atkinson.den {acid} R Documentation

## Atkinson Index for an Income Distribution

### Description

This function approximates the Atkinson index for a distribution specified by a vector of densities and a corresponding income vector. A point mass at zero is allowed.

### Usage

atkinson.den(incs, dens, epsilon = 1, pm0 = NA,
lower = NULL, upper = NULL, zero.approx = NULL)


### Arguments

 incs a vector with income values. dens a vector with the corresponding densities. epsilon inequality aversion parameter as denoted by Atkinson (1970). The default is epsilon=1. 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. zero.approx a scalar which replaces zero-incomes, such that the Atkinson index involving a logarithm return finite values.

### Value

 AIM the approximation of the selected Atkinson inequality measure. epsilon the inequality aversion parameter used. mean the approximated expected value of the distribution. 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. zero.approx the zero approximation used.

Alexander Sohn

### References

Atkinson, A.B. (1970): On the Measurment of Inequality, in: Journal of Economic Theory, Vol. 2(3), pp. 244-263.

atkinson , atkinson.md

### Examples

## without point mass at zero
incs<-seq(0,500,by=0.01)
dens<-dLOGNO(incs,2,1)
plot(incs,dens,type="l",xlim=c(0,100))
atkinson.den(incs=incs,dens=dens,epsilon=1)$AIM atkinson(rLOGNO(50000,2,1),epsilon=1) atkinson.den(incs=incs,dens=dens,epsilon=0.5)$AIM
atkinson(rLOGNO(50000,2,1),epsilon=0.5)

## with point mass at zero
incs<-c(seq(0,100,by=0.1),seq(100.1,1000,by=1),seq(1001,10000,by=10))
dens<-dLOGNO(incs,2,1)/2
dens[1]<-0.5
plot(incs,dens,type="l",ylim=c(0,max(dens[-1])),xlim=c(0,100))
#without zero approx zeros
atkinson.den(incs=incs,dens=dens,epsilon=1,pm0=0.5)$AIM atkinson(c(rep(0,25000),rLOGNO(25000,2,1)),epsilon=1) atkinson.den(incs=incs,dens=dens,epsilon=0.5,pm0=0.5)$AIM
atkinson(c(rep(0,25000),rLOGNO(25000,2,1)),epsilon=0.5)
#with zero approximation
atkinson.den(incs=incs,dens=dens,epsilon=0.5,pm0=0.5,zero.approx=1)$AIM atkinson(c(rep(1,25000),rLOGNO(25000,2,1)),epsilon=0.5) atkinson.den(incs=incs,dens=dens,epsilon=1,pm0=0.5,zero.approx=0.01)$AIM
atkinson(c(rep(0.01,250000),rLOGNO(250000,2,1)),epsilon=1)



[Package acid version 1.1 Index]