Mehran Bounds For Lorenz Curves
Computes the Mehran bounds for a Lorenz curve of grouped data
Lc.mehran(x,n)
x |
vector of class means. |
n |
vector of class frequencies. |
An object of class "Lc", but containing only
p and L.
F Mehran: Bounds on the Gini Index Based on Observed Points of the Lorenz Curve, 1975, JASA 70, 64-66.
# 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))
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