# r.cha: Concave measure of affluence In affluenceIndex: Affluence (Richness) Indices

## Description

Computes the measure of affluence analogous to the poverty index of Chakravarty (1983).

## Usage

 1 r.cha(x, weight, k, beta) 

## Arguments

 x the income vector weight vector of weights k multiple of the median income beta parameter of the index: beta > 0

## Details

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

R^{CHA}_{β}(\boldsymbol{x},\boldsymbol{w},ρ_w) = \frac{∑_{i=1}^n(1-(\frac{ρ_w}{x_i})^β)\boldsymbol{1}_{x_i > ρ_w}w_i}{∑_{i=1}^n{w_i}}, β > 0,

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 T1 (concave): a richness index should increase when a rank-preserving progressive transfer between two rich individuals takes place.

## Value

 r elements of the sum in the index formula r.cha the value of index

## Author(s)

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

## References

1. Chakravarty S.R. (1983) A new index of poverty. Mathematical Social Sciences, 6, pp. 307-313.
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.cha(affluence\$income, weight = NULL, 2, 2) 

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