Lc {ineq} | R Documentation |
computes the (empirical) ordinary and generalized Lorenz curve of a vector x
Lc(x, n=rep(1,length(x)), plot=F)
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 |
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
.
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 |
Achim Zeileis zeileis@ci.tuwien.ac.at
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.
Lc.plot
, Lc.mehran
,
theor.Lc.plot
# 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))