gini {GeoXp}R Documentation

Calculates a Gini Index

Description

The function `gini' calculates the Gini Index associated to the variable `var'.

Usage

gini(var)

Arguments

var a vector of numerical values of size n

Details

Let $x_k$, $k=1,..,K$ be the distinct values taken by $Var$. For each site, Gini.r returns two pairs of frequencies. The pair $(f,g)$ where f represents

f_k=frac{1}{n}sum_i 1(Var_i=x_k)

($n$ is the length of `var') and g represents

g_k=frac{x_k}{bar{x}}f_k

The pair $(F,G)$ represents the corresponding cumulative frequencies.
The Gini Index is calculated as :

I_G=frac{1}{2bar{x}}sum_{i=1}^Ksum_{j=1}^K|x_i-x_j|

Value

(f, F, g, G, gini) where f, F, g and G are vectors of size K and gini a numeric value.

Note

This function is used in ginimap.R but it is not an interactive function.

Author(s)

Thomas-Agnan C., Aragon Y., Ruiz-Gazen A., Laurent T., Robidou L.

References

Aragon Yves, Perrin Olivier, Ruiz-Gazen Anne, Thomas-Agnan Christine (2008), ``Statistique et Econométrie pour données géoréférencées : modèles et études de cas''

See Also

ginimap


[Package GeoXp version 1.3 Index]