Introduction to Python Exponential Distribution

Python Exponential Distribution

The exponential distribution is characterized by a single parameter, typically denoted as λ (lambda), which represents the rate parameter or the average number of events per unit of time.

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

f(x) = λ * e^(-λx)

Where x is the time between events and e is the base of the natural logarithm.

In Python, you can work with the exponential distribution using the numpy.random.exponential() function from the NumPy library. This function allows you to generate random numbers from an exponential distribution.

As an example:

import numpy as np

# Define the rate parameter (lambda)
lambda_val = 0.5

# Generate random numbers from an exponential distribution
size = 1000
random_numbers = np.random.exponential(scale=1/lambda_val, size=size)

In this example:, np.random.exponential(scale=1/lambda_val, size=size) generates an array of 1000 random numbers from an exponential distribution with a rate parameter of 0.5.

• The scale parameter is set to 1 divided by the rate parameter, as this is the inverse of the expected value of the distribution.
• The resulting array random_numbers will contain the generated random numbers.

The exponential distribution is commonly used in reliability analysis, queuing theory, and various other applications where the time between events follows an exponential pattern.