gini

A Gini coefficient calculator in Python.

Overview

This is a function that calculates the Gini coefficient of a numpy array. Gini coefficients are often used to quantify income inequality, read more here.

The function in gini.py is based on the third equation from here, which defines the Gini coefficient as:

Examples

For a very unequal sample, 999 zeros and a single one,

>>> from gini import *
>>> a = np.zeros((1000))
>>> a[0] = 1.0

the Gini coefficient is very close to 1.0:

>>> gini(a)
0.99890010998900103

For uniformly distributed random numbers, it will be low, around 0.33:

>>> s = np.random.uniform(-1,0,1000)
>>> gini(s)
0.3295183767105907

For a homogeneous sample, the Gini coefficient is 0.0:

>>> b = np.ones((1000))
>>> gini(b)
0.0

Input Assumptions

The Gini calculation by definition requires non-zero positive (ascending-order) sorted values within a 1d vector. This is dealt with within gini(). So these four assumptions can be violated, as they are controlled for:

def gini(array):
    """Calculate the Gini coefficient of a numpy array."""
    # based on bottom eq: http://www.statsdirect.com/help/content/image/stat0206_wmf.gif
    # from: http://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm
    array = array.flatten() #all values are treated equally, arrays must be 1d
    if np.amin(array) < 0:
        array -= np.amin(array) #values cannot be negative
    array += 0.0000001 #values cannot be 0
    array = np.sort(array) #values must be sorted
    index = np.arange(1,array.shape[0]+1) #index per array element
    n = array.shape[0]#number of array elements
    return ((np.sum((2 * index - n  - 1) * array)) / (n * np.sum(array))) #Gini coefficient

Notes

• It is significantly faster than (the current implementation of) PySAL's Gini coefficient function (see pysal.inequality.gini) and outputs are indistinguishable before approximately 6 decimal places. In other words, the two functions are arithmetically identical.

• It is slightly faster than the Gini coefficient function by David on Ellipsix.

Many other Gini coefficient functions found online do not produce equivalent results, hence why I wrote this.