| 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. |
Author(s)
Alexander Sohn
References
Atkinson, A.B. (1970): On the Measurment of Inequality, in: Journal of Economic Theory, Vol. 2(3), pp. 244-263.
See Also
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)