atkinson.GB2 {acid}

Atkinson Index for a Generalised Beta Distribution of Second Kind

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)