inequality.theil.Theil

class inequality.theil.Theil(y)

Classic Theil measure of inequality.

\[T = \sum_{i=1}^n \left( \frac{y_i}{\sum_{i=1}^n y_i} \ln \left[ N \frac{y_i}{\sum_{i=1}^n y_i}\right] \right )\]

Parameters:

ynumpy.array

An array in the shape \((n,t)\) or \((n,)\) with \(n\) taken as the observations across which inequality is calculated. If y is \((n,)\) then a scalar inequality value is determined. If y is \((n,t)\) then an array of inequality values are determined, one value for each column in y.

Notes

This computation involves natural logs. To prevent ln[0] from occurring, a small value is added to each element of y before beginning the computation.

Examples

>>> import libpysal
>>> import numpy
>>> from inequality.theil import Theil

>>> f = libpysal.io.open(libpysal.examples.get_path('mexico.csv'))
>>> vnames = [f'pcgdp{dec}' for dec in range(1940, 2010, 10)]
>>> y = numpy.array([f.by_col[v] for v in vnames]).T
>>> theil_y = Theil(y)

>>> theil_y.T
array([0.20894344, 0.15222451, 0.10472941, 0.10194725, 0.09560113,
       0.10511256, 0.10660832])

Attributes:

Tnumpy.array

An array in the shape \((t,)\) or \((1,)\) containing Theil’s T for each column of y.

__init__(y)

Methods

__init__(y)