IneqPy’s Package

This package provides statistics to carry on inequality’s analysis. Among the estimators provided by this package you can find:

Main Statistics	Inequality Indicators
Weighted Mean	Weighted Gini
Weighted Variance	Weighted Atkinson
Weighted Coefficient of variation	Weighted Theil
Weighted Kurtosis	Weighted Kakwani
Weighted Skewness	Weighted Lorenz curve

Installation

pip install ineqpy
# or from github's repo
pip install git+https://github.com/mmngreco/IneqPy.git

What you can find

Some examples of how use this package:

>>> import pandas as pd
>>> import numpy as np
>>> import ineqpy
>>> d = load_data()  # dataframe
>>> d
             renta   factor
0        -13004.12   1.0031
89900    141656.97   1.4145
179800     1400.38   4.4122
269700   415080.96   1.3295
359600    69165.22   1.3282
449500     9673.83  19.4605
539400    55057.72   1.2923
629300     -466.73   1.0050
719200     3431.86   2.2861
809100      423.24   1.1552
899000        0.00   1.0048
988900     -344.41   1.0028
1078800   56254.09   1.2752
1168700   60543.33   2.0159
1258600    2041.70   2.7381
1348500     581.38   7.9426
1438400   55646.05   1.2818
1528300       0.00   1.0281
1618200   69650.24   1.2315
1708100   -2770.88   1.0035
1798000    4088.63   1.1256
1887900       0.00   1.0251
1977800   10662.63  28.0409
2067700    3281.95   1.1670

Descriptive statistics

>>> ineqpy.mean(variable=d.renta, weights=d.factor)
20444.700666031338
>>> ineqpy.var(variable=d.renta, weights=d.factor)
2982220948.7413292
>>> x, w = d.renta.values, d.factor.values

Note that the standardized moment for order n, retrieve the value in that column:

n	value
1	0
2	1
3	Skew
4	Kurtosis

A helpful table of interpretation of the moments

>>> ineqpy.std_moment(variable=x, weights=w, order=1)  # ~= 0
2.4624948200717338e-17
>>> ineqpy.std_moment(variable=x, weights=w, order=2)  # = 1
1.0
>>> ineqpy.std_moment(variable=x, weights=w, order=3)  # = skew
5.9965055750379426
>>> ineqpy.skew(variable=x, weights=w)
5.9965055750379426
>>> ineqpy.std_moment(variable=x, weights=w, order=4)  # = kurtosis
42.319928851703004
>>> ineqpy.kurt(variable=x, weights=w)
42.319928851703004

Inequality’s estimators

# pass a pandas.DataFrame and inputs as strings
>>> ineqpy.gini(data=d, income='renta', weights='factor')
0.76739136365917116
# you can pass arrays too
>>> ineqpy.gini(income=d.renta.values, weights=d.factor.values)
0.76739136365917116

More examples and comparison with other packages:

We generate random weighted data to show how ineqpy works. The variables simulate being:

x : Income
w : Weights

To test with classical statistics we generate:

x_rep : Income values replicated w times each one.
w_rep : Ones column.

Additional information:

np : numpy package
sp : scipy package
pd : pandas package
gsl_stat : GNU Scientific Library written in C.
ineq : IneqPy

Mean

>>> np.mean(x_rep)       = 488.535714286
>>> ineq.mean(x, w)      = 488.535714286
>>> gsl_stat.wmean(w, x) = 488.5357142857143

Variance

>>> np.var(x_rep)                = 63086.1364796
>>> ineq.var(x, w)               = 63086.1364796
>>> ineq_stat.wvar(x, w, kind=1) = 63086.1364796
>>> ineq_stat.wvar(x, w, kind=2) = 63247.4820972
>>> gsl_stat.wvariance(w, x)     = 63993.161585889124
>>> ineq_stat.wvar(x, w, kind=3) = 63993.1615859

Covariance

>>> np.cov(x_rep, x_rep)            =  [[ 63247.48209719  63247.48209719]
 [ 63247.48209719  63247.48209719]]
>>> ineq_stat.wcov(x, x, w, kind=1) =  63086.1364796
>>> ineq_stat.wcov(x, x, w, kind=2) =  4.94065645841e-324
>>> ineq_stat.wcov(x, x, w, kind=3) =  9.88131291682e-324

Skewness

>>> gsl_stat.wskew(w, x) =  -0.05742668111416989
>>> sp_stat.skew(x_rep)  =  -0.058669605967865954
>>> ineq.skew(x, w)      =  -0.0586696059679

Kurtosis

>>> sp_stat.kurtosis(x_rep)  =  -0.7919389201857214
>>> gsl_stat.wkurtosis(w, x) =  -0.8540884810553052
>>> ineq.kurt(x, w) - 3      =  -0.791938920186

Percentiles

>>> ineq_stat.percentile(x, w, 25) =  293
>>> np.percentile(x_rep, 25)       =  293.0

>>> ineq_stat.percentile(x, w, 50) =  526
>>> np.percentile(x_rep, 50)       =  526.0

>>> ineq_stat.percentile(x, w, 90) =  839
>>> np.percentile(x_rep, 90)       =  839.0

Another way to use this is through the API module as shown below:

API’s module

Using API’s module:

>>> data = Survey(data=data, columns=columns, weights='w')
>>> data.df.head()
     x  w
0  111  3
1  711  4
2  346  4
3  667  1
4  944  1

Statistics

>>> data.weights = w
>>> df.mean(main_var)       = 488.535714286
>>> df.percentile(main_var) = 526
>>> df.var(main_var)        = 63086.1364796
>>> df.skew(main_var)       = -0.0586696059679
>>> df.kurt(main_var)       = 2.20806107981
>>> df.gini(main_var)       = 0.298494329293
>>> df.atkinson(main_var)   = 0.0925853855635
>>> df.theil(main_var)      = 0.156137490566