Python Data Science NumPy Random Pareto Data Distribution

Pareto Distribution: A distribution which follows Pareto's law i.e. The Pareto principle or "80-20 rule" stating that 80% of outcomes are due to 20% of causes was named in honour of Pareto.

Pareto's Law: Pareto created a mathematical formula in the early 20th century that described the inequalities in wealth distribution that existed in his native country of Italy.

Pareto observed that 80% of the country’s wealth was concentrated in the hands of only 20% of the population.

A distribution following Pareto's law i.e. 80-20 distribution (20% factors cause 80% outcome).

It has the following two parameters.

1. a - shape parameter.

2. size - The shape of the returned array.

Example 1: Draw out a sample for pareto distribution with shape of 2 with size 2x4.

Code

from numpy import random

x = random.pareto(a=2, size=(2, 4))

print(x)

the output will be

[[1.20162415e-03 3.41532724e-01 4.77248653e+00 2.67404461e-01]

[2.53190234e-01 3.50017605e-01 1.82569493e+00 2.34792348e-01]]

Note: Every time the code is run the output may vary because of random generation.

Visualization of Pareto Distribution

Example 2

Code

from numpy import random

import matplotlib.pyplot as plt

import seaborn as sns

sns.distplot(random.pareto(a=2, size=1000), kde=False)

plt.show()

the output will be