# r.fgt: Convex measure of affluence In affluenceIndex: Affluence (Richness) Indices

## Description

Computes the measure of affluence analogous to the convex version of Foster, Greer and Thorbecke (1984) family of poverty indices.

## Usage

 1 r.fgt(x, weight, k, alpha) 

## Arguments

 x the income vector weight vector of weights k multiple of the median income alpha parameter of the index: alpha > 1

## Details

Peichl et. al (2008) defined an affluence index. Weighted index (with weights w_1,w_2,...,w_n) is given by:

R_{α}^{FGT,T2}(\mathbf{x},\mathbf{w},ρ_w)=\frac{∑_{i=1}^{n} ≤ft( \frac{x_i - ρ_w}{ρ_w}\right)^{α}\mathbf{1}_{x_i>ρ_w}w_i}{∑_{i=1}^{n}w_i},α>1,

where x_i is an income of individual i, n is the number of individuals, ρ_w is the richness line, \boldsymbol{1}_{(\cdot)} denotes the indicator function, which is equal to 1 when its argument is true and 0 otherwise. Index satisfies transfer axiom T2 (convex): a richness index should decrease when a rank-preserving progressive transfer between two rich individuals takes place.

## Value

 r values of the sum in the index formula r.fgt the value of index

## Author(s)

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

## References

1. Foster J.E., Greer J., Thorbecke E. (1984) A class of decomposable poverty measures. Econometrica, 52, pp. 761-766.
2. Peichl A., Schaefer T., Scheicher C. (2008) Measuring richness and poverty - A micro data application to Europe and Germany. IZA Discussion Paper No. 3790, Institute for the Study of Labor (IZA).

## Examples

 1 2 data(affluence) r.fgt(affluence\$income, weight = NULL, 2, 1) 

affluenceIndex documentation built on Jan. 5, 2022, 5:07 p.m.