Zipf Distribution: How do I measure Zipf Distribution using Python / Numpy

Question

I have a file (lets say corpus.txt) of around 700 lines, each line containing numbers separated by -. For example:

86-55-267-99-121-72-336-89-211
59-127-245-343-75-245-245

First I need to read the data from the file, find the frequency of each number, measure the Zipf distribution of these numbers and then plot the distribution. I have done the first two parts of the task. I am stuck in drawing the Zipf distribution.

I know that numpy.random.zipf(a, size=None) should be used for this. But I am finding it extremely hard to use it. Any pointers or code snippet would be extremely helpful.

Code:

# Counts frequency as per given n
def calculateFrequency(fileDir):
  frequency = {}
  for line in fileDir:
    line = line.strip().split('-')
    for i in line:
      frequency.setdefault(i, 0)
      frequency[i] += 1
  return frequency

fileDir = open("corpus.txt")
frequency = calculateFrequency(fileDir)
fileDir.close()
print(frequency)

## TODO: Measure and draw zipf distribution

`numpy.random.zipf(a, size=None)` does not produce a Zipf distribution. It draws samples from a Zipf distribution. You need to fit your data into a parametric Zipf distribution and estimate the best fit parameters. — DYZ, Apr 25 '17 at 03:46
I am new to numpy and scipy stuff. How do I fit my data into a parametric Zipf distribution and estimate the best fit parameters ? As I said above, I have just the frequency count for the individual numbers. — RDM, Apr 25 '17 at 03:50
Since Zipf law is a special case of power law, you can take a log of both sides of its PMF: log(y)=log(a)+b log(x) and then do linear fit with NumPy linear fit https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html — DYZ, Apr 25 '17 at 03:57

score 3 · Accepted Answer · edited Sep 29 '19 at 12:28

As stated numpy.random.zipf(a, size=None) will produce plot of Samples that are drawn from a zipf distribution with specified parameter of a > 1.

However, since your question was difficulty in using numpy.random.zipf method, here is an naive attempt as discussed on scipy zipf documentation site.

Below is a simulated corpus.txt that has 10 lines of random data per line. However, each line may have duplicates as compared to other lines to simulate recurrance.

16-45-3-21-16-34-30-45-5-28
11-40-22-10-40-48-22-23-22-6
40-5-33-31-46-42-47-5-27-14
5-38-12-22-19-1-11-35-40-24
20-11-24-10-9-24-20-50-21-4
1-25-22-13-32-14-1-21-19-2
25-36-18-4-28-13-29-14-13-13
37-6-36-50-21-17-3-32-47-28
31-20-8-1-13-24-24-16-33-47
26-17-39-16-2-6-15-6-40-46

Working Code

import csv
from operator import itemgetter
import matplotlib.pyplot as plt
from scipy import special
import numpy as np

#Read '-' seperated corpus data and get its frequency in a dict
frequency = {}
with open('corpus.txt', 'rb') as csvfile:
    reader = csv.reader(csvfile, delimiter='-', quotechar='|')
    for line in reader:
        for word in line:            
            count = frequency.get(word,0)
            frequency[word] = count + 1

#define zipf distribution parameter
a = 2. 

#get list of values from frequency and convert to numpy array
s = frequency.values()
s = np.array(s)

# Display the histogram of the samples, along with the probability density function:
count, bins, ignored = plt.hist(s, 50, normed=True)
x = np.arange(1., 50.)
y = x**(-a) / special.zetac(a)
plt.plot(x, y/max(y), linewidth=2, color='r')
plt.show()

Plot of histogram of the samples, along with the probability density function

Zipf Distribution: How do I measure Zipf Distribution using Python / Numpy

1 Answers1