sgini.den: 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.

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.

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.

Examples

Run this code

## 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