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javaeventssimulationpoisson
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Reputation: 18180

How do I generate discrete random events with a Poisson distribution?

I'm aware of Knuth's algorithm for generating random Poisson distributed numbers (below in Java) but how do I translate that into calling a method, generateEvent(), randomly over time?

int poissonRandomNumber(int lambda) {
    double L = Math.exp(-lambda);
    int k = 0;
    double p = 1;
    do {
        k = k + 1;
        double u = Math.random();
        p = p * u;
    } while (p > L);
    return k - 1;
}

Upvotes: 8

Views: 10514

Answers (2)

Jay Elston
Jay Elston

Reputation: 2078

If you are looking to simulate the inter-event arrival time, you want the exponential distribution.

Take a look at Pseudorandom Number Generator - Exponential Distribution

Your code would then look like this:

// Note L == 1 / lambda
public double poissonRandomInterarrivalDelay(double L) {
    return (Math.log(1.0-Math.random())/-L;
}

...

while (true){
    // Note -- lambda is 5 seconds, convert to milleseconds
    long interval= (long)poissonRandomInterarrivalDelay(5.0*1000.0);
    try {
        Thread.sleep(interval);
        fireEvent();
}

Upvotes: 4

er0
er0

Reputation: 1834

The Poisson random numbers you are generating, as Scott mentioned, represent the frequency of your events. Once you have the frequency, you can fit their occurrences over the interval using a second distribution, say Uniform.

Suppose the number of events generated for an interval of N is k. Then you simply need to generate (k+1) random numbers that sum to N.

|<----------------------- N ------------------------->|
--r_0--(event)---r_1-..-(event_k)--r_(k+1)--

To do so, simply generate (k+1) random numbers and divide them by their sum, divided by N. The first k of these numbers become the timestamps of your events.

Upvotes: 0

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