# Compute Gini Coefficient

Recently, I was given a math assignment to calculate Gini Indexes for a table of percent distributions of aggregate income.

The table takes the form of:

Year    1st Quintile    2nd Quintile    3rd Quintile    4th Quintile    5th Quintile
----    ------------    ------------    ------------    ------------    ------------
1929        0.03             12.47           13.8           19.3              54.4
1935        4.1              9.2             14.1           20.9              51.7
...         ...              ...             ...            ...               ...


Because of the length of the actual table I wrote a short python script to calculate the Gini Indexes. However, I'm fairly new to Python so I'd like to see what needs improvement.

Method of Calculation:

Calculate the log of the percentages with the quintile as the base of the logarithm (i.e. log(0.0003)/log(0.2), log(0.1247)/log(0.4) ...) and then average these values to find an approximate exponent for the Lorenz curve. Calculate the Gini Index by finding twice the area between y=x and the Lorenz curve from 0 to 1.

import numpy as np
import scipy.integrate as integrate
import itertools as it

def log_slope(x, y):
return np.log(y)/np.log(x)

# read in data from file
years, data = read_values('Quintiles')  # shape: [[0.03, 0.12,...], [], []..., []]
accumulated_vals = [list(it.accumulate(v)) for v in data]

# percentiles; remove 0.0 and 1.0 after calculating
percentiles = np.linspace(0.0, 1.0, np.shape(accumulated_vals)[1] + 1)[1:-1]

for j, vals in enumerate(accumulated_vals):
sum = 0
for i, val in enumerate(vals[:-1]):  # exclude the last accumulated value, which should be 1.0
sum += log_slope(percentiles[i], val)
average = sum / (len(vals)-1)
gini = 2 * integrate.quad(lambda x: x - pow(x, average), 0.0, 1.0)[0]
print('{:d}: {} -> {:.5f}'.format(int(years[j]), [round(k, 4) for k in vals], gini))


Questions:

• The code produces correct values and is already pretty quick, but can its speed be improved? At the moment I'd like to keep the method of calculation the same because it's the method used in my calculus course, but are there any possible improvements to this method?
• Can the clarity of the code be improved? Are the variable names clear?
• Does the code follow standard python conventions? I'm new to Python so I'm not familiar with these.
• Minor Question/Bug: Printing the accumulated values will sometimes result in the last value being 1.00001 or 0.999 rather than 1.0. I presume this is due to precision errors, but it's seems odd when dealing with adding numbers with only 3 decimal places. Is there an easy fix for this?

# Stick closely to the sources

It's helpful when coding math in cases like this to base your approach on established methods and language.

It might seem a bit extreme, but this can include:

• Following a published method to the letter.

• Naming your variables and laying out your code as closely as possible to that description.

eg.

def gini_index(*args*):
"""
Calculates the Gini Index G given data of the form:
Using summation as described in:
*reference* (can be textbook, arxiv etc)
Via the formula:
*include formulae if possible*
Essentially as described here:
https://en.wikipedia.org/wiki/Gini_coefficient#Alternate_expressions
Example input:
Example output:
"""
#   your code proper starts here


An example of this is here, a collection of basic number theory and elliptic curve utilities that eventually became SageMath.

For example, were you actually to use this formula as a basis, you would name your counter i, your total number of values n, and use the summation functions provided in numpy.

Trust me, if you think you'll revisit your code at a later date (when memory fails), or have it used or modified by someone else, this is a lifesaver.

(Edit: As you are integrating a polynomial, you can use the integ method of poly1d included with numpy rather than importing scipy.)

• Thorough adherence to mathematical notation and descriptive comments are both very helpful hints, thank you. In regards to the method used, I'd like to use the 2 * ∫x-x^(avg)dx from 0 to 1 as it is what my current course is using. – Dando18 Dec 14 '16 at 5:47
• That's fine. I wasn't suggesting a different approach, just giving an example of naming variables based on convention. – Ryan Mills Dec 14 '16 at 7:41