Simulating a Poisson process

A Poisson process is a particular type of point process, a stochastic model that represents random occurrences of instantaneous events. Roughly speaking, the Poisson process is the least structured, or the most random, point process.

The Poisson process is a particular continuous-time Markov process.

Point processes, and notably Poisson processes, can model random instantaneous events such as the arrival of clients in a queue or on a server, telephone calls, radioactive disintegrations, action potentials of nerve cells, and many other phenomena.

In this recipe, we will show different methods to simulate a homogeneous stationary Poisson process.

How to do it...

1. Let's import NumPy and Matplotlib:

   >>> import numpy as np
       import matplotlib.pyplot as plt
       %matplotlib inline

2. Let's specify the rate value, that is, the average number of events per second:

   >>> rate = 20.  # average number of events per second

3. First, we will simulate the process...