Theoretical Lorenz Curves
Theoretical Lorenz curves of income distributions
theorLc(type=c("Singh-Maddala","Dagum","lognorm","Pareto","exponential"), parameter=0)
Lc.dagum(p, parameter=c(2,2))
Lc.singh(p, parameter=c(2,2))
Lc.pareto(p, parameter=2)
Lc.lognorm(p, parameter=1)
Lc.exp(p)type |
character string giving the income distribution. Must be one of the strings in the default argument (the first character is sufficient). Defaults to "Singh-Maddala". |
parameter |
vector containing parameter(s) of the distributions. |
p |
vector with elements from [0,1]. |
Lc.dagum, Lc.singh, Lc.pareto, Lc.lognorm,
Lc.exp are theoretical Lorenz curves of income distributions.
They are functions of class "theorLc" with plot- and a lines-
method, so that they can be added into an existing Lorenz curve plot.
theorLc returns a function of class "theorLc", that is a
one of the above theoretical Lorenz curves with fixed parameters.
Lc.dagum is the Lorenz curve of the Dagum distribution (2
parameters), Lc.singh the one of the Singh-Maddala
distribution (2 parameters), Lc.pareto the one of the Pareto
distribution (1 parameter), Lc.lognorm the one of the Lognormal
distribution (1 parameter) and Lc.exp the Lorenz curve of the
exponential distribution (no parameter).
A function of class "theorLc" or its value at p
respectively.
C Dagum: Income Distribution Models, 1983, in: Johnson / Kotz (Eds): Encyclopedia of Statistical Sciences Vol.4, 27-34.
J B McDonald: Some generalized functions for the size distribution of income, 1984, Econometrica 52, 647-664.
## Load and attach income (and metadata) set from Ilocos, Philippines data(Ilocos) attach(Ilocos) ## extract income for the province "Pangasinan" income.p <- income[province=="Pangasinan"] ## plot empirical Lorenz curve and add theoretical Lorenz curve of ## a lognormal distribution with an estimate of the standard ## deviation parameter Lc.p <- Lc(income.p) plot(Lc.p) lines(Lc.lognorm, parameter=sd(log(income.p)), col=4) # vector of percentages p <- (1:10)*0.1 # compute values of theoretic Lorenz curve of a Dagum-distribution Lc.dagum(p, parameter=c(3.4,2.6)) # or mydagum <- theorLc(type="Dagum", parameter=c(3.4,2.6)) mydagum(p)
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