# theorLc: Theoretical Lorenz Curves In ineq: Measuring Inequality, Concentration, and Poverty

## Description

Theoretical Lorenz curves of income distributions

## Usage

 ```1 2 3 4 5 6 7``` ```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

A function of class `"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`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```## 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) ```

### Example output

``` [1] 0.01309781 0.04457476 0.09148283 0.15291724 0.22887426 0.32020415
[7] 0.42897407 0.55962902 0.72335212 1.00000000
[1] 0.01309781 0.04457476 0.09148283 0.15291724 0.22887426 0.32020415
[7] 0.42897407 0.55962902 0.72335212 1.00000000
```

ineq documentation built on May 2, 2019, 7:29 a.m.