r.is: Income share of the top p %

In affluenceIndex: Affluence (Richness) Indices

Income share of the top p %

Description

Computes the income share of the top p %.

Usage

r.is(x, weight, p)

Arguments

x	the vector of income
weight	vector of weights
p	the order of quantile. Must be in [0,1] as probability

Details

The most popular measure of richness which takes a form (with weights w_1,w_2,...,w_n):

R^{IS}(\boldsymbol{x},\boldsymbol{w},p) = \frac{\sum_{i=1}^n{x_iw_i}\boldsymbol{1}_{x_i>q_{w(1-p)}}}{\sum_{i=1}^n{x_iw_i}},

where q_{w(1-p)} is the (1-p) quantile of the population and \boldsymbol{1}_{(\cdot)} denotes the indicator function, which is equal to 1 when its argument is true and 0 otherwise. There is always p % of rich individualsa in the population.

Value

r.2	the value of index

Author(s)

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

References

Brzezinski M. (2010) Income affluence in Poland. Social Indicators Research, 99, pp. 285-299.

Examples

data(affluence)
r.is(affluence$income, weight = NULL, 0.9)

affluenceIndex documentation built on Sept. 22, 2024, 1:06 a.m.