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

Description Usage Arguments Details Value Author(s) References Examples

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

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

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

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.

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

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

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).