inequality.gini – Gini inequality and decomposition measures

The inequality.gini module provides Gini inequality based measures

New in version 1.6.

Gini based Inequality Metrics

class pysal.inequality.gini.Gini(x)[source]

Classic Gini coefficient in absolute deviation form

Parameters:y (array (n,1)) – attribute
g

float – Gini coefficient

class pysal.inequality.gini.Gini_Spatial(x, w, permutations=99)[source]

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
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.