# theorLc

0th

Percentile

##### Theoretical Lorenz Curves

Theoretical Lorenz curves of income distributions

Keywords
misc
##### Usage
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)
##### Arguments
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].
##### Details

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).

##### Value

"theorLc" or its value at p respectively.

##### References

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.

Lc, plot.Lc, plot.theorLc

• theorLc
• Lc.dagum
• Lc.singh
• Lc.pareto
• Lc.lognorm
• Lc.exp
##### Examples
## 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)

Documentation reproduced from package ineq, version 0.2-13, License: GPL-2 | GPL-3

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