r.cha {affluenceIndex}R Documentation

Concave measure of affluence

Description

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

Usage

r.cha(x, k, beta)

Arguments

x

the income vector

k

multiple of the median income

beta

parameter of the index: beta > 0

Details

Peichl et. al (2008) defined an affluence index

R_{β}^{Cha}(\mathbf{x},ρ)=\frac{1}{n} ∑_{i=1}^{n} ≤ft( 1- ≤ft( \frac{ρ}{x_i} \right)^{β} \right)_{+}, β >0,

where x_i is an income of individual i, n is the number of individuals, ρ is the richness line. Index satisfies transfer axiom T1 (concave): a richness index should increase when a rank-preserving progressive transfer between two rich people takes place.

Value

r

elements of the sum in the index formula

r.cha

the value of index

Author(s)

Alicja Wolny-Dominiak

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

data(affluence)
r <-r.cha(affluence$income, 2, 2)
print(r)

[Package affluenceIndex version 1.0 Index]