A Gini coefficient calculator in Python.
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:
For a very unequal sample, 999 zeros and a single one,
>>> from gini import * >>> a = np.zeros((1000)) >>> a = 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
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+1) #index per array element n = array.shape#number of array elements return ((np.sum((2 * index - n - 1) * array)) / (n * np.sum(array))) #Gini coefficient
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.