The Pareto distribution, also known as the Pareto II or Lomax distribution, is a continuous probability distribution used to model situations where few events have large values, and many events have smaller values. or A distribution following Pareto’s law i.e. 80-20 distribution (20% factors cause 80% outcome). It’s implemented in NumPy using the np.random.pareto function.

Key Characteristics:

• Long Tail: The Pareto distribution exhibits a heavy tail, meaning the probability of observing extreme values is higher than for many other distributions. This “80/20 rule” scenario is often associated with the Pareto principle, where a small portion of the population or events account for a large portion of the outcome.

Parameter:

a – shape parameter.

size – The shape of the returned array.

Applications:

• Economics and Finance: Modeling income or wealth distribution, where a small percentage of individuals hold a significant portion of the wealth.
• Business and Engineering: Analyzing resource allocation, claim sizes in insurance, or city sizes.
• Natural Sciences: Studying earthquake magnitudes, internet traffic, or solar flare sizes.

Generating Random Samples with np.random.pareto:

import numpy as np
samples = np.random.pareto(a=2, size=(2,4))
print(samples)

Output
[[0.50500019 0.09785921 1.35369771 1.36639245]
 [0.09419555 0.39671036 0.36576457 0.31355683]]

Important Note: The Pareto distribution can be undefined for values less than the scale parameter. It’s crucial to consider this limitation when interpreting the generated samples.