Lc.mehran {ineq} | R Documentation |
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 |
a list like computed by Lc
, but containing only
p
and L
.
Achim Zeileis zeileis@ci.tuwien.ac.at
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 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))