ineq (version 0.2-13)

# theorLc: Theoretical Lorenz Curves

## Description

Theoretical Lorenz curves of income distributions

## 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].

## Value

`"theorLc"` or its value at `p` respectively.

## 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).

## 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.

## See Also

`Lc`, `plot.Lc`, `plot.theorLc`

## 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)
```