gini.w: Gini coefficient

In affluenceIndex: Affluence (Richness) Indices

Gini coefficient

Description

Computes the Gini coefficient.

Usage

gini.w(x, weight)

Arguments

x	income vector of population
weight	vector of weights

Details

The Gini coefficient is the most popular measure of income inequality. The formula taking into account the weights of income w_1,w_2,...,w_n is given by:

G_w = \frac{\sum_{i=1}^nw_i\sum_{j=1}^n w_j|x_i-x_j|}{2(\sum_{i=1}^nw_i)^2\mu_w},

where x_i,x_j are incomes of individuals i and j, respectively, n is the number of individuals, \mu_w is the mean income. The Gini coefficient ranges between 1 (perfect equality) and 1 (perfect inequality).

Value

GG	the value of coefficient

Author(s)

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

References

1. Creedy J. (2015). A note on computing the Gini inequality measure with weighted data. Workin Paper No. 3, Victoria University of Wellington.
2. Lerman R.I., Yitzhaki S. (1989) Improving the accuracy of estimates of Gini coefficients. Journal of Econometrics, 42(1), pp. 43-47.

Examples

data(affluence)
gini.w(affluence$income, affluence$hs_size)

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