CODEWITHSUNDEEP
pythonstatisticsprobability
All The Rage
All The Rage

Reputation: 831

Simulate Poisson arrival times given count of arrivals per day

I'm trying to model a process that has arrival times. I have sampled actual arrivals and have a series of arrival counts per day for many days. I want to use this measured data to make a series of actual arrival timestamps that follow a Poisson distribution.

For example, given: countPerDay = [2,3,1,...] compute: arrivalTimes = [0.324, 0.547, 1.223, 1.563, 1.844, 2.618, ...]

Observe that 2 arrive on the first day, 3 on the second day, 1 on the third day, etc.

I currently do this using a uniform distribution as follows:

arrivalTimes = []
for d,j in zip(range(len(countPerDay)), countPerDay):
    l = random.sample(range(ticksPerDay), j)
    arrivalTimes += [(d*ticksPerDay + v) for v in l]

How do I change this such that the arrival times are on a Poisson distribution rather than uniform? I know that the Exponential distribution is meant to provide Poisson inter-arrival times, but in this case where I need an exact number of arrivals per day I worry that it will bias all of the arrivals toward the beginning of each day.

And intuitively, what is different / better about Poisson arrival times than uniform?

Upvotes: 1

Views: 1534

Answers (1)

Ben G.
Ben G.

Reputation: 306

Your code is fine because it turns out that a randomly distributed set of arrival times will have subsequent times exponentially-distributed. To test, I used the following code:

n = int(1e8) # Many points
event_times = n * np.random.rand(n)
event_times.sort()
event_distances = event_times[1:] - event_times[:-1]
plt.hist(event_distances, bins=100)
plt.xlim(0, 8) # To show the part with high n
event_distances.mean()

Which returns a mean of 0.99999996740170383 and the following distribution:distances between randomly-timed events are exponentially distributed

Upvotes: 1

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