atkinson.GB2: Atkinson Index for a Generalised Beta Distribution of Second...

In acid: Analysing Conditional Income Distributions

Description

This function computes the Atkinson index (I(epsilon)) for Generalised Beta Distribution of Second Kind. The function is exact for the values epsilon=0, epsilon=1 and epsilon=2. For other values of epsilon, the function provides a numerical approximation.

Usage

atkinson.GB2(b, a, p, q, epsilon = NULL, ylim = c(0, 1e+06), zeroapprox = 0.01)

Arguments

b	the parameter b of the Dagum distribution as defined by Kleiber and Kotz (2003).
a	the parameter a of the Dagum distribution as defined by Kleiber and Kotz (2003).
p	the parameter p of the Dagum distribution as defined by Kleiber and Kotz (2003).
q	the parameter q of the Dagum distribution as defined by Kleiber and Kotz (2003).
epsilon	inequality aversion parameter as denoted by Atkinson (1970). The default is epsilon=1.
ylim	limits of the interval of y considered needed for the approximation of the entropy measure. The default is [0,1e+06].
zeroapprox	an approximation for zero needed for the approximation of the entropy measure. The default is 0.01.

Value

returns the selected Atkinson inequality index.

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.

Cowell, F.A. (2000): Measurement of Inequality, in: Atkinson and Bourguignon (eds.), Handbook of Income Distribution, pp. 87-166, Elsevier, Amsterdam.

See Also

ineq

Examples

a.test<- 4
b.test<- 20000
p.test<- 0.7
q.test<- 1
epsilon.test<-1
GB2sample<-rGB2(1000,b.test,a.test,p.test,q.test)
atkinson.GB2(b.test,a.test,p.test,q.test,epsilon=epsilon.test,ylim=c(0,1e+07))
atkinson(GB2sample, epsilon.test)

Example output

Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data

Attaching package: 'gamlss.data'

The following object is masked from 'package:datasets':

    sleep

Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: nlme
Loading required package: parallel
 **********   GAMLSS Version 5.1-3  ********** 
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.

Loading required package: Hmisc
Loading required package: lattice
Loading required package: survival
Loading required package: Formula
Loading required package: ggplot2

Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

    format.pval, units

[1] 0.1254838
[1] 0.148997

acid documentation built on May 1, 2019, 10:14 p.m.