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GeoXp (version 1.6.2)

gini: 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

Value

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

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

References

Thibault Laurent, Anne Ruiz-Gazen, Christine Thomas-Agnan (2012), GeoXp: An R Package for Exploratory Spatial Data Analysis. Journal of Statistical Software, 47(2), 1-23.

See Also

ginimap