ineq (version 0.2-13)

Lc.mehran: Mehran Bounds For Lorenz Curves

Description

Computes the Mehran bounds for a Lorenz curve of grouped data

Usage

Lc.mehran(x,n)

Arguments

x

vector of class means.

n

vector of class frequencies.

Value

"Lc", but containing only p and L.

References

F Mehran: Bounds on the Gini Index Based on Observed Points of the Lorenz Curve, 1975, JASA 70, 64-66.

See Also

Lc, plot.Lc, plot.theorLc

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
plot(Lc.min)
lines(Lc.max, col=4)

# add the theoretic Lorenz curve of a Lognormal-distribution with variance 0.78
lines(Lc.lognorm, parameter=0.78)
# add the theoretic Lorenz curve of a Dagum-distribution
lines(Lc.dagum, parameter=c(3.4,2.6))