atkinson.GB2 {acid} R Documentation

## 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.

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.

`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)
```

[Package acid version 1.1 Index]