r.is: Income share of the top p %
| r.is | R Documentation |
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)
