lorenzdominancerelation {TUGLab}R Documentation

Lorenz dominance relation

Description

Given two awards vectors, this function returns the Lorenz dominance relation between them.

Usage

lorenzdominancerelation(x, y)

Arguments

x

A vector.

y

A vector.

Details

In order to compare two vectors x,y\in \mathbb{R}^n through the Lorenz criterion, both of them must be rearranged in non-decreasing order; thus, let \bar{x} and \bar{y} be the vectors obtained by rearranging x and y, respectively, in non-decreasing order. It is said that x Lorenz-dominates y (or that y is Lorenz-dominated by x) if all the cumulative sums of \bar{x} are not less than those of \bar{y}. That is, x Lorenz-dominates y if \sum_{j=1}^{n}\bar{x}_j=\sum_{j=1}^{n}\bar{y}_j and, for each k=1,\dots,n-1,

\sum_{j=1}^{k}\bar{x}_j \geq \sum_{j=1}^{k}\bar{y}_j.

If x Lorenz-dominates y and y Lorenz-dominates x, then x and y are said to be Lorenz-equal.

If x does not Lorenz-dominate y and y does not Lorenz-dominate x, then x and y are not Lorenz-comparable.

Value

There are four possible outputs:

-1

if the introduced vectors are not Lorenz-comparable.

0

if the vectors are Lorenz-equal.

1

if the vectors are not Lorenz-equal and the first one Lorenz-dominates the second one.

2

if the vectors are not Lorenz-equal and the second one Lorenz-dominates the first one.

References

Lorenz, M. O. (1905). Methods of Measuring the Concentration of Wealth. Publications of the American Statistical Association, 9(70), 209-219.

Examples

lorenzdominancerelation(c(1,2,3), c(1,1,4))
lorenzdominancerelation(c(1,2,7,2), c(1,1,4,6))

[Package TUGLab version 0.0.1 Index]