# Lc: Lorenz Curve In ineq: Measuring Inequality, Concentration, and Poverty

## Description

Computes the (empirical) ordinary and generalized Lorenz curve of a vector x

## Usage

 `1` ```Lc(x, n = rep(1,length(x)), plot = FALSE) ```

## Arguments

 `x` a vector containing non-negative elements. `n` a vector of frequencies, must be same length as `x`. `plot` logical. If TRUE the empirical Lorenz curve will be plotted.

## Details

`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`.

## Value

A list of class `"Lc"` 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

## References

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.

`plot.Lc`, `Lc.mehran`, `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 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```## Load and attach income (and metadata) set from Ilocos, Philippines data(Ilocos) attach(Ilocos) ## extract and rescale income for the provinces "Pangasinan" und "La Union" income.p <- income[province=="Pangasinan"]/10000 income.u <- income[province=="La Union"]/10000 ## compute the Lorenz curves Lc.p <- Lc(income.p) Lc.u <- Lc(income.u) ## it can be seen the the inequality in La Union is higher than in ## Pangasinan because the respective Lorenz curve takes smaller values. plot(Lc.p) lines(Lc.u, col=2) ## the picture becomes even clearer with generalized Lorenz curves plot(Lc.p, general=TRUE) lines(Lc.u, general=TRUE, col=2) ## inequality measures emphasize these results, e.g. Atkinson's measure ineq(income.p, type="Atkinson") ineq(income.u, type="Atkinson") ## or Theil's entropy measure ineq(income.p, type="Theil", parameter=0) ineq(income.u, type="Theil", parameter=0) # 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 plot(Lc.min) lines(Lc.max, col=4) # add the theoretic Lorenz curve of a Lognormal-distribution with variance 0.78 lines(Lc.lognorm, parameter=0.78) # add the theoretic Lorenz curve of a Dagum-distribution lines(Lc.dagum, parameter=c(3.4,2.6)) ```

### Example output   ``` 0.1291856
 0.1672924
 0.2837236
 0.3622122
```

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