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Introduction to Python Pareto Distribution

Python Pareto Distribution​

The Pareto distribution is characterized by two parameters: the scale parameter (xₘ) and the shape parameter (α). The scale parameter represents the minimum possible value of the distribution, while the shape parameter controls the shape of the distribution.

The probability density function (PDF) of the Pareto distribution is given by:

f(x) = (α * xₘ^α) / (x^(α+1))

Where x is the random variable.

In Python, you can work with the Pareto distribution using the numpy.random.pareto() function from the NumPy library.

This function allows you to generate random numbers from a Pareto distribution.

As an example:

import numpy as np

# Define the shape parameter
alpha = 2

# Define the scale parameter
x_m = 1

# Generate random numbers from a Pareto distribution
size = 1000
random_numbers = np.random.pareto(alpha, size=size) + x_m

In this example:

  • np.random.pareto(alpha, size=size) + x_m generates an array of 1000 random numbers from a Pareto distribution with a shape parameter of 2 and a scale parameter of 1.
  • The resulting array random_numbers will contain the generated random numbers.
tip

Note that the Pareto distribution is defined only for positive values of x and has a heavy tail, meaning that it allows for the existence of extreme values.