Lc {ineq}R Documentation

Lorenz Curve

Description

computes the (empirical) ordinary and generalized Lorenz curve of a vector x

Usage

Lc(x, n=rep(1,length(x)), plot=F) 

Arguments

x a vector containing non-negative elements
n a vector of frequencies, must be same length as x
plot logical flag. If TRUE the empirical Lorenz curve will be plotted

Details

Lc(x) computes the empirical ordinary Lorenz curve of x as well as the generalized Lorenz curve (= ordinary Lorenz curve * mean(x)). the result can be interpreted like this: p*100 percent have L(p)*100 percent of x.

if n is changed to anything but the default x is interpreted as a vector of class means and n as a vector of class frequencies: in this case Lc will compute the minimal Lorenz curve (= no inequality within each group). a maximal curve can be computed with Lc.mehran.

Value

a list with the following components:

p vector of percentages
L vector with values of the ordinary Lorenz curve
L.general vector with values of the generalized Lorenz curve

Author(s)

Achim Zeileis zeileis@ci.tuwien.ac.at

References

B C Arnold: Majorization and the Lorenz Order: A Brief Introduction, 1987, Springer,

F A Cowell: Measurement of Inequality, 2000, in A B Atkinson / F Bourguignon (Eds): Handbook of Income Distribution, Amsterdam,

F A Cowell: Measuring Inequality, 1995 Prentice Hall/Harvester Wheatshef.

See Also

Lc.plot, Lc.mehran, theor.Lc.plot

Examples

# income distribution of the USA in 1968 (in 10 classes)
# x vector of class means, n vector of class frequencies
x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261)
n <- c(482, 825, 722, 690, 661, 760, 745, 2140, 1911, 1024)

# compute minimal Lorenz curve (= no inequality in each group)
Lc.min <- Lc(x, n=n)
# compute maximal Lorenz curve (limits of Mehran)
Lc.max <- Lc.mehran(x,n)
# plot both Lorenz curves in one plot                        
Lc.plot(Lc.min)
Lc.plot(Lc.max, new=T, col=4)

# add the theoretic Lorenz curve of a Lognormal-distribution with (var=0.78)
theor.Lc.plot(type="lognorm", parameter=0.78)
# add the theoretic Lorenz curve of a Dagum-distribution
theor.Lc.plot(type="Dagum", parameter=c(3.4,2.6))