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.

### See Also

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]