Is random.expovariate equivalent to a Poisson Process

Question

I read somewhere that the python library function random.expovariate produces intervals equivalent to Poisson Process events.
Is that really the case or should I impose some other function on the results?

Solution 1

On a strict reading of your question, yes, that is what random.expovariate does.

expovariate gives you random floating point numbers, exponentially distributed. In a Poisson process the size of the interval between consecutive events is exponential.

However, there are two other ways I could imagine modelling poisson processes

1. Just generate random numbers, uniformly distributed and sort them.
2. Generate integers which have a Poisson distribution (i.e. they are distributed like the number of events within a fixed interval in a Poisson process). Use numpy.random.poisson to do this.

Of course all three things are quite different. The right choice depends on your application.

Solution 2

https://stackoverflow.com/a/10250877/1587329 gives a nice explanation of why this works (not only in python), and some code. In short

simulate the first 10 events in a poisson process with an averate rate of 15 arrivals per second like this:

import random
for i in range(1,10):
   print random.expovariate(15)

Comments

[Basj]

About 1., @AdrianRatnapala, does a sequence of uniformly distributed random numbers on [0, 100], sorted, model a Poisson process? Why?

[Adrian Ratnapala]

@Basj The need to sort also depends on the application. The Poission process is a set (i.e. unordered) of uniformly distributed events. A list or array of generated data would also contain "unwanted" information about what order they were generated in. Sorting destroys that information.