𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Egghe's construction of Lorenz curves resolved

✍ Scribed by Quentin L. Burrell

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
224 KB
Volume
58
Category
Article
ISSN
1532-2882

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In a recent article (Burrell, 2006), the author pointed out that the version of Lorenz concentration theory presented by Egghe (2005a, 2005b) does not conform to the classical statistical/econometric approach. Rousseau (2007) asserts confusion on our part and a failure to grasp Egghe's construction, even though we simply reported what Egghe stated. Here the author shows that Egghe's construction rather than β€œincluding the standard case,” as claimed by Rousseau, actually leads to the Leimkuhler curve of the dual function, in the sense of Egghe. (Note that here we distinguish between the Lorenz curve, a convex form arising from ranking from smallest to largest, and the Leimkuhler curve, a concave form arising from ranking from largest to smallest. The two presentations are equivalent. See Burrell, 1991, 2005; Rousseau, 2007.)

πŸ“œ SIMILAR VOLUMES

On Egghe's construction of Lorenz curves
On Egghe's construction of Lorenz curves
✍ Ronald Rousseau πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 195 KB

## Abstract Contrary to Burrell's statements, Egghe's theory of continuous concentration does include the construction of a standard Lorenz curve.

Construction of Linear Systems on Hypere
Construction of Linear Systems on Hyperelliptic Curves
✍ T.G. Berry πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 448 KB

An algorithm for constructing a basis of a linear system L(D) on a hyperelliptic curve is described. Algorithms by Cantor and Chebychev for computing in the Jacobian of a hyperelliptic curve are derived as special cases. The final section describes Chebychev's application of his algorithm to element

On the Construction of Complete Sets of
On the Construction of Complete Sets of Geometric Invariants for Algebraic Curves
✍ Mustafa Unel; William A. Wolovich πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 153 KB

We provide a solution to the important problem of constructing complete independent sets of Euclidean and affine invariants for algebraic curves. We first simplify algebraic curves through polynomial decompositions and then use some classical geometric results to construct functionally independent s