gini.coefficient: Diversity as disparity: Gini's Coefficient
In DLEIVA/diversity: Diversity indexes for organizational research

Description Usage Arguments Details Value Author(s) References Examples

This function computes Gini's coefficient for quantifying diversity as disparity.

1	gini.coefficient(X, min, max)

`X`	A numeric vector with group data.
`min`	The minimum value for the random variable.
`max`	The maximum value for the random variable.

gini.coefficient computes Gini's Coefficient for a group according the following formula:

	G = {Δ \over {2\bar x}} = {{∑\limits_{i = 1}^n {∑\limits_{j = i + 1}^n {≤ft\| {x_i - x_j } \right\|} } } \over {n^2 \bar x}} .

It also provides maximum values for Gini's Coefficient.

The function returns a list of class gini with following components:

`call`	Function call.
`data`	Original data vector.
`min`	Minimum value for the random variable.
`max`	Maximum value for the random variable.
`gini`	Gini's Coefficient.
`gini.max`	Maximum value of Gini's Coefficient.

Antonio Solanas, Rejina M. Selvam, Jose Navarro and David Leiva.

Solanas, A., Selvam, R. M., Navarro, J., & Leiva, D. (2010). On the measurement of diversity in organizations. Unpublished manuscript.

ex.1 <- c(30,rep(60,3))
gini.coefficient(ex.1,30,60)  

ex.2 <- c(60,rep(30,3))
gini.coefficient(ex.2,30,60)

ex.3 <- c(rep(30,2),rep(60,2))
gini.coefficient(ex.3,30,60)

# Gini coefficient does not behave as disparity index when minimum value is greater than 0. #
# Then, a translation of scale is suitable for solving this problem. #
ex.4 <- ex.1 - 30
gini.coefficient(ex.4,0,30) 

ex.5 <- ex.2 - 30
gini.coefficient(ex.5,0,30) 

ex.6 <- ex.3 - 30
gini.coefficient(ex.6,0,30)