sgini.den {acid} R Documentation

## Single-parameter Gini Coefficient for an Income Distribution

### Description

This function approximates the Single-parameter Gini coefficient for a distribution specified by a vector of densities and a corresponding income vector. A point mass at zero is allowed.

### Usage

```sgini.den(incs, dens, nu = 2, pm0 = NA, lower = NULL, upper = NULL)
```

### Arguments

 `incs` a vector with sorted income values. `dens` a vector with the corresponding densities. `nu` a scalar entailing the parameter that tunes the degree of the policy maker's aversion to inequality. See Yaari, 1988 for details. `pm0` the point mass for zero incomes. If not specified no point mass is assumed. `lower` the lower bound of the income range considered. `upper` the upper bound of the income range considered.

### Value

 `Gini` the approximation of the Gini coefficient. `pm0` the point mass for zero incomes used. `lower` the lower bound of the income range considered used. `upper` the upper bound of the income range considered used.

Alexander Sohn

### References

van Kerm, P. (2009): sgini - Generalized Gini and Concentration coefficients (with factor decomposition) in Stata', CEPS/INSTEAD, Differdange, Luxembourg.

Yaari, M.E. (1988): A Controversal Proposal Concerning Inequality Measurement, Journal of Economic Theory, Vol. 44, pp. 381-397.

`gini`

### Examples

```## without point mass
set.seed(123)
x <- rnorm(1000,10,1)
incs <- seq(1,20,length.out=1000)
dens <- dnorm(incs,10,1)
lower=NULL;upper=NULL;pm0<-NA
gini(x)\$Gini
sgini(x,nu=2)\$Gini
sgini.den(incs,dens)\$Gini

## with point mass
set.seed(123)
x <- c(rep(0,1000),rnorm(1000,10,1))
incs <- c(0,seq(1,20,length.out=1000))
dens <- c(0.5,dnorm(incs[-1],10,1)/2)
gini(x)\$Gini
sgini(x,nu=2)\$Gini
sgini.den(incs,dens,pm = 0.5)\$Gini
```

[Package acid version 1.1 Index]