# Source code for pysal.inequality.gini

```"""
Gini based Inequality Metrics
"""

__author__ = "Sergio J. Rey <srey@asu.edu> "

import numpy as np
from scipy.stats import norm as NORM

__all__ = ['Gini', 'Gini_Spatial']

def _gini(x):
"""
Memory efficient calculation of Gini coefficient in relative mean difference form

Parameters
----------

x : array-like

Attributes
----------

g : float
Gini coefficient

Notes
-----
Based on http://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm

"""
n = len(x)
try:
x_sum = x.sum()
except AttributeError:
x = np.asarray(x)
x_sum = x.sum()
n_x_sum = n * x_sum
r_x = (2. * np.arange(1, len(x)+1) * x[np.argsort(x)]).sum()
return (r_x - n_x_sum - x_sum) / n_x_sum

[docs]class Gini:
"""
Classic Gini coefficient in absolute deviation form

Parameters
----------

y : array (n,1)
attribute

Attributes
----------

g : float
Gini coefficient

"""

def __init__(self, x):

self.g = _gini(x)

[docs]class Gini_Spatial:
"""
Spatial Gini coefficient

Provides for computationally based inference regarding the contribution of
spatial neighbor pairs to overall inequality across a set of regions. [Rey2013]_

Parameters
----------

y : array (n,1)
attribute

w : binary spatial weights object

permutations : int (default = 99)
number of permutations for inference

Attributes
----------

g : float
Gini coefficient

wg : float
Neighbor inequality component (geographic inequality)

wcg : float
Non-neighbor inequality component (geographic complement inequality)

wcg_share : float
Share of inequality in non-neighbor component

If Permuations > 0

p_sim : float
pseudo p-value for spatial gini

e_wcg : float
expected value of non-neighbor inequality component (level) from permutations

s_wcg : float
standard deviation non-neighbor inequality component (level) from permutations

z_wcg : float
z-value non-neighbor inequality component (level) from permutations

p_z_sim : float
pseudo  p-value based on standard normal approximation of permutation based values

Examples
--------
>>> import pysal
>>> import numpy as np

Use data from the 32 Mexican States, Decade frequency 1940-2010

>>> f=pysal.open(pysal.examples.get_path("mexico.csv"))
>>> vnames=["pcgdp%d"%dec for dec in range(1940,2010,10)]
>>> y=np.transpose(np.array([f.by_col[v] for v in vnames]))

Define regime neighbors

>>> regimes=np.array(f.by_col('hanson98'))
>>> w = pysal.block_weights(regimes)
>>> np.random.seed(12345)
>>> gs = pysal.inequality.gini.Gini_Spatial(y[:,0],w)
>>> gs.p_sim
0.040000000000000001
>>> gs.wcg
4353856.0
>>> gs.e_wcg
4170356.7474747472

Thus, the amount of inequality between pairs of states that are not in the
same regime (neighbors) is significantly higher than what is expected
under the null of random spatial inequality.

"""
def __init__(self, x, w, permutations=99):

x = np.asarray(x)
g = _gini(x)
self.g = g
n = len(x)
den = x.mean() * 2 * n**2
d = g * den
wg = self._calc(x, w)
wcg = d - wg
self.g = g
self.wcg = wcg
self.wg = wg
self.dtotal = d
self.den = den
self.wcg_share = wcg / den

if permutations:
ids = np.arange(n)
wcgp = np.zeros((permutations, ))
for perm in range(permutations):
np.random.shuffle(ids)
wcgp[perm] = d - self._calc(x[ids], w)
above = wcgp >= self.wcg
larger = above.sum()
if (permutations - larger) < larger:
larger = permutations - larger
self.wcgp = wcgp
self.p_sim = (larger + 1.) / (permutations + 1.)
self.e_wcg = wcgp.mean()
self.s_wcg = wcgp.std()
self.z_wcg = (self.wcg - self.e_wcg) / self.s_wcg
self.p_z_sim = 1.0 - NORM.cdf(self.z_wcg)

def _calc(self, x, w):