai¹,

Rajesh

Abdul-Sathar

2014

Sri Lankan J App Stats

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“…It is usually denoted by L(p), and it can be defined in several equivalent ways. One of them is the following one (see Pietra [10], and Gastwirth [5]):…”

Section: Introductionmentioning

confidence: 99%