Construction of concentration measures for General Lorenz curves using Riemann-Stieltjes integrals

Riemann-Stieltjes integrals

This short note gives an introduction to the Riemann-Stieltjes integral on R and Rn. Some natural and important applications in probability theory are discussed. The reason for discussing the Riemann-Stieltjes integral instead of the more general Lebesgue and LebesgueStieltjes integrals are that most applications in elementary probability theory are satisfactorily covered by the Riemann-Stieltj...

Cauchy-stieltjes and Riemann-stielt Jes Integrals

Two Point Gauss–legendre Quadrature Rule for Riemann–stieltjes Integrals

In order to approximate the Riemann–Stieltjes integral ∫ b a f (t) dg (t) by 2–point Gaussian quadrature rule, we introduce the quadrature rule ∫ 1 −1 f (t) dg (t) ≈ Af ( − √ 3 3 ) + Bf (√ 3 3 ) , for suitable choice of A and B. Error estimates for this approximation under various assumptions for the functions involved are provided as well.

Decomposing Lorenz and Concentration Curves*

We decompose the Lorenz curve and its associated concentration curve by population subgroups. To illustrate these decompositions, we examine changes in earnings inequality among West Germans, East Germans, and foreign guest workers during the recent German unification. We show that East German earnings have become less concentrated in the lower deciles of the overall German earnings distributio...

Engel Analysis with Lorenz and Concentration Curves

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...